(TSEQ_HARMONIC,(((c--> @ (^[V0]: (clift @ (creal_inv @ (creal_of_num @ V0))))) @ (cvec @ (cNUMERAL @ c_0))) @ csequentially))
(TTREAL_INV_0,((ctreal_eq @ (ctreal_inv @ (ctreal_of_num @ (cNUMERAL @ c_0)))) @ (ctreal_of_num @ (cNUMERAL @ c_0))))
(TTAGGED_DIVISION_OF_EMPTY,((ctagged_division_of @ cEMPTY) @ cEMPTY))
(TSWAPSEQ_I,((cswapseq @ (cNUMERAL @ c_0)) @ cI))
(TREAL_LT_01,((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TREAL_LE_01,((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TOPERATIVE_CONTENT,((coperative @ creal_add) @ ccontent))
(TNADD_INV_0,((cnadd_eq @ (cnadd_inv @ (cnadd_of_num @ (cNUMERAL @ c_0)))) @ (cnadd_of_num @ (cNUMERAL @ c_0))))
(TLOCALLY_PATH_CONNECTED_UNIV,((clocally @ cpath_connected) @ cUNIV))
(TLOCALLY_CONNECTED_UNIV,((clocally @ cconnected) @ cUNIV))
(TLOCALLY_COMPACT_UNIV,((clocally @ ccompact) @ cUNIV))
(TINT_LT_01,((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TINT_LE_01,((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(THAS_MEASURE_STD_SIMPLEX,((chas_measure @ ((chull @ cconvex) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cbasis @ V1))))))))) @ (creal_inv @ (creal_of_num @ (cFACT @ (cdimindex @ cUNIV))))))
(THAS_MEASURE_EMPTY,((chas_measure @ cEMPTY) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TPERMUTED_RULES_conjunct0,((cPERMUTED @ cNIL) @ cNIL))
(TISO_REFL,((cISO @ (^[V0]: V0)) @ (^[V0]: V0)))
(TENDS_IN_UNIT_INTERVAL_conjunct1,((cIN @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))
(TENDS_IN_UNIT_INTERVAL_conjunct0,((cIN @ (cvec @ (cNUMERAL @ c_0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))
(THAS_SIZE_MULTIVECTOR,((cHAS_SIZE @ cUNIV) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))))
(TDIMINDEX_HAS_SIZE_FINITE_SUM,((cHAS_SIZE @ cUNIV) @ ((c+ @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))))
(THAS_SIZE_STDBASIS,((cHAS_SIZE @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cbasis @ V1))))))) @ (cdimindex @ cUNIV)))
(THAS_SIZE_BOOL,((cHAS_SIZE @ cUNIV) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))
(THAS_SIZE_4,((cHAS_SIZE @ cUNIV) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))
(THAS_SIZE_3,((cHAS_SIZE @ cUNIV) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))
(THAS_SIZE_2,((cHAS_SIZE @ cUNIV) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))
(THAS_SIZE_1,((cHAS_SIZE @ cUNIV) @ (cNUMERAL @ (cBIT1 @ c_0))))
(TARITH_GE_conjunct1,((c>= @ c_0) @ c_0))
(TCARD_EQ_RATIONAL,((c=_c @ crational) @ cUNIV))
(TCARD_EQ_INTEGER,((c=_c @ cinteger) @ cUNIV))
(TCARD_EQ_REAL,((c=_c @ cUNIV) @ cUNIV))
(TCARD_SQUARE_NUM,((c=_c @ ((c*_c @ cUNIV) @ cUNIV)) @ cUNIV))
(TCARD_EQ_COUNTABLE_SUBSETS_REAL,((c=_c @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (cCOUNTABLE @ V1)) @ V1)))))) @ cUNIV))
(TCARD_EQ_REAL_SEQUENCES,((c=_c @ cUNIV) @ cUNIV))
(TCARD_EQ_OPEN_SETS,((c=_c @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (copen @ V1)) @ V1)))))) @ cUNIV))
(TCARD_EQ_COMPACT_SETS,((c=_c @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (ccompact @ V1)) @ V1)))))) @ cUNIV))
(TCARD_EQ_CLOSED_SETS,((c=_c @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (cclosed @ V1)) @ V1)))))) @ cUNIV))
(TCARD_FUNSPACE_CURRY,((c=_c @ cUNIV) @ cUNIV))
(TCARD_EQ_EUCLIDEAN,((c=_c @ cUNIV) @ cUNIV))
(TISOMORPHISMS_UNIV_UNIV,((c==> @ ((c= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))) @ (c? @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c= @ (cvector_norm @ (V0 @ V2))) @ (cvector_norm @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c= @ (cvector_norm @ (V1 @ V2))) @ (cvector_norm @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c= @ (V1 @ (V0 @ V2))) @ V2)))) @ (c! @ (^[V2]: ((c= @ (V0 @ (V1 @ V2))) @ V2))))))))))))))
(TISOMETRY_UNIV_UNIV,((c==> @ ((c<= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))) @ (c? @ (^[V0]: ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V1]: ((c= @ (cvector_norm @ (V0 @ V1))) @ (cvector_norm @ V1)))))))))
(TCARD_FUNSPACE_CONG,((c==> @ ((c/__caret__ @ ((c=_c @ cUNIV) @ cUNIV)) @ ((c=_c @ cUNIV) @ cUNIV))) @ ((c=_c @ cUNIV) @ cUNIV)))
(TCARD_FUNSPACE_LE,((c==> @ ((c/__caret__ @ ((c<=_c @ cUNIV) @ cUNIV)) @ ((c<=_c @ cUNIV) @ cUNIV))) @ ((c<=_c @ cUNIV) @ cUNIV)))
(TCARD_FUNSPACE_UNIV,((c==> @ ((c/__caret__ @ (cFINITE @ cUNIV)) @ (cFINITE @ cUNIV))) @ ((c= @ (cCARD @ cUNIV)) @ ((cEXP @ (cCARD @ cUNIV)) @ (cCARD @ cUNIV)))))
(TFINITE_FUNSPACE_UNIV,((c==> @ ((c/__caret__ @ (cFINITE @ cUNIV)) @ (cFINITE @ cUNIV))) @ (cFINITE @ cUNIV)))
(TCARD_EQ_LIST,((c==> @ (cINFINITE @ cUNIV)) @ ((c=_c @ cUNIV) @ cUNIV)))
(TCARD_EQ_CART,((c==> @ (cINFINITE @ cUNIV)) @ ((c=_c @ cUNIV) @ cUNIV)))
(TCARD_CART_UNIV,((c==> @ (cFINITE @ cUNIV)) @ ((c= @ (cCARD @ cUNIV)) @ ((cEXP @ (cCARD @ cUNIV)) @ (cdimindex @ cUNIV)))))
(TFINITE_CART_UNIV,((c==> @ (cFINITE @ cUNIV)) @ (cFINITE @ cUNIV)))
(TCOUNTABLE_LIST,((c==> @ (cCOUNTABLE @ cUNIV)) @ (cCOUNTABLE @ cUNIV)))
(Teuclideanreal,((c= @ ceuclideanreal) @ (ctopology @ creal_open)))
(Teuclidean,((c= @ ceuclidean) @ (ctopology @ copen)))
(TBOTTOM,((c= @ cBOTTOM) @ (c_mk_rec @ cZBOT)))
(TNORM_BASIS_1,((c= @ (cvector_norm @ (cbasis @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TNORM_0,((c= @ (cvector_norm @ (cvec @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TTRACE_I,((c= @ (ctrace @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cdimindex @ cUNIV))))
(TTRACE_0,((c= @ (ctrace @ (cmat @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TSQRT_1,((c= @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TSQRT_0,((c= @ (csqrt @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TSIGN_I,((c= @ (csign @ cI)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TSCHNIRELMANN_UNIV,((c= @ (cschnirelmann @ cUNIV)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TREAL_SGN_0,((c= @ (creal_sgn @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TREAL_NEG_0,((c= @ (creal_neg @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TREAL_INV1,((c= @ (creal_inv @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TREAL_INV_0,((c= @ (creal_inv @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TABS_1,((c= @ (creal_abs @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TABS_0,((c= @ (creal_abs @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TONORM_ID,((c= @ (conorm @ (^[V0]: V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TONORM_I,((c= @ (conorm @ cI)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TNEUTRAL_REAL_MUL,((c= @ (cneutral @ creal_mul)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TNEUTRAL_REAL_ADD,((c= @ (cneutral @ creal_add)) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TMEASURE_EMPTY,((c= @ (cmeasure @ cEMPTY)) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TINFNORM_0,((c= @ (cinfnorm @ (cvec @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TDIAMETER_EMPTY,((c= @ (cdiameter @ cEMPTY)) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TDET_I,((c= @ (cdet @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TDET_0,((c= @ (cdet @ (cmat @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TCONTENT_UNIT_1,((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TCONTENT_UNIT,((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TCONTENT_EMPTY,((c= @ (ccontent @ cEMPTY)) @ (creal_of_num @ (cNUMERAL @ c_0))))
(TARITH_EXP_conjunct1,((c= @ ((cEXP @ c_0) @ c_0)) @ (cBIT1 @ c_0)))
(TARITH_SUB_conjunct1,((c= @ ((c- @ c_0) @ c_0)) @ c_0))
(TARITH_ADD_conjunct1,((c= @ ((c+ @ c_0) @ c_0)) @ c_0))
(TARITH_MULT_conjunct1,((c= @ ((c* @ c_0) @ c_0)) @ c_0))
(TSIGMA_1,((c= @ (csigma @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0))))
(TSIGMA_0,((c= @ (csigma @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)))
(TRANK_I,((c= @ (crank @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cdimindex @ cUNIV)))
(TRANK_0,((c= @ (crank @ (cmat @ (cNUMERAL @ c_0)))) @ (cNUMERAL @ c_0)))
(TPHI_1,((c= @ (cphi @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0))))
(TPHI_2,((c= @ (cphi @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))))
(TPHI_0,((c= @ (cphi @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)))
(TNEUTRAL_ADD,((c= @ (cneutral @ c+)) @ (cNUMERAL @ c_0)))
(TNEUTRAL_MUL,((c= @ (cneutral @ c*)) @ (cNUMERAL @ (cBIT1 @ c_0))))
(TDIMINDEX_MULTIVECTOR,((c= @ (cdimindex @ cUNIV)) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))))
(TDIMINDEX_FINITE_SUM,((c= @ (cdimindex @ cUNIV)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))))
(TDIMINDEX_4,((c= @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))
(TDIMINDEX_3,((c= @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))
(TDIMINDEX_2,((c= @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))
(TDIMINDEX_1,((c= @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))
(TDIM_UNIV,((c= @ (cdim @ cUNIV)) @ (cdimindex @ cUNIV)))
(TDIM_EMPTY,((c= @ (cdim @ cEMPTY)) @ (cNUMERAL @ c_0)))
(TARITH_SUC_conjunct1,((c= @ (cSUC @ c_0)) @ (cBIT1 @ c_0)))
(TPRE_conjunct0,((c= @ (cPRE @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)))
(TARITH_PRE_conjunct1,((c= @ (cPRE @ c_0)) @ c_0))
(TARITH_ZERO_conjunct0,((c= @ (cNUMERAL @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)))
(TONE,((c= @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cSUC @ (cNUMERAL @ c_0))))
(TTWO,((c= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cSUC @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TLENGTH_conjunct0,((c= @ (cLENGTH @ cNIL)) @ (cNUMERAL @ c_0)))
(TISQRT_0,((c= @ (cISQRT @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)))
(TFACT_conjunct0,((c= @ (cFACT @ (cNUMERAL @ c_0))) @ (cNUMERAL @ (cBIT1 @ c_0))))
(TCARD_STDBASIS,((c= @ (cCARD @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cbasis @ V1)))))))) @ (cdimindex @ cUNIV)))
(TCARD_BOOL,((c= @ (cCARD @ cUNIV)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))
(TCARD_CLAUSES_conjunct0,((c= @ (cCARD @ cEMPTY)) @ (cNUMERAL @ c_0)))
(TBIT0_DEF_conjunct0,((c= @ (cBIT0 @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)))
(TARITH_ZERO_conjunct1,((c= @ (cBIT0 @ c_0)) @ c_0))
(TZERO_DEF,((c= @ c_0) @ (cmk_num @ cIND_0)))
(Tsequentially,((c= @ csequentially) @ (cmk_net @ (^[V0]: (^[V1]: ((c>= @ V0) @ V1))))))
(Tat_infinity,((c= @ cat_infinity) @ (cmk_net @ (^[V0]: (^[V1]: ((creal_ge @ (cvector_norm @ V0)) @ (cvector_norm @ V1)))))))
(Tmempty,((c= @ cmempty) @ (cmultiset @ (^[V0]: (cNUMERAL @ c_0)))))
(TPOLY_NEG_CLAUSES_conjunct0,((c= @ (cpoly_neg @ cNIL)) @ cNIL))
(TPOLY_DIFF_CLAUSES_conjunct0,((c= @ (cpoly_diff @ cNIL)) @ cNIL))
(TZIP_conjunct0,((c= @ ((cZIP @ cNIL) @ cNIL)) @ cNIL))
(TREVPERM_conjunct0,((c= @ (cREVPERM @ (cNUMERAL @ c_0))) @ cNIL))
(TREVERSE_conjunct0,((c= @ (cREVERSE @ cNIL)) @ cNIL))
(TLIST_OF_SET_EMPTY,((c= @ (clist_of_set @ cEMPTY)) @ cNIL))
(TBUTLAST_conjunct0,((c= @ (cBUTLAST @ cNIL)) @ cNIL))
(TINT_SGN_0,((c= @ (cint_sgn @ (cint_of_num @ (cNUMERAL @ c_0)))) @ (cint_of_num @ (cNUMERAL @ c_0))))
(TINT_NEG_0,((c= @ (cint_neg @ (cint_of_num @ (cNUMERAL @ c_0)))) @ (cint_of_num @ (cNUMERAL @ c_0))))
(TINT_ABS_1,((c= @ (cint_abs @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TINT_ABS_0,((c= @ (cint_abs @ (cint_of_num @ (cNUMERAL @ c_0)))) @ (cint_of_num @ (cNUMERAL @ c_0))))
(TAFF_DIM_UNIV,((c= @ (caff_dim @ cUNIV)) @ (cint_of_num @ (cdimindex @ cUNIV))))
(TAFF_DIM_EMPTY,((c= @ (caff_dim @ cEMPTY)) @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))
(THREAL_INV_0,((c= @ (chreal_inv @ (chreal_of_num @ (cNUMERAL @ c_0)))) @ (chreal_of_num @ (cNUMERAL @ c_0))))
(TIMAGE_DROP_UNIV,((c= @ ((cIMAGE @ cdrop) @ cUNIV)) @ cUNIV))
(TTOPSPACE_EUCLIDEANREAL,((c= @ (ctopspace @ ceuclideanreal)) @ cUNIV))
(Tuniverse,((c= @ cuniverse) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V0) @ ((cIN @ V2) @ (csetlevel @ V1))) @ ((c__comma__ @ V1) @ V2))))))))))
(TMUL_C_UNIV,((c= @ ((c*_c @ cUNIV) @ cUNIV)) @ cUNIV))
(Tdenumber,((c= @ cdenumber) @ cnumber))
(TZBOT,((c= @ cZBOT) @ ((cINJP @ (cINJN @ (cNUMERAL @ c_0))) @ (c__at__ @ (^[V0]: cT)))))
(TNUMSEG_2,((c= @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cINSERT @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((cINSERT @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ cEMPTY))))
(TNEUTRAL_SUMSET,((c= @ (cneutral @ c+++)) @ ((cINSERT @ (cNUMERAL @ c_0)) @ cEMPTY)))
(TFROM_0,((c= @ (cfrom @ (cNUMERAL @ c_0))) @ cUNIV))
(TBITSET_0,((c= @ (cbitset @ (cNUMERAL @ c_0))) @ cEMPTY))
(TMULTIVECTOR_IMAGE,((c= @ cUNIV) @ ((cIMAGE @ cmk_multivector) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((cSUBSET @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ V1))))))))
(Tpoly_neg,((c= @ cpoly_neg) @ (cpoly_cmul @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TMAP_I,((c= @ (cMAP @ cI)) @ cI))
(Trepeating,((c= @ crepeating) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c>= @ V3) @ V2)) @ (V1 @ V3))))))) @ V1)))))))
(Tcanonical,((c= @ ccanonical) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((c>= @ V3) @ V2)) @ (c~ @ (V1 @ V3)))))))) @ V1)))))))
(TCOMPONENTS_UNIV,((c= @ (ccomponents @ cUNIV)) @ ((cINSERT @ cUNIV) @ cEMPTY)))
(TCOMPONENTS_EMPTY,((c= @ (ccomponents @ cEMPTY)) @ cEMPTY))
(TEXISTS_UNIQUE_DEF,((c= @ c?!) @ (^[V0]: ((c/__caret__ @ (c? @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))))
(TEXISTS_DEF,((c= @ c?) @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ V1)))) @ V1))))))
(TEXISTS_THM,((c= @ c?) @ (^[V0]: (V0 @ (c__at__ @ V0)))))
(TFORALL_DEF,((c= @ c!) @ (^[V0]: ((c= @ V0) @ (^[V1]: cT)))))
(Tproduct,((c= @ cproduct) @ (citerate @ creal_mul)))
(Tnproduct,((c= @ cnproduct) @ (citerate @ c*)))
(Tmsum,((c= @ cmsum) @ (citerate @ cmatrix_add)))
(Tnsum,((c= @ cnsum) @ (citerate @ c+)))
(TPOWERSET_CLAUSES_conjunct0,((c= @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((cSUBSET @ V1) @ cEMPTY)) @ V1)))))) @ ((cINSERT @ cEMPTY) @ cEMPTY)))
(T_FUNCTION,((c= @ c_FUNCTION) @ (^[V0]: (^[V1]: (((cCOND @ (c?! @ (V0 @ V1))) @ (c__at__ @ (V0 @ V1))) @ (c__at__ @ (^[V2]: cF)))))))
(T_SEQPATTERN,((c= @ c_SEQPATTERN) @ (^[V0]: (^[V1]: (^[V2]: (((cCOND @ (c? @ (^[V3]: ((V0 @ V2) @ V3)))) @ (V0 @ V2)) @ (V1 @ V2)))))))
(TFINITE_SUM_IMAGE,((c= @ cUNIV) @ ((cIMAGE @ cmk_finite_sum) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c+ @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))))))
(TFINITE_IMAGE_IMAGE,((c= @ cUNIV) @ ((cIMAGE @ cfinite_index) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))))
(TSPAN_MBASIS,((c= @ (cspan @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((cSUBSET @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ (cmbasis @ V1)))))))) @ cUNIV))
(Tstd_tetrahedron,((c= @ cstd_tetrahedron) @ ((chull @ cconvex) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ cEMPTY)))))))
(Tstd_octahedron,((c= @ cstd_octahedron) @ ((chull @ cconvex) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ cEMPTY)))))))))
(TSTD_ICOSAHEDRON,((c= @ cstd_icosahedron) @ ((chull @ cconvex) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ ((creal_add @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_div @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ cEMPTY)))))))))))))))
(Tstd_icosahedron,((c= @ cstd_icosahedron) @ ((cLET @ (^[V0]: (cLET_END @ ((chull @ cconvex) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ V0) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ V0)) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ V0) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ V0)) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ V0) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ V0)) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ V0) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ V0)) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ V0) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ V0)) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ V0) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ V0)) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ cEMPTY)))))))))))))))) @ ((creal_div @ ((creal_add @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))
(TSTD_DODECAHEDRON,((c= @ cstd_dodecahedron) @ ((chull @ cconvex) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ 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(Tstd_dodecahedron,((c= @ cstd_dodecahedron) @ ((cLET @ (^[V0]: (cLET_END @ ((chull @ cconvex) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_inv @ V0)) @ ((cCONS @ V0) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_inv @ V0)) @ ((cCONS @ (creal_neg @ V0)) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_inv @ V0))) @ ((cCONS @ V0) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_inv @ V0))) @ ((cCONS @ (creal_neg @ V0)) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_inv @ V0)) @ ((cCONS @ V0) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_inv @ V0)) @ ((cCONS @ (creal_neg @ V0)) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_inv @ V0))) @ ((cCONS @ V0) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_inv @ V0))) @ ((cCONS @ (creal_neg @ V0)) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ V0) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_inv @ V0)) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ V0)) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_inv @ V0)) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ V0) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_inv @ V0))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ V0)) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_neg @ (creal_inv @ V0))) @ cNIL))))) @ cEMPTY)))))))))))))))))))))))) @ ((creal_div @ ((creal_add @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (csqrt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))
(Tstd_cube,((c= @ cstd_cube) @ ((chull @ cconvex) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))) @ ((cINSERT @ (cvector @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cCONS @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ cEMPTY)))))))))))
(TIMAGE_LIFT_UNIV,((c= @ ((cIMAGE @ clift) @ cUNIV)) @ cUNIV))
(TSTD_SIMPLEX,((c= @ ((chull @ cconvex) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cbasis @ V1))))))))) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V1) @ V2)))))) @ ((creal_le @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V2]: ((c$ @ V1) @ V2)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ V1)))))))
(TCONVEX_HULL_UNIV,((c= @ ((chull @ cconvex) @ cUNIV)) @ cUNIV))
(TAFFINE_HULL_UNIV,((c= @ ((chull @ caffine) @ cUNIV)) @ cUNIV))
(TTOPSPACE_EUCLIDEAN,((c= @ (ctopspace @ ceuclidean)) @ cUNIV))
(TSPAN_STDBASIS,((c= @ (cspan @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cbasis @ V1)))))))) @ cUNIV))
(TSPAN_UNIV,((c= @ (cspan @ cUNIV)) @ cUNIV))
(TOUTSIDE_EMPTY,((c= @ (coutside @ cEMPTY)) @ cUNIV))
(TINTERIOR_STD_SIMPLEX,((c= @ (cinterior @ ((chull @ cconvex) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cbasis @ V1)))))))))) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V1) @ V2)))))) @ ((creal_lt @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V2]: ((c$ @ V1) @ V2)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ V1)))))))
(TINTERIOR_UNIV,((c= @ (cinterior @ cUNIV)) @ cUNIV))
(TFRONTIER_UNIV,((c= @ (cfrontier @ cUNIV)) @ cEMPTY))
(TCLOSURE_DYADIC_RATIONALS,((c= @ (cclosure @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V0) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (cinteger @ ((c$ @ V2) @ V3)))))) @ ((c% @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))) @ V2)))))))))) @ cUNIV))
(TCLOSURE_IRRATIONAL_COORDINATES,((c= @ (cclosure @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (c~ @ (crational @ ((c$ @ V1) @ V2))))))) @ V1))))))) @ cUNIV))
(TCLOSURE_RATIONAL_COORDINATES,((c= @ (cclosure @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (crational @ ((c$ @ V1) @ V2)))))) @ V1))))))) @ cUNIV))
(TCLOSURE_UNIV,((c= @ (cclosure @ cUNIV)) @ cUNIV))
(TUNIT_INTERVAL_CONVEX_HULL,((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ ((chull @ cconvex) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c__caret__/ @ ((c= @ ((c$ @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ ((c$ @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ V1))))))))
(TINSIDE_EMPTY,((c= @ (cinside @ cEMPTY)) @ cEMPTY))
(TRELATIVE_FRONTIER_EMPTY,((c= @ (crelative_frontier @ cEMPTY)) @ cEMPTY))
(TRELATIVE_INTERIOR_EMPTY,((c= @ (crelative_interior @ cEMPTY)) @ cEMPTY))
(TCONVEX_CONE_HULL_EMPTY,((c= @ ((chull @ cconvex_cone) @ cEMPTY)) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ cEMPTY)))
(TCONVEX_HULL_EMPTY,((c= @ ((chull @ cconvex) @ cEMPTY)) @ cEMPTY))
(TCONIC_HULL_EMPTY,((c= @ ((chull @ cconic) @ cEMPTY)) @ cEMPTY))
(TAFFINE_HULL_EMPTY,((c= @ ((chull @ caffine) @ cEMPTY)) @ cEMPTY))
(TEMPTY_AS_INTERVAL,((c= @ cEMPTY) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cvec @ (cNUMERAL @ c_0)))) @ cNIL))))
(TFRONTIER_EMPTY,((c= @ (cfrontier @ cEMPTY)) @ cEMPTY))
(TCLOSURE_EMPTY,((c= @ (cclosure @ cEMPTY)) @ cEMPTY))
(TINTERIOR_EMPTY,((c= @ (cinterior @ cEMPTY)) @ cEMPTY))
(TREFLECT_ALONG_ZERO,((c= @ (creflect_along @ (cvec @ (cNUMERAL @ c_0)))) @ cI))
(TSPAN_EMPTY,((c= @ (cspan @ cEMPTY)) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ cEMPTY)))
(TUNIV_PCROSS_UNIV,((c= @ ((cPCROSS @ cUNIV) @ cUNIV)) @ cUNIV))
(T_GUARDED_PATTERN,((c= @ c_GUARDED_PATTERN) @ (^[V0]: (^[V1]: (^[V2]: ((c/__caret__ @ V0) @ ((c/__caret__ @ V1) @ V2)))))))
(T_UNGUARDED_PATTERN,((c= @ c_UNGUARDED_PATTERN) @ (^[V0]: (^[V1]: ((c/__caret__ @ V0) @ V1)))))
(TOR_DEF,((c= @ c__caret__/) @ (^[V0]: (^[V1]: (c! @ (^[V2]: ((c==> @ ((c==> @ V0) @ V2)) @ ((c==> @ ((c==> @ V1) @ V2)) @ V2))))))))
(TIMP_DEF,((c= @ c==>) @ (^[V0]: (^[V1]: ((c= @ ((c/__caret__ @ V0) @ V1)) @ V0)))))
(TAND_DEF,((c= @ c/__caret__) @ (^[V0]: (^[V1]: ((c= @ (^[V2]: ((V2 @ V0) @ V1))) @ (^[V2]: ((V2 @ cT) @ cT)))))))
(TCOND_DEF,((c= @ cCOND) @ (^[V0]: (^[V1]: (^[V2]: (c__at__ @ (^[V3]: ((c/__caret__ @ ((c==> @ ((c= @ V0) @ cT)) @ ((c= @ V3) @ V1))) @ ((c==> @ ((c= @ V0) @ cF)) @ ((c= @ V3) @ V2))))))))))
(TNOT_DEF,((c= @ c~) @ (^[V0]: ((c==> @ V0) @ cF))))
(Tsetlevel_conjunct1,((c= @ (csetlevel @ cUr_ind)) @ ((cIMAGE @ cI_IND) @ cUNIV)))
(Tsetlevel_conjunct0,((c= @ (csetlevel @ cUr_bool)) @ ((cIMAGE @ cI_BOOL) @ cUNIV)))
(TTRUE,((c= @ cTRUE) @ (^[V0]: cT)))
(TFALSE,((c= @ cFALSE) @ (^[V0]: cF)))
(Tset_of_list_conjunct0,((c= @ (cset_of_list @ cNIL)) @ cEMPTY))
(TINTERS_0,((c= @ (cINTERS @ cEMPTY)) @ cUNIV))
(Tre_universe,((c= @ cre_universe) @ (^[V0]: cT)))
(Tre_null,((c= @ cre_null) @ (^[V0]: cF)))
(TUNIV,((c= @ cUNIV) @ (^[V0]: cT)))
(TEMPTY,((c= @ cEMPTY) @ (^[V0]: cF)))
(TI_DEF,((c= @ cI) @ (^[V0]: V0)))
(TINVERSE_I,((c= @ (cinverse @ cI)) @ cI))
(TUNIV_GSPEC,((c= @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ cT) @ V1)))))) @ cUNIV))
(TEMPTY_GSPEC,((c= @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ cF) @ V1)))))) @ cEMPTY))
(TUNIONS_0,((c= @ (cUNIONS @ cEMPTY)) @ cEMPTY))
(T_MATCH,((c= @ c_MATCH) @ (^[V0]: (^[V1]: (((cCOND @ (c?! @ (V1 @ V0))) @ (c__at__ @ (V1 @ V0))) @ (c__at__ @ (^[V2]: cF)))))))
(TABORT,((c= @ cABORT) @ ((cWhile @ cTRUE) @ cSKIP)))
(TSKIP,((c= @ cSKIP) @ (cAssign @ cI)))
(TNEUTRAL_OUTER,((c= @ (cneutral @ couter)) @ (cmbasis @ cEMPTY)))
(TCROSS_BASIS_conjunct4,((c= @ ((ccross @ (cbasis @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cbasis @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cbasis @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))
(TCROSS_BASIS_conjunct3,((c= @ ((ccross @ (cbasis @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cbasis @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cvector_neg @ (cbasis @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TCROSS_BASIS_conjunct5,((c= @ ((ccross @ (cbasis @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cbasis @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ (cvector_neg @ (cbasis @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))
(TCROSS_BASIS_conjunct0,((c= @ ((ccross @ (cbasis @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cbasis @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cbasis @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))
(TCROSS_BASIS_conjunct2,((c= @ ((ccross @ (cbasis @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cbasis @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ (cbasis @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TCROSS_BASIS_conjunct1,((c= @ ((ccross @ (cbasis @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cbasis @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cvector_neg @ (cbasis @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))
(Tii,((c= @ cii) @ (ccomplex @ ((c__comma__ @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TINTERVAL_BOUNDS_EMPTY_1,((c= @ (cinterval_upperbound @ cEMPTY)) @ (cinterval_lowerbound @ cEMPTY)))
(TNEUTRAL_VECTOR_ADD,((c= @ (cneutral @ cvector_add)) @ (cvec @ (cNUMERAL @ c_0))))
(TVECTOR_NEG_0,((c= @ (cvector_neg @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))
(TMATRIX_INV_I,((c= @ (cmatrix_inv @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TCOFACTOR_I,((c= @ (ccofactor @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TCOFACTOR_0,((c= @ (ccofactor @ (cmat @ (cNUMERAL @ c_0)))) @ (((cCOND @ ((c= @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cmat @ (cNUMERAL @ c_0)))))
(TNEUTRAL_MATRIX_ADD,((c= @ (cneutral @ cmatrix_add)) @ (cmat @ (cNUMERAL @ c_0))))
(TMATRIX_I,((c= @ (cmatrix @ cI)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TMATRIX_ID,((c= @ (cmatrix @ (^[V0]: V0))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TMATRIX_NEG_0,((c= @ (cmatrix_neg @ (cmat @ (cNUMERAL @ c_0)))) @ (cmat @ (cNUMERAL @ c_0))))
(TARITH_EQ_conjunct1,((c= @ ((c= @ c_0) @ c_0)) @ cT))
(TARITH_LE_conjunct1,((c= @ ((c<= @ c_0) @ c_0)) @ cT))
(TARITH_LT_conjunct1,((c= @ ((c< @ c_0) @ c_0)) @ cF))
(TNOT_CLAUSES_WEAK_conjunct0,((c= @ (c~ @ cT)) @ cF))
(TNOT_CLAUSES_WEAK_conjunct1,((c= @ (c~ @ cF)) @ cT))
(TNEUTRAL_AND,((c= @ (cneutral @ c/__caret__)) @ cT))
(Tisasetlevel_conjunct1,((c= @ (cisasetlevel @ cUr_ind)) @ cF))
(Tisasetlevel_conjunct0,((c= @ (cisasetlevel @ cUr_bool)) @ cF))
(TEVENPERM_I,((c= @ (cevenperm @ cI)) @ cT))
(TODD_conjunct0,((c= @ (cODD @ (cNUMERAL @ c_0))) @ cF))
(TARITH_ODD_conjunct1,((c= @ (cODD @ c_0)) @ cF))
(TNULL_conjunct0,((c= @ (cNULL @ cNIL)) @ cT))
(TEVEN_conjunct0,((c= @ (cEVEN @ (cNUMERAL @ c_0))) @ cT))
(TARITH_EVEN_conjunct1,((c= @ (cEVEN @ c_0)) @ cT))
(TT_DEF,((c= @ cT) @ ((c= @ (^[V0]: V0)) @ (^[V0]: V0))))
(TF_DEF,((c= @ cF) @ (c! @ (^[V0]: V0))))
(Tone_DEF,((c= @ cone) @ (c__at__ @ (^[V0]: cT))))
(TI_AXIOM_conjunct0,((c<_c @ cUNIV) @ cUNIV))
(TCARD_BOOL_LT_I,((c<_c @ cUNIV) @ cUNIV))
(TCANTOR_THM_UNIV,((c<_c @ cUNIV) @ cUNIV))
(TENDS_IN_UNIT_INTERVAL_conjunct3,(c~ @ ((cIN @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (copen_interval @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TENDS_IN_UNIT_INTERVAL_conjunct2,(c~ @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ (copen_interval @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TARITH_GT_conjunct1,(c~ @ ((c> @ c_0) @ c_0)))
(Ttype_DISTINCT_conjunct3,(c~ @ ((c= @ cBool) @ cInd)))
(Tsetlevel_DISTINCT_conjunct0,(c~ @ ((c= @ cUr_bool) @ cUr_ind)))
(TREAL_10,(c~ @ ((c= @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))
(Tquat_DISTINCT_conjunct4,(c~ @ ((c= @ cZERO) @ cTOP)))
(Tquat_DISTINCT_conjunct3,(c~ @ ((c= @ cZERO) @ cONE)))
(Tquat_DISTINCT_conjunct0,(c~ @ ((c= @ cX) @ cZERO)))
(Tquat_DISTINCT_conjunct2,(c~ @ ((c= @ cX) @ cTOP)))
(Tquat_DISTINCT_conjunct1,(c~ @ ((c= @ cX) @ cONE)))
(Tquat_DISTINCT_conjunct5,(c~ @ ((c= @ cONE) @ cTOP)))
(TUNIT_INTERVAL_NONEMPTY_conjunct1,(c~ @ ((c= @ (copen_interval @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ cEMPTY)))
(TUNIT_INTERVAL_NONEMPTY_conjunct0,(c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ cEMPTY)))
(TUNIV_NOT_EMPTY,(c~ @ ((c= @ cUNIV) @ cEMPTY)))
(TEMPTY_NOT_UNIV,(c~ @ ((c= @ cEMPTY) @ cUNIV)))
(TBOOL_EQ_DISTINCT_conjunct0,(c~ @ ((c= @ cT) @ cF)))
(TBOOL_EQ_DISTINCT_conjunct1,(c~ @ ((c= @ cF) @ cT)))
(TTRIVIAL_LIMIT_SEQUENTIALLY,(c~ @ (ctrivial_limit @ csequentially)))
(TTRIVIAL_LIMIT_AT_INFINITY,(c~ @ (ctrivial_limit @ cat_infinity)))
(TPRIME_1,(c~ @ (cprime @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TPRIME_0,(c~ @ (cprime @ (cNUMERAL @ c_0))))
(TNOT_NEGLIGIBLE_UNIV,(c~ @ (cnegligible @ cUNIV)))
(TINT_PRIME_1,(c~ @ (cint_prime @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TINT_PRIME_0,(c~ @ (cint_prime @ (cint_of_num @ (cNUMERAL @ c_0)))))
(TUNCOUNTABLE_CANONICAL,(c~ @ (ccountable @ ccanonical)))
(TNOT_BOUNDED_UNIV,(c~ @ (cbounded @ cUNIV)))
(TAFFINE_INDEPENDENT_STDBASIS,(c~ @ (caffine_dependent @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cbasis @ V1))))))))))
(TAFFINE_INDEPENDENT_EMPTY,(c~ @ (caffine_dependent @ cEMPTY)))
(TUNCOUNTABLE_REAL,(c~ @ (cCOUNTABLE @ cUNIV)))
(TUNCOUNTABLE_EUCLIDEAN,(c~ @ (cCOUNTABLE @ cUNIV)))
(TNOT_AR_EMPTY,(c~ @ (cAR @ cEMPTY)))
(TDOUBLE_THE_CUBE_ALGEBRA,(c~ @ (c? @ (^[V0]: ((c/__caret__ @ (cradical @ V0)) @ ((c= @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))
(THARMONIC_DIVERGES,(c~ @ (c? @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V2) @ V3)) @ ((creal_lt @ (creal_abs @ ((creal_sub @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ (^[V4]: ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ V4))))) @ V0))) @ V1)))))))))))))
(TCANTOR_THM_INJ,(c~ @ (c? @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))))
(TCANTOR_THM_SURJ,(c~ @ (c? @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))))))
(TSUBSPACE_UNIV,(csubspace @ cUNIV))
(TSUBSPACE_TRIVIAL,(csubspace @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ cEMPTY)))
(TSTARLIKE_UNIV,(cstarlike @ cUNIV))
(TSIMPLY_CONNECTED_EMPTY,(csimply_connected @ cEMPTY))
(TREAL_OPEN_UNIV,(creal_open @ cUNIV))
(TREAL_OPEN_EMPTY,(creal_open @ cEMPTY))
(TREAL_CLOSED_UNIV,(creal_closed @ cUNIV))
(TREAL_CLOSED_EMPTY,(creal_closed @ cEMPTY))
(TPRIME_2,(cprime @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))
(TPOLYTOPE_EMPTY,(cpolytope @ cEMPTY))
(TPOLYHEDRON_POSITIVE_ORTHANT,(cpolyhedron @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V1) @ V2)))))) @ V1)))))))
(TPOLYHEDRON_UNIV,(cpolyhedron @ cUNIV))
(TPOLYHEDRON_EMPTY,(cpolyhedron @ cEMPTY))
(TPERMUTATION_I,(cpermutation @ cI))
(TPATH_CONNECTED_UNIV,(cpath_connected @ cUNIV))
(TPATH_CONNECTED_EMPTY,(cpath_connected @ cEMPTY))
(TORTHOGONAL_TRANSFORMATION_I,(corthogonal_transformation @ cI))
(TORTHOGONAL_TRANSFORMATION_ID,(corthogonal_transformation @ (^[V0]: V0)))
(TORTHOGONAL_MATRIX_ID,(corthogonal_matrix @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))
(TOPEN_UNIV,(copen @ cUNIV))
(TOPEN_EMPTY,(copen @ cEMPTY))
(TNEGLIGIBLE_EMPTY,(cnegligible @ cEMPTY))
(TMULTIPLICATIVE_DELTA,(cmultiplicative @ (^[V0]: (((cCOND @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ c_0)))))
(TMULTIPLICATIVE_ID,(cmultiplicative @ (^[V0]: V0)))
(TMULTIPLICATIVE_TAU,(cmultiplicative @ ctau))
(TMULTIPLICATIVE_SIGMA,(cmultiplicative @ csigma))
(TMULTIPLICATIVE_PHI,(cmultiplicative @ cphi))
(TMONOIDAL_REAL_MUL,(cmonoidal @ creal_mul))
(TMONOIDAL_REAL_ADD,(cmonoidal @ creal_add))
(TMONOIDAL_ADD,(cmonoidal @ c+))
(TMONOIDAL_MUL,(cmonoidal @ c*))
(TMONOIDAL_SUMSET,(cmonoidal @ c+++))
(TMONOIDAL_VECTOR_ADD,(cmonoidal @ cvector_add))
(TMONOIDAL_MATRIX_ADD,(cmonoidal @ cmatrix_add))
(TMONOIDAL_AND,(cmonoidal @ c/__caret__))
(TMEASURABLE_EMPTY,(cmeasurable @ cEMPTY))
(TLINEAR_SNDCART,(clinear @ csndcart))
(TLINEAR_FSTCART,(clinear @ cfstcart))
(TLINEAR_NEGATION,(clinear @ cvector_neg))
(TLINEAR_ZERO,(clinear @ (^[V0]: (cvec @ (cNUMERAL @ c_0)))))
(TLINEAR_I,(clinear @ cI))
(TLINEAR_ID,(clinear @ (^[V0]: V0)))
(TLEBESGUE_MEASURABLE_UNIV,(clebesgue_measurable @ cUNIV))
(TLEBESGUE_MEASURABLE_EMPTY,(clebesgue_measurable @ cEMPTY))
(Tis_nadd_0,(cis_nadd @ (^[V0]: (cNUMERAL @ c_0))))
(TIS_INTERVAL_UNIV,(cis_interval @ cUNIV))
(TIS_INTERVAL_EMPTY,(cis_interval @ cEMPTY))
(TINT_PRIME_2,(cint_prime @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))
(TINDEPENDENT_STDBASIS,(cindependent @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cbasis @ V1))))))))
(TINDEPENDENT_EMPTY,(cindependent @ cEMPTY))
(TGAUGE_TRIVIAL,(cgauge @ (^[V0]: (cball @ ((c__comma__ @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TCOUNTABLE_REPEATING,(ccountable @ crepeating))
(TCOPLANAR_EMPTY,(ccoplanar @ cEMPTY))
(TCONVEX_CONE_SING,(cconvex_cone @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ cEMPTY)))
(TCONVEX_POSITIVE_ORTHANT,(cconvex @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V1) @ V2)))))) @ V1)))))))
(TCONVEX_UNIV,(cconvex @ cUNIV))
(TCONVEX_EMPTY,(cconvex @ cEMPTY))
(TCONTRACTIBLE_UNIV,(ccontractible @ cUNIV))
(TCONTRACTIBLE_EMPTY,(ccontractible @ cEMPTY))
(TCONNECTED_UNIV,(cconnected @ cUNIV))
(TCONNECTED_EMPTY,(cconnected @ cEMPTY))
(TCONIC_POSITIVE_ORTHANT,(cconic @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V1) @ V2)))))) @ V1)))))))
(TCONIC_UNIV,(cconic @ cUNIV))
(TCONIC_EMPTY,(cconic @ cEMPTY))
(TCOMPLETE_UNIV,(ccomplete @ cUNIV))
(TCOMPACT_EMPTY,(ccompact @ cEMPTY))
(TCOLLINEAR_EMPTY,(ccollinear @ cEMPTY))
(TCLOSED_POSITIVE_ORTHANT,(cclosed @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V1) @ V2)))))) @ V1)))))))
(TCLOSED_UNIV,(cclosed @ cUNIV))
(TCLOSED_EMPTY,(cclosed @ cEMPTY))
(TBOUNDED_EMPTY,(cbounded @ cEMPTY))
(TBILINEAR_INNER,(cbilinear @ cinner))
(TBILINEAR_OUTER,(cbilinear @ couter))
(TBILINEAR_GEOM,(cbilinear @ cgeom_mul))
(TBILINEAR_CROSS,(cbilinear @ ccross))
(TBILINEAR_DROP_MUL,(cbilinear @ (^[V0]: (^[V1]: ((c% @ (cdrop @ V0)) @ V1)))))
(TBILINEAR_DOT,(cbilinear @ (^[V0]: (^[V1]: (clift @ ((cdot @ V0) @ V1))))))
(TAFFINE_UNIV,(caffine @ cUNIV))
(TAFFINE_EMPTY,(caffine @ cEMPTY))
(TZRECSPACE_RULES_conjunct0,(cZRECSPACE @ cZBOT))
(TWF_num,(cWF @ c<))
(TWF_FALSE,(cWF @ (^[V0]: (^[V1]: cF))))
(TPERMUTATION_NIL,(cPERMUTATION @ cNIL))
(TNUM_REP_RULES_conjunct0,(cNUM_REP @ cIND_0))
(TLIST_UNIQ_conjunct0,(cLIST_UNIQ @ cNIL))
(TLIST_UNIQ_RULES_conjunct0,(cLIST_UNIQ @ cNIL))
(TINFINITE_RATIONAL,(cINFINITE @ crational))
(TINFINITE_INTEGER,(cINFINITE @ cinteger))
(Treal_INFINITE,(cINFINITE @ cUNIV))
(TPRIMES_INFINITE,(cINFINITE @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (cprime @ V1)) @ V1)))))))
(Tnum_INFINITE,(cINFINITE @ cUNIV))
(Tstring_INFINITE,(cINFINITE @ cUNIV))
(TINT_PRIMES_INFINITE,(cINFINITE @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (cint_prime @ V1)) @ V1)))))))
(TEUCLIDEAN_SPACE_INFINITE,(cINFINITE @ cUNIV))
(TI_INFINITE,(cINFINITE @ cUNIV))
(TFINITE_MULTIVECTOR,(cFINITE @ cUNIV))
(TFINITE_FINITE_IMAGE,(cFINITE @ cUNIV))
(TFINITE_STDBASIS,(cFINITE @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cbasis @ V1))))))))
(TFINITE_BOOL,(cFINITE @ cUNIV))
(TFINITE_RULES_conjunct0,(cFINITE @ cEMPTY))
(TFINITE_EMPTY,(cFINITE @ cEMPTY))
(TENR_UNIV,(cENR @ cUNIV))
(TENR_EMPTY,(cENR @ cEMPTY))
(TCOUNTABLE_RATIONAL,(cCOUNTABLE @ crational))
(TCOUNTABLE_INTEGER,(cCOUNTABLE @ cinteger))
(TNUM_COUNTABLE,(cCOUNTABLE @ cUNIV))
(TCOUNTABLE_RATIONAL_COORDINATES,(cCOUNTABLE @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (crational @ ((c$ @ V1) @ V2)))))) @ V1)))))))
(TCOUNTABLE_INTEGER_COORDINATES,(cCOUNTABLE @ (cGSPEC @ (^[V0]: (c? @ (^[V1]: (((cSETSPEC @ V0) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (cinteger @ ((c$ @ V1) @ V2)))))) @ V1)))))))
(TCOUNTABLE_EMPTY,(cCOUNTABLE @ cEMPTY))
(TAR_UNIV,(cAR @ cUNIV))
(TANR_UNIV,(cANR @ cUNIV))
(TANR_EMPTY,(cANR @ cEMPTY))
(Tv_tybij_th,(c? @ (^[V0]: ((cIN @ V0) @ cuniverse))))
(TAXIOM_3,(c? @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V2))) @ (c~ @ (c? @ (^[V3]: ((c/__caret__ @ ((con @ V0) @ V3)) @ ((c/__caret__ @ ((con @ V1) @ V3)) @ ((con @ V2) @ V3))))))))))))))))
(TNUMSEG_DIMINDEX_NONEMPTY,(c? @ (^[V0]: ((cIN @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))))
(Tind_model_tybij_th,(c? @ (^[V0]: ((cIN @ V0) @ (c__at__ @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (cFINITE @ V1))))))))
(Tinacc_tybij_th,(c? @ (^[V0]: ((cIN @ V0) @ cUNIV))))
(TLINE_AXIOM_3,(c? @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V2))) @ (c~ @ (c? @ (^[V3]: ((c/__caret__ @ ((cperpl @ V0) @ V3)) @ ((c/__caret__ @ ((cperpl @ V1) @ V3)) @ ((cperpl @ V2) @ V3))))))))))))))))
(TREAL_HREAL_LEMMA2,(c? @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: ((c= @ (V0 @ (V1 @ V2))) @ V2)))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c= @ (V1 @ (V0 @ V2))) @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V2))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((chreal_le @ V2) @ V3)) @ ((creal_le @ (V1 @ V2)) @ (V1 @ V3)))))))))))))))
(Tsum_EXISTS,(c? @ (^[V0]: ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((V0 @ ((c__comma__ @ V2) @ (cNUMERAL @ c_0))) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((V0 @ ((c__comma__ @ V3) @ (cSUC @ V2))) @ V1)) @ ((creal_add @ ((V0 @ ((c__comma__ @ V3) @ V2)) @ V1)) @ (V1 @ ((c+ @ V3) @ V2))))))))))))))
(TI_PAIR_EXISTS,(c? @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))))
(TUNIV_SECOND_COUNTABLE_SEQUENCE,(c? @ (^[V0]: ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))) @ ((c/__caret__ @ (c! @ (^[V1]: (copen @ (V0 @ V1))))) @ (c! @ (^[V1]: ((c==> @ (copen @ V1)) @ (c? @ (^[V2]: ((c= @ V1) @ (cUNIONS @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ V2)) @ (V0 @ V4))))))))))))))))))
(Tmultivector_tybij_th,(c? @ (^[V0]: ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))))
(TINST_CORE_EXISTS,(c? @ (^[V0]: ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((V0 @ V1) @ V2) @ ((cVar @ V3) @ V4))) @ (((cLET @ (^[V5]: (^[V6]: (cLET_END @ (((cCOND @ ((c= @ (((cREV_ASSOCD @ V6) @ V1) @ V5)) @ V5)) @ (cResult @ V6)) @ (cClash @ V6)))))) @ ((cVar @ V3) @ V4)) @ ((cVar @ V3) @ ((cTYPE_SUBST @ V2) @ V4))))))))))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((V0 @ V1) @ V2) @ (cEqual @ V3))) @ (cResult @ (cEqual @ ((cTYPE_SUBST @ V2) @ V3))))))))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((V0 @ V1) @ V2) @ (cSelect @ V3))) @ (cResult @ (cSelect @ ((cTYPE_SUBST @ V2) @ V3))))))))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((V0 @ V1) @ V2) @ ((cComb @ V3) @ V4))) @ ((cLET @ (^[V5]: (cLET_END @ (((cCOND @ (cIS_CLASH @ V5)) @ V5) @ ((cLET @ (^[V6]: (cLET_END @ (((cCOND @ (cIS_CLASH @ V6)) @ V6) @ (((cLET @ (^[V7]: (^[V8]: (cLET_END @ (cResult @ ((cComb @ V7) @ V8)))))) @ (cRESULT @ V5)) @ (cRESULT @ V6)))))) @ (((V0 @ V1) @ V2) @ V4)))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c= @ (((V0 @ V1) @ V2) @ (((cAbs @ V3) @ V4) @ V5))) @ ((cLET @ (^[V6]: (cLET_END @ ((cLET @ (^[V7]: (cLET_END @ ((cLET @ (^[V8]: (cLET_END @ (((cCOND @ (cIS_RESULT @ V8)) @ (cResult @ (((cAbs @ V3) @ V6) @ (cRESULT @ V8)))) @ ((cLET @ (^[V9]: (cLET_END @ (((cCOND @ (c~ @ ((c= @ V9) @ ((cVar @ V3) @ V6)))) @ V8) @ ((cLET @ (^[V10]: (cLET_END @ (((V0 @ V1) @ V2) @ (((cAbs @ V10) @ V4) @ ((cVSUBST @ ((cCONS @ ((c__comma__ @ ((cVar @ V10) @ V4)) @ ((cVar @ V3) @ V4))) @ cNIL)) @ V5)))))) @ (((cVARIANT @ (cRESULT @ (((V0 @ cNIL) @ V2) @ V5))) @ V3) @ V6)))))) @ (cCLASH @ V8)))))) @ (((V0 @ V7) @ V2) @ V5))))) @ ((cCONS @ ((c__comma__ @ ((cVar @ V3) @ V4)) @ ((cVar @ V3) @ V6))) @ V1))))) @ ((cTYPE_SUBST @ V2) @ V4))))))))))))))))))))
(TI_IND_EXISTS,(c? @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))))
(TINFINITY_AX,(c? @ (^[V0]: ((c/__caret__ @ (cONE_ONE @ V0)) @ (c~ @ (cONTO @ V0))))))
(TIND_SUC_0_EXISTS,(c? @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))) @ (c! @ (^[V2]: (c~ @ ((c= @ (V0 @ V2)) @ V1))))))))))
(TREAL_HREAL_LEMMA1,(c? @ (^[V0]: ((c/__caret__ @ (c! @ (^[V1]: ((c= @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c? @ (^[V2]: ((c= @ V1) @ (V0 @ V2)))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chreal_le @ V1) @ V2)) @ ((creal_le @ (V0 @ V1)) @ (V0 @ V2)))))))))))
(TUNIV_SECOND_COUNTABLE,(c? @ (^[V0]: ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (copen @ V1))))) @ (c! @ (^[V1]: ((c==> @ (copen @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c= @ V1) @ (cUNIONS @ V2)))))))))))))
(TELEMENTARY_EMPTY,(c? @ (^[V0]: ((cdivision_of @ V0) @ cEMPTY))))
(Ttopology_tybij_th,(c? @ (^[V0]: (cistopology @ V0))))
(TI_BOOL_EXISTS,(c? @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))))
(Tmultiset_tybij_th,(c? @ (^[V0]: (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c~ @ ((c= @ (V0 @ V2)) @ (cNUMERAL @ c_0)))) @ V2)))))))))
(TPAIR_EXISTS_THM,(c? @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ ((cmk_pair @ V1) @ V2)))))))))
(TDIRECTION_AXIOM_3,(c? @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c|| @ V0) @ V1))) @ ((c/__caret__ @ (c~ @ ((c|| @ V1) @ V2))) @ ((c/__caret__ @ (c~ @ ((c|| @ V0) @ V2))) @ (c~ @ (c? @ (^[V3]: ((c/__caret__ @ ((c_|_ @ V0) @ V3)) @ ((c/__caret__ @ ((c_|_ @ V1) @ V3)) @ ((c_|_ @ V2) @ V3))))))))))))))))
(TTARSKI_AXIOM_8_EUCLIDEAN,(c? @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((cbetween @ V1) @ ((c__comma__ @ V0) @ V2)))) @ ((c/__caret__ @ (c~ @ ((cbetween @ V2) @ ((c__comma__ @ V1) @ V0)))) @ (c~ @ ((cbetween @ V0) @ ((c__comma__ @ V2) @ V1))))))))))))
(TEXISTS_ONE_REP,(c? @ (^[V0]: V0)))
(Thas_type_RULES_conjunct2,(c! @ (^[V0]: ((chas_type @ (cSelect @ V0)) @ ((cFun @ ((cFun @ V0) @ cBool)) @ V0)))))
(Thas_type_RULES_conjunct1,(c! @ (^[V0]: ((chas_type @ (cEqual @ V0)) @ ((cFun @ V0) @ ((cFun @ V0) @ cBool))))))
(Ttypeof_conjunct2,(c! @ (^[V0]: ((c= @ (ctypeof @ (cSelect @ V0))) @ ((cFun @ ((cFun @ V0) @ cBool)) @ V0)))))
(Ttypeof_conjunct1,(c! @ (^[V0]: ((c= @ (ctypeof @ (cEqual @ V0))) @ ((cFun @ V0) @ ((cFun @ V0) @ cBool))))))
(Tsizeof_conjunct2,(c! @ (^[V0]: ((c= @ (csizeof @ (cSelect @ V0))) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(Tsizeof_conjunct1,(c! @ (^[V0]: ((c= @ (csizeof @ (cEqual @ V0))) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TWELLTYPED_CLAUSES_conjunct2,(c! @ (^[V0]: (cwelltyped @ (cSelect @ V0)))))
(TWELLTYPED_CLAUSES_conjunct1,(c! @ (^[V0]: (cwelltyped @ (cEqual @ V0)))))
(Tdomain,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdomain @ ((cFun @ V1) @ V0))) @ V1))))))
(Tcodomain,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccodomain @ ((cFun @ V0) @ V1))) @ V1))))))
(Tterm_INJ_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cSelect @ V0)) @ (cSelect @ V1))) @ ((c= @ V0) @ V1)))))))
(Tterm_INJ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cEqual @ V0)) @ (cEqual @ V1))) @ ((c= @ V0) @ V1)))))))
(Ttype_DISTINCT_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c= @ cInd) @ ((cFun @ V0) @ V1))))))))
(Ttype_DISTINCT_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c= @ cBool) @ ((cFun @ V0) @ V1))))))))
(Tterm_DISTINCT_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c= @ (cEqual @ V0)) @ (cSelect @ V1))))))))
(Ttype_INJ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cFun @ V0) @ V1)) @ ((cFun @ V2) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V2)) @ ((c= @ V1) @ V3))))))))))))
(TVFREE_IN_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cVFREE_IN @ V1) @ (cSelect @ V0))) @ ((c= @ (cSelect @ V0)) @ V1)))))))
(TVFREE_IN_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cVFREE_IN @ V1) @ (cEqual @ V0))) @ ((c= @ (cEqual @ V0)) @ V1)))))))
(TVFREE_IN_FINITE_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cVFREE_IN @ ((cVar @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TVARIANT_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: (c~ @ ((cVFREE_IN @ ((cVar @ V2) @ V0)) @ V1)))))))))
(Tterm_DISTINCT_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c~ @ ((c= @ (cSelect @ V0)) @ ((cComb @ V1) @ V2))))))))))
(Tterm_DISTINCT_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c~ @ ((c= @ (cEqual @ V0)) @ ((cComb @ V1) @ V2))))))))))
(TTYPE_SUBST_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cTYPE_SUBST @ V1) @ ((cFun @ V0) @ V2))) @ ((cFun @ ((cTYPE_SUBST @ V1) @ V0)) @ ((cTYPE_SUBST @ V1) @ V2))))))))))
(Tterm_DISTINCT_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c~ @ ((c= @ (cSelect @ V0)) @ (((cAbs @ V1) @ V2) @ V3))))))))))))
(Tterm_DISTINCT_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c~ @ ((c= @ (cEqual @ V0)) @ (((cAbs @ V1) @ V2) @ V3))))))))))))
(TOPEN_IN_CLAUSES_conjunct0,(c! @ (^[V0]: ((copen_in @ V0) @ cEMPTY))))
(Ttopology_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (ctopology @ (copen_in @ V0))) @ V0))))
(TCLOSED_IN_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cclosed_in @ V0) @ V2)))))) @ ((cclosed_in @ V0) @ (cINTERS @ V1))))))))
(TOPEN_IN_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((copen_in @ V0) @ V2))))))) @ ((copen_in @ V0) @ (cINTERS @ V1))))))))
(TOPEN_IN_CLAUSES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((copen_in @ V0) @ V2))))) @ ((copen_in @ V0) @ (cUNIONS @ V1))))))))
(TOPEN_IN_SUBOPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((copen_in @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((copen_in @ V0) @ V3)) @ ((c/__caret__ @ ((cIN @ V2) @ V3)) @ ((cSUBSET @ V3) @ V1))))))))))))))
(TISTOPLOGY_SUBTOPOLOGY,(c! @ (^[V0]: (c! @ (^[V1]: (cistopology @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((copen_in @ V0) @ V3)) @ ((cINTER @ V3) @ V1))))))))))))
(TOPEN_IN_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((copen_in @ V0) @ V1)) @ ((copen_in @ V0) @ V2))) @ ((copen_in @ V0) @ ((cINTER @ V1) @ V2))))))))))
(TOPEN_IN_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((copen_in @ V0) @ V1)) @ ((cclosed_in @ V0) @ V2))) @ ((copen_in @ V0) @ ((cDIFF @ V1) @ V2))))))))))
(TCLOSED_IN_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ V0) @ V1)) @ ((copen_in @ V0) @ V2))) @ ((cclosed_in @ V0) @ ((cDIFF @ V1) @ V2))))))))))
(TCLOSED_IN_SUBTOPOLOGY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cclosed_in @ ((csubtopology @ V0) @ V2)) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cclosed_in @ V0) @ V3)) @ ((c= @ V1) @ ((cINTER @ V3) @ V2)))))))))))))
(TOPEN_IN_SUBTOPOLOGY_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ V0) @ V1)) @ V3)) @ ((copen_in @ ((csubtopology @ V0) @ V2)) @ V3))) @ ((copen_in @ ((csubtopology @ V0) @ ((cUNION @ V1) @ V2))) @ V3)))))))))))
(TCLOSED_IN_SUBTOPOLOGY_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ V0) @ V1)) @ V3)) @ ((cclosed_in @ ((csubtopology @ V0) @ V2)) @ V3))) @ ((cclosed_in @ ((csubtopology @ V0) @ ((cUNION @ V1) @ V2))) @ V3)))))))))))
(TCLOSED_IN_IMP_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cclosed_in @ ((csubtopology @ V0) @ V2)) @ V1)) @ ((cSUBSET @ V1) @ V2)))))))))
(TOPEN_IN_IMP_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((copen_in @ ((csubtopology @ V0) @ V2)) @ V1)) @ ((cSUBSET @ V1) @ V2)))))))))
(TSUBTOPOLOGY_UNIV,(c! @ (^[V0]: ((c= @ ((csubtopology @ V0) @ cUNIV)) @ V0))))
(TSUBTOPOLOGY_TOPSPACE,(c! @ (^[V0]: ((c= @ ((csubtopology @ V0) @ (ctopspace @ V0))) @ V0))))
(TCLOSED_IN_SUBTOPOLOGY_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cclosed_in @ ((csubtopology @ V0) @ cEMPTY)) @ V1)) @ ((c= @ V1) @ cEMPTY)))))))
(TOPEN_IN_SUBTOPOLOGY_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((copen_in @ ((csubtopology @ V0) @ cEMPTY)) @ V1)) @ ((c= @ V1) @ cEMPTY)))))))
(TTOPSPACE_SUBTOPOLOGY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctopspace @ ((csubtopology @ V0) @ V1))) @ ((cINTER @ (ctopspace @ V0)) @ V1)))))))
(TOPEN_IN_SUBTOPOLOGY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((copen_in @ ((csubtopology @ V0) @ V2)) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((copen_in @ V0) @ V3)) @ ((c= @ V1) @ ((cINTER @ V3) @ V2)))))))))))))
(Tsubtopology,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((csubtopology @ V0) @ V1)) @ (ctopology @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((copen_in @ V0) @ V3)) @ ((cINTER @ V3) @ V1)))))))))))))
(TCLOSED_IN_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cclosed_in @ V0) @ V2)))))) @ ((cclosed_in @ V0) @ (cUNIONS @ V1))))))))
(TOPEN_IN_CLOSED_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V1) @ (ctopspace @ V0))) @ ((c= @ ((copen_in @ V0) @ V1)) @ ((cclosed_in @ V0) @ ((cDIFF @ (ctopspace @ V0)) @ V1)))))))))
(TOPEN_IN_CLOSED_IN_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((copen_in @ V0) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ (ctopspace @ V0))) @ ((cclosed_in @ V0) @ ((cDIFF @ (ctopspace @ V0)) @ V1)))))))))
(TCLOSED_IN_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ V0) @ V1)) @ ((cclosed_in @ V0) @ V2))) @ ((cclosed_in @ V0) @ ((cINTER @ V1) @ V2))))))))))
(TCLOSED_IN_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ V0) @ V1)) @ ((cclosed_in @ V0) @ V2))) @ ((cclosed_in @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TCLOSED_IN_TOPSPACE,(c! @ (^[V0]: ((cclosed_in @ V0) @ (ctopspace @ V0)))))
(TCLOSED_IN_EMPTY,(c! @ (^[V0]: ((cclosed_in @ V0) @ cEMPTY))))
(Tclosed_in,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cclosed_in @ V0) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ (ctopspace @ V0))) @ ((copen_in @ V0) @ ((cDIFF @ (ctopspace @ V0)) @ V1)))))))))
(TOPEN_IN_TOPSPACE,(c! @ (^[V0]: ((copen_in @ V0) @ (ctopspace @ V0)))))
(TOPEN_IN_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((copen_in @ V0) @ V1)) @ ((copen_in @ V0) @ V2))) @ ((copen_in @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TOPEN_IN_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((copen_in @ V0) @ V2))))) @ ((copen_in @ V0) @ (cUNIONS @ V1))))))))
(TOPEN_IN_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((copen_in @ V0) @ V1)) @ ((copen_in @ V0) @ V2))) @ ((copen_in @ V0) @ ((cINTER @ V1) @ V2))))))))))
(TOPEN_IN_EMPTY,(c! @ (^[V0]: ((copen_in @ V0) @ cEMPTY))))
(Ttopspace,(c! @ (^[V0]: ((c= @ (ctopspace @ V0)) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((copen_in @ V0) @ V2)) @ V2))))))))))
(TTOPOLOGY_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ ((copen_in @ V0) @ V2)) @ ((copen_in @ V1) @ V2))))))))))
(TISTOPOLOGY_OPEN_IN,(c! @ (^[V0]: (cistopology @ (copen_in @ V0)))))
(TACONV_REFL,(c! @ (^[V0]: ((cACONV @ V0) @ V0))))
(Tprove_RULES_conjunct5,(c! @ (^[V0]: ((c==> @ ((chas_type @ V0) @ cBool)) @ ((c|- @ ((cCONS @ V0) @ cNIL)) @ V0)))))
(Tprove_RULES_conjunct0,(c! @ (^[V0]: ((c==> @ (cwelltyped @ V0)) @ ((c|- @ cNIL) @ ((c=== @ V0) @ V0))))))
(TRESULT,(c! @ (^[V0]: ((c= @ (cRESULT @ (cResult @ V0))) @ V0))))
(TCLASH,(c! @ (^[V0]: ((c= @ (cCLASH @ (cClash @ V0))) @ V0))))
(TWELLTYPED,(c! @ (^[V0]: ((c= @ (cwelltyped @ V0)) @ ((chas_type @ V0) @ (ctypeof @ V0))))))
(Twelltyped,(c! @ (^[V0]: ((c= @ (cwelltyped @ V0)) @ (c? @ (^[V1]: ((chas_type @ V0) @ V1)))))))
(TIS_RESULT_conjunct1,(c! @ (^[V0]: ((c= @ (cIS_RESULT @ (cResult @ V0))) @ cT))))
(TIS_RESULT_conjunct0,(c! @ (^[V0]: ((c= @ (cIS_RESULT @ (cClash @ V0))) @ cF))))
(TIS_CLASH_conjunct1,(c! @ (^[V0]: ((c= @ (cIS_CLASH @ (cResult @ V0))) @ cF))))
(TIS_CLASH_conjunct0,(c! @ (^[V0]: ((c= @ (cIS_CLASH @ (cClash @ V0))) @ cT))))
(TVFREE_IN_FINITE,(c! @ (^[V0]: (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cVFREE_IN @ V2) @ V0)) @ V2)))))))))
(TWELLTYPED_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_type @ V0) @ V1)) @ ((c= @ (ctypeof @ V0)) @ V1)))))))
(Thas_type_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_type @ V0) @ V1)) @ ((c__caret__/ @ (c? @ (^[V2]: ((c= @ V0) @ ((cVar @ V2) @ V1))))) @ ((c__caret__/ @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ V0) @ (cEqual @ V2))) @ ((c= @ V1) @ ((cFun @ V2) @ ((cFun @ V2) @ cBool))))))) @ ((c__caret__/ @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ V0) @ (cSelect @ V2))) @ ((c= @ V1) @ ((cFun @ ((cFun @ V2) @ cBool)) @ V2)))))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((cComb @ V2) @ V3))) @ ((c/__caret__ @ ((chas_type @ V2) @ ((cFun @ V4) @ V1))) @ ((chas_type @ V3) @ V4)))))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ (((cAbs @ V2) @ V3) @ V4))) @ ((c/__caret__ @ ((c= @ V1) @ ((cFun @ V3) @ V5))) @ ((chas_type @ V4) @ V5)))))))))))))))))))))
(TACONV_TYPE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cACONV @ V0) @ V1)) @ ((c==> @ ((c/__caret__ @ (cwelltyped @ V0)) @ (cwelltyped @ V1))) @ ((c= @ (ctypeof @ V0)) @ (ctypeof @ V1)))))))))
(Ttypeof_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctypeof @ ((cComb @ V1) @ V0))) @ (ccodomain @ (ctypeof @ V1))))))))
(Tequation,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c=== @ V0) @ V1)) @ ((cComb @ ((cComb @ (cEqual @ (ctypeof @ V0))) @ V0)) @ V1)))))))
(Tsizeof_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csizeof @ ((cComb @ V0) @ V1))) @ ((c+ @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c+ @ (csizeof @ V0)) @ (csizeof @ V1)))))))))
(TEQUATION_HAS_TYPE_BOOL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_type @ ((c=== @ V0) @ V1)) @ cBool)) @ ((c/__caret__ @ (cwelltyped @ V0)) @ ((c/__caret__ @ (cwelltyped @ V1)) @ ((c= @ (ctypeof @ V0)) @ (ctypeof @ V1))))))))))
(TACONV,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cACONV @ V0) @ V1)) @ ((cRACONV @ cNIL) @ ((c__comma__ @ V0) @ V1))))))))
(Tresult_INJ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cResult @ V0)) @ (cResult @ V1))) @ ((c= @ V0) @ V1)))))))
(Tresult_INJ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cClash @ V0)) @ (cClash @ V1))) @ ((c= @ V0) @ V1)))))))
(TWELLTYPED_CLAUSES_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cwelltyped @ ((cComb @ V0) @ V1))) @ ((c/__caret__ @ (cwelltyped @ V0)) @ ((c/__caret__ @ (cwelltyped @ V1)) @ (c? @ (^[V2]: ((c= @ (ctypeof @ V0)) @ ((cFun @ (ctypeof @ V1)) @ V2))))))))))))
(Tresult_DISTINCT,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c= @ (cClash @ V0)) @ (cResult @ V1))))))))
(Thas_type_RULES_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_type @ V0) @ ((cFun @ V2) @ V3))) @ ((chas_type @ V1) @ V2))) @ ((chas_type @ ((cComb @ V0) @ V1)) @ V3)))))))))))
(TVFREE_IN_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cVFREE_IN @ V1) @ ((cComb @ V0) @ V2))) @ ((c__caret__/ @ ((cVFREE_IN @ V1) @ V0)) @ ((cVFREE_IN @ V1) @ V2))))))))))
(Tterm_INJ_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cComb @ V0) @ V1)) @ ((cComb @ V2) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V2)) @ ((c= @ V1) @ V3))))))))))))
(TRACONV_conjunct18,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((cRACONV @ V2) @ ((c__comma__ @ ((cComb @ V0) @ V3)) @ ((cComb @ V1) @ V4)))) @ ((c/__caret__ @ ((cRACONV @ V2) @ ((c__comma__ @ V0) @ V1))) @ ((cRACONV @ V2) @ ((c__comma__ @ V3) @ V4)))))))))))))))
(Tterm_DISTINCT_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c~ @ ((c= @ ((cComb @ V0) @ V1)) @ (((cAbs @ V2) @ V3) @ V4))))))))))))))
(TTERM_UNION_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cTERM_UNION @ ((cCONS @ V0) @ V1)) @ V2)) @ ((cLET @ (^[V3]: (cLET_END @ (((cCOND @ ((cEX @ (cACONV @ V0)) @ V3)) @ V3) @ ((cCONS @ V0) @ V3))))) @ ((cTERM_UNION @ V1) @ V2))))))))))
(TVSUBST_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cVSUBST @ V1) @ ((cComb @ V0) @ V2))) @ ((cComb @ ((cVSUBST @ V1) @ V0)) @ ((cVSUBST @ V1) @ V2))))))))))
(TVFREE_IN_ACONV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cACONV @ V0) @ V3)) @ ((c= @ ((cVFREE_IN @ ((cVar @ V1) @ V2)) @ V0)) @ ((cVFREE_IN @ ((cVar @ V1) @ V2)) @ V3))))))))))))
(TVSUBST_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cVSUBST @ V3) @ (((cAbs @ V1) @ V2) @ V0))) @ ((cLET @ (^[V4]: (cLET_END @ ((cLET @ (^[V5]: (cLET_END @ (((cCOND @ ((cEX @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ ((c/__caret__ @ ((cVFREE_IN @ ((cVar @ V1) @ V2)) @ V7)) @ ((cVFREE_IN @ V8) @ V0)))))))))) @ V4)) @ ((cLET @ (^[V6]: (cLET_END @ ((cLET @ (^[V7]: (cLET_END @ (((cAbs @ V6) @ V2) @ ((cVSUBST @ V7) @ V0))))) @ ((cCONS @ ((c__comma__ @ ((cVar @ V6) @ V2)) @ ((cVar @ V1) @ V2))) @ V4))))) @ (((cVARIANT @ V5) @ V1) @ V2))) @ (((cAbs @ V1) @ V2) @ V5))))) @ ((cVSUBST @ V4) @ V0))))) @ ((cFILTER @ (cGABS @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((cGEQ @ (V4 @ ((c__comma__ @ V5) @ V6))) @ (c~ @ ((c= @ V6) @ ((cVar @ V1) @ V2))))))))))) @ V3))))))))))))
(TVFREE_IN_VSUBST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cVFREE_IN @ ((cVar @ V1) @ V2)) @ ((cVSUBST @ V3) @ V0))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((cVFREE_IN @ ((cVar @ V4) @ V5)) @ V0)) @ ((cVFREE_IN @ ((cVar @ V1) @ V2)) @ (((cREV_ASSOCD @ ((cVar @ V4) @ V5)) @ V3) @ ((cVar @ V4) @ V5))))))))))))))))))
(Tsum_CASES,(c! @ (^[V0]: ((c__caret__/ @ (c? @ (^[V1]: ((c= @ V0) @ (cINL @ V1))))) @ (c? @ (^[V1]: ((c= @ V0) @ (cINR @ V1))))))))
(TEMPTY_SET_conjunct0,(c! @ (^[V0]: ((c= @ (clevel @ (cemptyset @ V0))) @ V0))))
(Tdroplevel,(c! @ (^[V0]: ((c= @ (cdroplevel @ (cPowerset @ V0))) @ V0))))
(Tsetlevel_conjunct3,(c! @ (^[V0]: ((c= @ (csetlevel @ (cPowerset @ V0))) @ ((cIMAGE @ (cI_SET @ (csetlevel @ V0))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cSUBSET @ V2) @ (csetlevel @ V0))) @ V2))))))))))
(Tisasetlevel_conjunct3,(c! @ (^[V0]: ((c= @ (cisasetlevel @ (cPowerset @ V0))) @ cT))))
(TSETLEVEL_CARD,(c! @ (^[V0]: ((c<_c @ (csetlevel @ V0)) @ cUNIV))))
(Tsetlevel_DISTINCT_conjunct3,(c! @ (^[V0]: (c~ @ ((c= @ cUr_ind) @ (cPowerset @ V0))))))
(Tsetlevel_DISTINCT_conjunct1,(c! @ (^[V0]: (c~ @ ((c= @ cUr_bool) @ (cPowerset @ V0))))))
(TLEVEL_SET_EXISTS,(c! @ (^[V0]: (c? @ (^[V1]: ((c= @ (clevel @ V1)) @ V0))))))
(TSETLEVEL_EXISTS,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ ((c= @ (clevel @ V1)) @ (cPowerset @ V0))) @ (c! @ (^[V2]: ((c= @ ((c<__colon__ @ V2) @ V1)) @ ((c/__caret__ @ ((c= @ (clevel @ V2)) @ V0)) @ ((cIN @ (celement @ V2)) @ (csetlevel @ V0))))))))))))
(TEMPTY_EXISTS,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ ((c= @ (clevel @ V1)) @ V0)) @ (c! @ (^[V2]: (c~ @ ((c<__colon__ @ V2) @ V1))))))))))
(TLEVEL_NONEMPTY,(c! @ (^[V0]: (c? @ (^[V1]: ((cIN @ V1) @ (csetlevel @ V0)))))))
(Tsetlevel_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csetlevel @ ((cCartprod @ V0) @ V1))) @ ((cIMAGE @ cI_PAIR) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ (csetlevel @ V0))) @ ((cIN @ V4) @ (csetlevel @ V1)))) @ ((c__comma__ @ V3) @ V4)))))))))))))))
(Tsetlevel_INJ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cPowerset @ V0)) @ (cPowerset @ V1))) @ ((c= @ V0) @ V1)))))))
(Tisasetlevel_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cisasetlevel @ ((cCartprod @ V0) @ V1))) @ cF))))))
(Tsetlevel_DISTINCT_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c= @ cUr_ind) @ ((cCartprod @ V0) @ V1))))))))
(Tsetlevel_DISTINCT_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c= @ cUr_bool) @ ((cCartprod @ V0) @ V1))))))))
(Tsetlevel_DISTINCT_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c~ @ ((c= @ (cPowerset @ V0)) @ ((cCartprod @ V1) @ V2))))))))))
(Tsetlevel_INJ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cCartprod @ V0) @ V1)) @ ((cCartprod @ V2) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V2)) @ ((c= @ V1) @ V3))))))))))))
(TMK_V_SET_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V1) @ (csetlevel @ V0))) @ ((c= @ (cset @ (cmk_V @ ((c__comma__ @ (cPowerset @ V0)) @ ((cI_SET @ (csetlevel @ V0)) @ V1))))) @ V1)))))))
(TMK_V_SET_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V1) @ (csetlevel @ V0))) @ ((c= @ (celement @ (cmk_V @ ((c__comma__ @ (cPowerset @ V0)) @ ((cI_SET @ (csetlevel @ V0)) @ V1))))) @ ((cI_SET @ (csetlevel @ V0)) @ V1))))))))
(TI_SET_SETLEVEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ (csetlevel @ V0))) @ ((c/__caret__ @ ((cSUBSET @ V2) @ (csetlevel @ V0))) @ ((c= @ ((cI_SET @ (csetlevel @ V0)) @ V1)) @ ((cI_SET @ (csetlevel @ V0)) @ V2))))) @ ((c= @ V1) @ V2)))))))))
(TEMPTY_SET_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c<__colon__ @ V1) @ (cemptyset @ V0))))))))
(TMK_V_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ (csetlevel @ V0))) @ ((c= @ (celement @ (cmk_V @ ((c__comma__ @ V0) @ V1)))) @ V1)))))))
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(TFLOOR_FRAC_conjunct2,(c! @ (^[V0]: ((creal_lt @ (cfrac @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TSQUARE_BOUND_LEMMA,(c! @ (^[V0]: ((creal_lt @ V0) @ ((creal_mul @ ((creal_add @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ ((creal_add @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))))
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(TREAL_LE_SQUARE,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_mul @ V0) @ V0)))))
(TABS_POS,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_abs @ V0)))))
(TFLOOR_FRAC_conjunct1,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cfrac @ V0)))))
(TFLOOR_DOUBLE_conjunct1,(c! @ (^[V0]: ((creal_le @ (cfloor @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))) @ ((creal_add @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cfloor @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
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(TABS_LE,(c! @ (^[V0]: ((creal_le @ V0) @ (creal_abs @ V0)))))
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(TREAL_DIV_LZERO,(c! @ (^[V0]: ((c= @ ((creal_div @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))))
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(TREAL_ADD_LID,(c! @ (^[V0]: ((c= @ ((creal_add @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ V0))))
(TREAL_ADD_LINV,(c! @ (^[V0]: ((c= @ ((creal_add @ (creal_neg @ V0)) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TREAL_ADD_RID,(c! @ (^[V0]: ((c= @ ((creal_add @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V0))))
(TREAL_ADD_RINV,(c! @ (^[V0]: ((c= @ ((creal_add @ V0) @ (creal_neg @ V0))) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TREAL_DOUBLE,(c! @ (^[V0]: ((c= @ ((creal_add @ V0) @ V0)) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))))
(TPOLY_X,(c! @ (^[V0]: ((c= @ ((cpoly @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))) @ V0)) @ V0))))
(Tpoly_conjunct0,(c! @ (^[V0]: ((c= @ ((cpoly @ cNIL) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TMINL_conjunct0,(c! @ (^[V0]: ((c= @ ((cMINL @ cNIL) @ V0)) @ V0))))
(TMAXL_conjunct0,(c! @ (^[V0]: ((c= @ ((cMAXL @ cNIL) @ V0)) @ V0))))
(TLIFT_COMPONENT,(c! @ (^[V0]: ((c= @ ((c$ @ (clift @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))
(TNORM_LIFT,(c! @ (^[V0]: ((c= @ (cvector_norm @ (clift @ V0))) @ (creal_abs @ V0)))))
(Tvalue_conjunct0,(c! @ (^[V0]: ((c= @ (cvalue @ (cConstant @ V0))) @ V0))))
(TSUP_SING,(c! @ (^[V0]: ((c= @ (csup @ ((cINSERT @ V0) @ cEMPTY))) @ V0))))
(TPOW_2_SQRT_ABS,(c! @ (^[V0]: ((c= @ (csqrt @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_abs @ V0)))))
(Tsqrt,(c! @ (^[V0]: ((c= @ (csqrt @ V0)) @ (c__at__ @ (^[V1]: ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c= @ ((creal_pow @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))))))))
(TREAL_SGN_NEG,(c! @ (^[V0]: ((c= @ (creal_sgn @ (creal_neg @ V0))) @ (creal_neg @ (creal_sgn @ V0))))))
(TREAL_SGN_INV,(c! @ (^[V0]: ((c= @ (creal_sgn @ (creal_inv @ V0))) @ (creal_sgn @ V0)))))
(Treal_sgn,(c! @ (^[V0]: ((c= @ (creal_sgn @ V0)) @ (((cCOND @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (((cCOND @ ((creal_lt @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TREAL_SGN,(c! @ (^[V0]: ((c= @ (creal_sgn @ V0)) @ ((creal_div @ V0) @ (creal_abs @ V0))))))
(TREAL_NEGNEG,(c! @ (^[V0]: ((c= @ (creal_neg @ (creal_neg @ V0))) @ V0))))
(TREAL_NEG_MINUS1,(c! @ (^[V0]: ((c= @ (creal_neg @ V0)) @ ((creal_mul @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)))))
(Treal_neg,(c! @ (^[V0]: ((c= @ (creal_neg @ V0)) @ (cmk_real @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((ctreal_eq @ (ctreal_neg @ V2)) @ V1)) @ ((cdest_real @ V0) @ V2))))))))))
(TREAL_INV_NEG,(c! @ (^[V0]: ((c= @ (creal_inv @ (creal_neg @ V0))) @ (creal_neg @ (creal_inv @ V0))))))
(TREAL_INV_INV,(c! @ (^[V0]: ((c= @ (creal_inv @ (creal_inv @ V0))) @ V0))))
(TREAL_INV_1OVER,(c! @ (^[V0]: ((c= @ (creal_inv @ V0)) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)))))
(Treal_inv,(c! @ (^[V0]: ((c= @ (creal_inv @ V0)) @ (cmk_real @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((ctreal_eq @ (ctreal_inv @ V2)) @ V1)) @ ((cdest_real @ V0) @ V2))))))))))
(TABS_POW2,(c! @ (^[V0]: ((c= @ (creal_abs @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))
(TREAL_ABS_SGN,(c! @ (^[V0]: ((c= @ (creal_abs @ (creal_sgn @ V0))) @ (creal_sgn @ (creal_abs @ V0))))))
(TABS_NEG,(c! @ (^[V0]: ((c= @ (creal_abs @ (creal_neg @ V0))) @ (creal_abs @ V0)))))
(TREAL_ABS_INV,(c! @ (^[V0]: ((c= @ (creal_abs @ (creal_inv @ V0))) @ (creal_inv @ (creal_abs @ V0))))))
(TABS_ABS,(c! @ (^[V0]: ((c= @ (creal_abs @ (creal_abs @ V0))) @ (creal_abs @ V0)))))
(Treal_abs,(c! @ (^[V0]: ((c= @ (creal_abs @ V0)) @ (((cCOND @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ V0) @ (creal_neg @ V0))))))
(TINF_SING,(c! @ (^[V0]: ((c= @ (cinf @ ((cINSERT @ V0) @ cEMPTY))) @ V0))))
(TFRAC_FLOOR,(c! @ (^[V0]: ((c= @ (cfrac @ V0)) @ ((creal_sub @ V0) @ (cfloor @ V0))))))
(TLIFT_DROP_conjunct1,(c! @ (^[V0]: ((c= @ (cdrop @ (clift @ V0))) @ V0))))
(TFLOOR_FRAC_conjunct3,(c! @ (^[V0]: ((c= @ V0) @ ((creal_add @ (cfloor @ V0)) @ (cfrac @ V0))))))
(Tdepth_conjunct0,(c! @ (^[V0]: ((c= @ (cdepth @ (cConstant @ V0))) @ (cNUMERAL @ c_0)))))
(TPOLY_CMUL_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((cpoly_cmul @ V0) @ cNIL)) @ cNIL))))
(TPOLY_DIFF_CLAUSES_conjunct1,(c! @ (^[V0]: ((c= @ (cpoly_diff @ ((cCONS @ V0) @ cNIL))) @ cNIL))))
(Tradicals_conjunct0,(c! @ (^[V0]: ((c= @ (cradicals @ (cConstant @ V0))) @ cEMPTY))))
(TCBALL_INTERVAL_0,(c! @ (^[V0]: ((c= @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvector_neg @ (clift @ V0))) @ (clift @ V0))) @ cNIL))))))
(TBALL_INTERVAL_0,(c! @ (^[V0]: ((c= @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V0))) @ (copen_interval @ ((c__comma__ @ (cvector_neg @ (clift @ V0))) @ (clift @ V0)))))))
(TNEGATIONS_SPHERE,(c! @ (^[V0]: ((c= @ ((cIMAGE @ cvector_neg) @ (csphere @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V0)))) @ (csphere @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V0))))))
(TNEGATIONS_CBALL,(c! @ (^[V0]: ((c= @ ((cIMAGE @ cvector_neg) @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V0)))) @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V0))))))
(TNEGATIONS_BALL,(c! @ (^[V0]: ((c= @ ((cIMAGE @ cvector_neg) @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V0)))) @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V0))))))
(TCX_DEF,(c! @ (^[V0]: ((c= @ (cCx @ V0)) @ (ccomplex @ ((c__comma__ @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TLIFT_NEG,(c! @ (^[V0]: ((c= @ (clift @ (creal_neg @ V0))) @ (cvector_neg @ (clift @ V0))))))
(TLIFT_EQ_CMUL,(c! @ (^[V0]: ((c= @ (clift @ V0)) @ ((c% @ V0) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(Tlift,(c! @ (^[V0]: ((c= @ (clift @ V0)) @ (clambda @ (^[V1]: V0))))))
(TVECTOR_MUL_RZERO,(c! @ (^[V0]: ((c= @ ((c% @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))))
(TMATRIX_CMUL_RZERO,(c! @ (^[V0]: ((c= @ ((c%% @ V0) @ (cmat @ (cNUMERAL @ c_0)))) @ (cmat @ (cNUMERAL @ c_0))))))
(TREAL_LT_HALF2,(c! @ (^[V0]: ((c= @ ((creal_lt @ ((creal_div @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_SGN_INEQS_conjunct6,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_sgn @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_lt @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_LT_SQUARE,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_mul @ V0) @ V0))) @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TREAL_LT_HALF1,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_div @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_SGN_INEQS_conjunct1,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_sgn @ V0))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_NEG_GT0,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_neg @ V0))) @ ((creal_lt @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_LT_INV_EQ,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_inv @ V0))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_FRAC_POS_LT,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cfrac @ V0))) @ (c~ @ (cinteger @ V0))))))
(TREAL_ARCH_INV,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_inv @ (creal_of_num @ V1)))) @ ((creal_lt @ (creal_inv @ (creal_of_num @ V1))) @ V0)))))))))
(TREAL_NEG_LT0,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_neg @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_FLOOR_LT,(c! @ (^[V0]: ((c= @ ((creal_lt @ (cfloor @ V0)) @ V0)) @ (c~ @ (cinteger @ V0))))))
(TREAL_SGN_INEQS_conjunct5,(c! @ (^[V0]: ((c= @ ((creal_le @ (creal_sgn @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_le @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_LE_DOUBLE,(c! @ (^[V0]: ((c= @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_add @ V0) @ V0))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_SGN_INEQS_conjunct0,(c! @ (^[V0]: ((c= @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_sgn @ V0))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_NEG_GE0,(c! @ (^[V0]: ((c= @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_neg @ V0))) @ ((creal_le @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_LE_INV_EQ,(c! @ (^[V0]: ((c= @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_inv @ V0))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TFLOOR_POS_LE,(c! @ (^[V0]: ((c= @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cfloor @ V0))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_NEG_LE0,(c! @ (^[V0]: ((c= @ ((creal_le @ (creal_neg @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_LE_NEGL,(c! @ (^[V0]: ((c= @ ((creal_le @ (creal_neg @ V0)) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_LE_NEGR,(c! @ (^[V0]: ((c= @ ((creal_le @ V0) @ (creal_neg @ V0))) @ ((creal_le @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_SGN_INEQS_conjunct8,(c! @ (^[V0]: ((c= @ ((creal_gt @ (creal_sgn @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_gt @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_SGN_INEQS_conjunct3,(c! @ (^[V0]: ((c= @ ((creal_gt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_sgn @ V0))) @ ((creal_gt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_SGN_INEQS_conjunct7,(c! @ (^[V0]: ((c= @ ((creal_ge @ (creal_sgn @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_ge @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_SGN_INEQS_conjunct2,(c! @ (^[V0]: ((c= @ ((creal_ge @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_sgn @ V0))) @ ((creal_ge @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TSQRT_POW2,(c! @ (^[V0]: ((c= @ ((c= @ ((creal_pow @ (csqrt @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_SGN_EQ_conjunct1,(c! @ (^[V0]: ((c= @ ((c= @ (creal_sgn @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_gt @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_SGN_EQ_conjunct0,(c! @ (^[V0]: ((c= @ ((c= @ (creal_sgn @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_SGN_EQ_conjunct2,(c! @ (^[V0]: ((c= @ ((c= @ (creal_sgn @ V0)) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((creal_lt @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_SGN_INEQS_conjunct4,(c! @ (^[V0]: ((c= @ ((c= @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_sgn @ V0))) @ ((c= @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_NEG_EQ0,(c! @ (^[V0]: ((c= @ ((c= @ (creal_neg @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TREAL_INV_EQ_1,(c! @ (^[V0]: ((c= @ ((c= @ (creal_inv @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TREAL_INV_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (creal_inv @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TABS_ZERO,(c! @ (^[V0]: ((c= @ ((c= @ (creal_abs @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TABS_REFL,(c! @ (^[V0]: ((c= @ ((c= @ (creal_abs @ V0)) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TREAL_FRAC_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cfrac @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (cinteger @ V0)))))
(TREAL_FRAC_EQ,(c! @ (^[V0]: ((c= @ ((c= @ (cfrac @ V0)) @ V0)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_lt @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TFLOOR_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cfloor @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_lt @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TREAL_FLOOR_EQ,(c! @ (^[V0]: ((c= @ ((c= @ (cfloor @ V0)) @ V0)) @ (cinteger @ V0)))))
(TABS_NZ,(c! @ (^[V0]: ((c= @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_abs @ V0))))))
(Twellformed_conjunct0,(c! @ (^[V0]: ((c= @ (cwellformed @ (cConstant @ V0))) @ (crational @ V0)))))
(Ttranscendental,(c! @ (^[V0]: ((c= @ (ctranscendental @ V0)) @ (c~ @ (calgebraic @ V0))))))
(TRATIONAL_NEG_EQ,(c! @ (^[V0]: ((c= @ (crational @ (creal_neg @ V0))) @ (crational @ V0)))))
(TRATIONAL_INV_EQ,(c! @ (^[V0]: ((c= @ (crational @ (creal_inv @ V0))) @ (crational @ V0)))))
(Trational,(c! @ (^[V0]: ((c= @ (crational @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cinteger @ V1)) @ ((c/__caret__ @ (cinteger @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ V0) @ ((creal_div @ V1) @ V2)))))))))))))
(TRATIONAL_ALT,(c! @ (^[V0]: ((c= @ (crational @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ (creal_abs @ V0)) @ ((creal_div @ (creal_of_num @ V1)) @ (creal_of_num @ V2))))))))))))
(TRATIONAL_LOWEST,(c! @ (^[V0]: ((c= @ (crational @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V1) @ V2))) @ ((c= @ (creal_abs @ V0)) @ ((creal_div @ (creal_of_num @ V1)) @ (creal_of_num @ V2)))))))))))))
(Tradical_CASES,(c! @ (^[V0]: ((c= @ (cradical @ V0)) @ ((c__caret__/ @ (crational @ V0)) @ ((c__caret__/ @ (c? @ (^[V1]: ((c/__caret__ @ ((c= @ V0) @ (creal_neg @ V1))) @ (cradical @ V1))))) @ ((c__caret__/ @ (c? @ (^[V1]: ((c/__caret__ @ ((c= @ V0) @ (creal_inv @ V1))) @ ((c/__caret__ @ (cradical @ V1)) @ (c~ @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ ((c__caret__/ @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c= @ V0) @ ((creal_add @ V1) @ V2))) @ ((c/__caret__ @ (cradical @ V1)) @ (cradical @ V2)))))))) @ ((c__caret__/ @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c= @ V0) @ ((creal_mul @ V1) @ V2))) @ ((c/__caret__ @ (cradical @ V1)) @ (cradical @ V2)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((c= @ V0) @ (csqrt @ V1))) @ ((c/__caret__ @ (cradical @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))))))))))))))
(TRADICAL_EXPRESSION,(c! @ (^[V0]: ((c= @ (cradical @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (cwellformed @ V1)) @ ((c= @ V0) @ (cvalue @ V1)))))))))
(TINTEGER_NEG,(c! @ (^[V0]: ((c= @ (cinteger @ (creal_neg @ V0))) @ (cinteger @ V0)))))
(TINTEGER_ABS,(c! @ (^[V0]: ((c= @ (cinteger @ (creal_abs @ V0))) @ (cinteger @ V0)))))
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(Tint_rep,(c! @ (^[V0]: ((c= @ (cinteger @ V0)) @ ((c= @ (creal_of_int @ (cint_of_real @ V0))) @ V0)))))
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(TREAL_ARCH_SIMPLE,(c! @ (^[V0]: (c? @ (^[V1]: ((creal_le @ V0) @ (creal_of_num @ V1)))))))
(TREAL_SUB_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ ((creal_sub @ (creal_abs @ V0)) @ (creal_abs @ V1))) @ (creal_abs @ ((creal_sub @ V0) @ V1))))))))
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(TREAL_MAX_MAX_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ V0) @ ((creal_max @ V0) @ V1)))))))
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(TRADICAL_LINEAR_EQUATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cradical @ V0)) @ ((c/__caret__ @ (cradical @ V1)) @ ((c/__caret__ @ (c~ @ ((c/__caret__ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((c= @ ((creal_add @ ((creal_mul @ V0) @ V2)) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ (cradical @ V2)))))))))
(TCUBIC_ROOT_INTEGER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cinteger @ V0)) @ ((c/__caret__ @ (cinteger @ V1)) @ ((c/__caret__ @ (cinteger @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (cradical @ V3)) @ ((c= @ ((creal_add @ ((creal_pow @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ V0) @ ((creal_pow @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V1) @ V3)) @ V2)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))) @ (c? @ (^[V3]: ((c/__caret__ @ (cinteger @ V3)) @ ((c= @ ((creal_add @ ((creal_pow @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ V0) @ ((creal_pow @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V1) @ V3)) @ V2)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))))
(TREAL_EQ_LMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((c= @ V0) @ V2)) @ ((c= @ ((creal_mul @ V1) @ V0)) @ ((creal_mul @ V1) @ V2)))))))))))
(TREAL_SUB_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_mul @ ((creal_sub @ V0) @ V1)) @ V2)) @ ((creal_sub @ ((creal_mul @ V0) @ V2)) @ ((creal_mul @ V1) @ V2))))))))))
(TREAL_MUL_AC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_mul @ ((creal_mul @ V0) @ V1)) @ V2)) @ ((creal_mul @ V0) @ ((creal_mul @ V1) @ V2))))))))))
(TREAL_ADD_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_mul @ ((creal_add @ V0) @ V1)) @ V2)) @ ((creal_add @ ((creal_mul @ V0) @ V2)) @ ((creal_mul @ V1) @ V2))))))))))
(TREAL_SUB_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_mul @ V1) @ ((creal_sub @ V0) @ V2))) @ ((creal_sub @ ((creal_mul @ V1) @ V0)) @ ((creal_mul @ V1) @ V2))))))))))
(TREAL_MUL_AC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_mul @ V1) @ ((creal_mul @ V0) @ V2))) @ ((creal_mul @ V0) @ ((creal_mul @ V1) @ V2))))))))))
(TREAL_ADD_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_mul @ V1) @ ((creal_add @ V0) @ V2))) @ ((creal_add @ ((creal_mul @ V1) @ V0)) @ ((creal_mul @ V1) @ V2))))))))))
(TREAL_MUL_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_mul @ V0) @ ((creal_mul @ V1) @ V2))) @ ((creal_mul @ ((creal_mul @ V0) @ V1)) @ V2)))))))))
(TREAL_POLY_CLAUSES_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_mul @ V0) @ ((creal_add @ V1) @ V2))) @ ((creal_add @ ((creal_mul @ V0) @ V1)) @ ((creal_mul @ V0) @ V2))))))))))
(TREAL_MIN_ACI_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_min @ ((creal_min @ V0) @ V1)) @ V2)) @ ((creal_min @ V0) @ ((creal_min @ V1) @ V2))))))))))
(TREAL_MIN_ACI_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_min @ V1) @ ((creal_min @ V0) @ V2))) @ ((creal_min @ V0) @ ((creal_min @ V1) @ V2))))))))))
(TREAL_MIN_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_min @ V0) @ ((creal_min @ V1) @ V2))) @ ((creal_min @ ((creal_min @ V0) @ V1)) @ V2)))))))))
(TREAL_MAX_ACI_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_max @ ((creal_max @ V0) @ V1)) @ V2)) @ ((creal_max @ V0) @ ((creal_max @ V1) @ V2))))))))))
(TREAL_MAX_ACI_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_max @ V1) @ ((creal_max @ V0) @ V2))) @ ((creal_max @ V0) @ ((creal_max @ V1) @ V2))))))))))
(TREAL_MAX_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_max @ V0) @ ((creal_max @ V1) @ V2))) @ ((creal_max @ ((creal_max @ V0) @ V1)) @ V2)))))))))
(TREAL_SUB_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_add @ ((creal_sub @ V1) @ V0)) @ ((creal_sub @ V0) @ V2))) @ ((creal_sub @ V1) @ V2)))))))))
(TREAL_ADD_AC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_add @ ((creal_add @ V0) @ V1)) @ V2)) @ ((creal_add @ V0) @ ((creal_add @ V1) @ V2))))))))))
(TREAL_ADD_AC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_add @ V1) @ ((creal_add @ V0) @ V2))) @ ((creal_add @ V0) @ ((creal_add @ V1) @ V2))))))))))
(TREAL_ADD_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_add @ V0) @ ((creal_add @ V1) @ V2))) @ ((creal_add @ ((creal_add @ V0) @ V1)) @ V2)))))))))
(Treal_mod,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((creal_mod @ V2) @ V0) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ (cinteger @ V3)) @ ((c= @ ((creal_sub @ V0) @ V1)) @ ((creal_mul @ V3) @ V2)))))))))))))
(TREAL_LT_SUB_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ ((creal_sub @ V0) @ V2)) @ V1)) @ ((creal_lt @ V0) @ ((creal_add @ V1) @ V2))))))))))
(TREAL_MIN_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ ((creal_min @ V0) @ V1)) @ V2)) @ ((c__caret__/ @ ((creal_lt @ V0) @ V2)) @ ((creal_lt @ V1) @ V2))))))))))
(TMAX_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ ((creal_max @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((creal_lt @ V0) @ V2)) @ ((creal_lt @ V1) @ V2))))))))))
(TREAL_LT_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ ((creal_add @ V1) @ V0)) @ ((creal_add @ V2) @ V0))) @ ((creal_lt @ V1) @ V2)))))))))
(TREAL_LT_ADDNEG2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ ((creal_add @ V0) @ (creal_neg @ V2))) @ V1)) @ ((creal_lt @ V0) @ ((creal_add @ V1) @ V2))))))))))
(TREAL_LT_ADD_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ ((creal_add @ V0) @ V2)) @ V1)) @ ((creal_lt @ V0) @ ((creal_sub @ V1) @ V2))))))))))
(TREAL_LT_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ ((creal_add @ V0) @ V1)) @ ((creal_add @ V0) @ V2))) @ ((creal_lt @ V1) @ V2)))))))))
(TMIN_GT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ V1) @ ((creal_min @ V0) @ V2))) @ ((c/__caret__ @ ((creal_lt @ V1) @ V0)) @ ((creal_lt @ V1) @ V2))))))))))
(TREAL_LT_MAX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ V1) @ ((creal_max @ V0) @ V2))) @ ((c__caret__/ @ ((creal_lt @ V1) @ V0)) @ ((creal_lt @ V1) @ V2))))))))))
(TREAL_LT_SUB_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ V0) @ ((creal_sub @ V2) @ V1))) @ ((creal_lt @ ((creal_add @ V0) @ V1)) @ V2)))))))))
(TREAL_LT_ADDNEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_lt @ V0) @ ((creal_add @ V2) @ (creal_neg @ V1)))) @ ((creal_lt @ ((creal_add @ V0) @ V1)) @ V2)))))))))
(TREAL_LE_SUB_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_le @ ((creal_sub @ V0) @ V2)) @ V1)) @ ((creal_le @ V0) @ ((creal_add @ V1) @ V2))))))))))
(TREAL_MIN_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_le @ ((creal_min @ V0) @ V1)) @ V2)) @ ((c__caret__/ @ ((creal_le @ V0) @ V2)) @ ((creal_le @ V1) @ V2))))))))))
(TREAL_MAX_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_le @ ((creal_max @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((creal_le @ V0) @ V2)) @ ((creal_le @ V1) @ V2))))))))))
(TREAL_LE_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_le @ ((creal_add @ V1) @ V0)) @ ((creal_add @ V2) @ V0))) @ ((creal_le @ V1) @ V2)))))))))
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(TREAL_LE_MIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_le @ V1) @ ((creal_min @ V0) @ V2))) @ ((c/__caret__ @ ((creal_le @ V1) @ V0)) @ ((creal_le @ V1) @ V2))))))))))
(TREAL_LE_MAX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_le @ V1) @ ((creal_max @ V0) @ V2))) @ ((c__caret__/ @ ((creal_le @ V1) @ V0)) @ ((creal_le @ V1) @ V2))))))))))
(TREAL_LE_SUB_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_le @ V0) @ ((creal_sub @ V2) @ V1))) @ ((creal_le @ ((creal_add @ V0) @ V1)) @ V2)))))))))
(TREAL_EQ_SUB_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((creal_sub @ V0) @ V2)) @ V1)) @ ((c= @ V0) @ ((creal_add @ V1) @ V2))))))))))
(TREAL_EQ_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((creal_mul @ V1) @ V0)) @ ((creal_mul @ V2) @ V0))) @ ((c__caret__/ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ V2))))))))))
(TREAL_EQ_MUL_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((creal_mul @ V0) @ V2)) @ ((creal_mul @ V1) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))
(TREAL_EQ_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((creal_mul @ V0) @ V1)) @ ((creal_mul @ V0) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ V2))))))))))
(TREAL_EQ_ADD_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((creal_add @ V1) @ V0)) @ ((creal_add @ V2) @ V0))) @ ((c= @ V1) @ V2)))))))))
(TREAL_EQ_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((creal_add @ V0) @ V1)) @ ((creal_add @ V0) @ V2))) @ ((c= @ V1) @ V2)))))))))
(TREAL_EQ_SUB_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ V0) @ ((creal_sub @ V2) @ V1))) @ ((c= @ ((creal_add @ V0) @ V1)) @ V2)))))))))
(TABS_BETWEEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c/__caret__ @ ((creal_lt @ ((creal_sub @ V1) @ V2)) @ V0)) @ ((creal_lt @ V0) @ ((creal_add @ V1) @ V2))))) @ ((creal_lt @ (creal_abs @ ((creal_sub @ V0) @ V1))) @ V2)))))))))
(TREAL_ABS_TRIANGLE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_lt @ ((creal_add @ (creal_abs @ ((creal_sub @ V0) @ V2))) @ (creal_abs @ ((creal_sub @ V1) @ V0)))) @ V3)) @ ((creal_lt @ (creal_abs @ ((creal_sub @ V1) @ V2))) @ V3)))))))))))
(TREAL_AFFINITY_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c= @ ((creal_lt @ ((creal_add @ ((creal_mul @ V3) @ V0)) @ V2)) @ V1)) @ ((creal_lt @ V0) @ ((creal_add @ ((creal_mul @ (creal_inv @ V3)) @ V1)) @ (creal_neg @ ((creal_div @ V2) @ V3)))))))))))))))
(TREAL_AFFINITY_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c= @ ((creal_le @ ((creal_add @ ((creal_mul @ V3) @ V0)) @ V2)) @ V1)) @ ((creal_le @ V0) @ ((creal_add @ ((creal_mul @ (creal_inv @ V3)) @ V1)) @ (creal_neg @ ((creal_div @ V2) @ V3)))))))))))))))
(TREAL_LT_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c= @ ((creal_lt @ V0) @ ((creal_add @ ((creal_mul @ V2) @ V3)) @ V1))) @ ((creal_lt @ ((creal_add @ ((creal_mul @ (creal_inv @ V2)) @ V0)) @ (creal_neg @ ((creal_div @ V1) @ V2)))) @ V3))))))))))))
(TREAL_LE_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c= @ ((creal_le @ V0) @ ((creal_add @ ((creal_mul @ V2) @ V3)) @ V1))) @ ((creal_le @ ((creal_add @ ((creal_mul @ (creal_inv @ V2)) @ V0)) @ (creal_neg @ ((creal_div @ V1) @ V2)))) @ V3))))))))))))
(TRAT_LEMMA4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((c= @ ((creal_le @ ((creal_div @ V0) @ V3)) @ ((creal_div @ V2) @ V1))) @ ((creal_le @ ((creal_mul @ V0) @ V1)) @ ((creal_mul @ V2) @ V3)))))))))))))
(TRAT_LEMMA5,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((c= @ ((c= @ ((creal_div @ V0) @ V3)) @ ((creal_div @ V2) @ V1))) @ ((c= @ ((creal_mul @ V0) @ V1)) @ ((creal_mul @ V2) @ V3)))))))))))))
(TRAT_LEMMA3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ ((c= @ ((creal_sub @ ((creal_div @ V0) @ V2)) @ ((creal_div @ V1) @ V3))) @ ((creal_mul @ ((creal_sub @ ((creal_mul @ V0) @ V3)) @ ((creal_mul @ V1) @ V2))) @ ((creal_mul @ (creal_inv @ V2)) @ (creal_inv @ V3))))))))))))))
(TRAT_LEMMA2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ ((c= @ ((creal_add @ ((creal_div @ V0) @ V2)) @ ((creal_div @ V1) @ V3))) @ ((creal_mul @ ((creal_add @ ((creal_mul @ V0) @ V3)) @ ((creal_mul @ V1) @ V2))) @ ((creal_mul @ (creal_inv @ V2)) @ (creal_inv @ V3))))))))))))))
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(cBIT0 @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V6))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))) @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_div @ ((creal_pow @ V5) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_pow @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V6))) @ ((creal_div @ ((creal_sub @ ((creal_sub @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ V5) @ V6))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ V7))) @ ((creal_pow @ V5) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V3)))))) @ ((c__caret__/ @ ((c= @ V8) @ ((creal_add @ ((creal_div @ (creal_neg @ V5)) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_add @ ((creal_div @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_div @ V2) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((c= @ V8) @ ((creal_add @ ((creal_sub @ ((creal_div @ (creal_neg @ V5)) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_div @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_div @ V4) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))) @ ((c= @ ((creal_add @ ((creal_pow @ V8) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V5) @ ((creal_pow @ V8) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V6) @ ((creal_pow @ V8) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V7) @ V8)) @ V9))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))))))))))))
(TQUARTIC_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((c= @ ((creal_add @ ((creal_sub @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ V2) @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_add @ ((creal_sub @ ((creal_mul @ ((creal_sub @ ((creal_mul @ V7) @ V3)) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V4))) @ V0)) @ ((creal_mul @ ((creal_pow @ V7) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V4))) @ ((creal_sub @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ V2) @ V4))) @ ((creal_pow @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ ((creal_pow @ V8) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_sub @ ((creal_div @ ((creal_pow @ V7) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ V2)) @ V0))) @ ((c/__caret__ @ ((c= @ ((creal_pow @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V4)))) @ ((c/__caret__ @ ((c= @ ((creal_pow @ V5) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (((cCOND @ ((c= @ V8) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_add @ ((creal_sub @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_div @ ((creal_pow @ V7) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))) @ ((creal_add @ ((creal_sub @ ((creal_sub @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_div @ ((creal_pow @ V7) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_pow @ V8) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2))) @ ((creal_div @ ((creal_sub @ ((creal_sub @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ V7) @ V2))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ V3))) @ ((creal_pow @ V7) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V8)))))) @ ((c= @ ((creal_pow @ V9) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (((cCOND @ ((c= @ V8) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_sub @ ((creal_sub @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_div @ ((creal_pow @ V7) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))) @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_div @ ((creal_pow @ V7) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_pow @ V8) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2))) @ ((creal_div @ ((creal_sub @ ((creal_sub @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ V7) @ V2))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ V3))) @ ((creal_pow @ V7) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V8)))))))))) @ ((c= @ ((c= @ ((creal_add @ ((creal_pow @ V6) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V7) @ ((creal_pow @ V6) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V2) @ ((creal_pow @ V6) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V3) @ V6)) @ V4))))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V6) @ ((creal_add @ ((creal_div @ (creal_neg @ V7)) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_add @ ((creal_div @ V8) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_div @ V5) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((c__caret__/ @ ((c= @ V6) @ ((creal_add @ ((creal_div @ (creal_neg @ V7)) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_sub @ ((creal_div @ V8) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_div @ V5) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((c__caret__/ @ ((c= @ V6) @ ((creal_add @ ((creal_sub @ ((creal_div @ (creal_neg @ V7)) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_div @ V8) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_div @ V9) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((c= @ V6) @ ((creal_sub @ ((creal_sub @ ((creal_div @ (creal_neg @ V7)) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_div @ V8) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_div @ V9) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))))))))))))))))))))
(TSTEP_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ (c! @ (^[V8]: (V4 @ (creal_of_num @ V8))))) @ ((c/__caret__ @ (c! @ (^[V8]: ((c==> @ (V4 @ V8)) @ (V4 @ (creal_neg @ V8)))))) @ ((c/__caret__ @ (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ (V4 @ V8)) @ (c~ @ ((c= @ V8) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ (V4 @ (creal_inv @ V8)))))) @ ((c/__caret__ @ (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ (V4 @ V8)) @ (V4 @ V9))) @ (V4 @ ((creal_add @ V8) @ V9)))))))) @ (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ (V4 @ V8)) @ (V4 @ V9))) @ (V4 @ ((creal_mul @ V8) @ V9)))))))))))) @ ((c==> @ ((c/__caret__ @ (V4 @ V5)) @ ((c/__caret__ @ (V4 @ V6)) @ ((c/__caret__ @ (V4 @ V7)) @ ((c/__caret__ @ ((c= @ ((creal_add @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ V5) @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V6) @ V0)) @ V7)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (V4 @ V1)) @ ((c/__caret__ @ (V4 @ V2)) @ ((c/__caret__ @ (V4 @ ((creal_mul @ V3) @ V3))) @ ((c= @ V0) @ ((creal_add @ V1) @ ((creal_mul @ V2) @ V3))))))))))) @ (c? @ (^[V8]: ((c/__caret__ @ (V4 @ V8)) @ ((c= @ ((creal_add @ ((creal_pow @ V8) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ V5) @ ((creal_pow @ V8) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V6) @ V8)) @ V7)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))))))))))))
(TSTEP_LEMMA_SQRT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ (c! @ (^[V8]: (V4 @ (creal_of_num @ V8))))) @ ((c/__caret__ @ (c! @ (^[V8]: ((c==> @ (V4 @ V8)) @ (V4 @ (creal_neg @ V8)))))) @ ((c/__caret__ @ (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ (V4 @ V8)) @ (c~ @ ((c= @ V8) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ (V4 @ (creal_inv @ V8)))))) @ ((c/__caret__ @ (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ (V4 @ V8)) @ (V4 @ V9))) @ (V4 @ ((creal_add @ V8) @ V9)))))))) @ (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ (V4 @ V8)) @ (V4 @ V9))) @ (V4 @ ((creal_mul @ V8) @ V9)))))))))))) @ ((c==> @ ((c/__caret__ @ (V4 @ V5)) @ ((c/__caret__ @ (V4 @ V6)) @ ((c/__caret__ @ (V4 @ V7)) @ ((c/__caret__ @ ((c= @ ((creal_add @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ V5) @ ((creal_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V6) @ V0)) @ V7)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (V4 @ V1)) @ ((c/__caret__ @ (V4 @ V2)) @ ((c/__caret__ @ (V4 @ V3)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c= @ V0) @ ((creal_add @ V1) @ ((creal_mul @ V2) @ (csqrt @ V3))))))))))))) @ (c? @ (^[V8]: ((c/__caret__ @ (V4 @ V8)) @ ((c= @ ((creal_add @ ((creal_pow @ V8) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ V5) @ ((creal_pow @ V8) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V6) @ V8)) @ V7)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))))))))))))
(TREAL_LE_SUP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ V3)) @ ((c/__caret__ @ ((creal_le @ V2) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((creal_le @ V4) @ V1))))))) @ ((creal_le @ V2) @ (csup @ V3))))))))))))
(TREAL_SUB_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c= @ ((creal_sub @ ((creal_pow @ V0) @ V2)) @ ((creal_pow @ V1) @ V2))) @ ((creal_mul @ ((creal_sub @ V0) @ V1)) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (^[V3]: ((creal_mul @ ((creal_pow @ V0) @ V3)) @ ((creal_pow @ V1) @ ((c- @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3)))))))))))))))
(TREAL_POW_LT2_ODD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_lt @ V0) @ V1)) @ (cODD @ V2))) @ ((creal_lt @ ((creal_pow @ V0) @ V2)) @ ((creal_pow @ V1) @ V2))))))))))
(TPOW_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_le @ V0) @ V1))) @ ((creal_le @ ((creal_pow @ V0) @ V2)) @ ((creal_pow @ V1) @ V2))))))))))
(TREAL_POW_LE2_ODD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_le @ V0) @ V1)) @ (cODD @ V2))) @ ((creal_le @ ((creal_pow @ V0) @ V2)) @ ((creal_pow @ V1) @ V2))))))))))
(TREAL_POW_LT2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_lt @ V0) @ V1)))) @ ((creal_lt @ ((creal_pow @ V0) @ V2)) @ ((creal_pow @ V1) @ V2))))))))))
(TPOWDIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_sub @ ((creal_pow @ V0) @ (cSUC @ V2))) @ ((creal_pow @ V1) @ (cSUC @ V2)))) @ ((creal_mul @ ((creal_sub @ V0) @ V1)) @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ (cSUC @ V2))) @ (^[V3]: ((creal_mul @ ((creal_pow @ V0) @ V3)) @ ((creal_pow @ V1) @ ((c- @ V2) @ V3))))))))))))))
(TPOW_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_pow @ ((creal_mul @ V0) @ V1)) @ V2)) @ ((creal_mul @ ((creal_pow @ V0) @ V2)) @ ((creal_pow @ V1) @ V2))))))))))
(TREAL_POW_DIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_pow @ ((creal_div @ V0) @ V1)) @ V2)) @ ((creal_div @ ((creal_pow @ V0) @ V2)) @ ((creal_pow @ V1) @ V2))))))))))
(TPOWDIFF_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ (cSUC @ V2))) @ (^[V3]: ((creal_mul @ ((creal_pow @ V0) @ V3)) @ ((creal_pow @ V1) @ ((c- @ (cSUC @ V2)) @ V3)))))) @ ((creal_mul @ V1) @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ (cSUC @ V2))) @ (^[V3]: ((creal_mul @ ((creal_pow @ V0) @ V3)) @ ((creal_pow @ V1) @ ((c- @ V2) @ V3))))))))))))))
(TPOLY_CMUL_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpoly_cmul @ V1) @ ((cCONS @ V0) @ V2))) @ ((cCONS @ ((creal_mul @ V1) @ V0)) @ ((cpoly_cmul @ V1) @ V2))))))))))
(TPOLY_MUL_CLAUSES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cpoly_mul @ ((cCONS @ V0) @ ((cCONS @ V1) @ V2))) @ V3)) @ ((cpoly_add @ ((cpoly_cmul @ V0) @ V3)) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cpoly_mul @ ((cCONS @ V1) @ V2)) @ V3)))))))))))))
(TPOLY_ADD_CLAUSES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cpoly_add @ ((cCONS @ V0) @ V2)) @ ((cCONS @ V1) @ V3))) @ ((cCONS @ ((creal_add @ V0) @ V1)) @ ((cpoly_add @ V2) @ V3))))))))))))
(TREAL_SUP_BOUNDS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ ((creal_le @ V1) @ V3)) @ ((creal_le @ V3) @ V0))))))) @ ((creal_le @ V1) @ (csup @ V2))))))))))
(TREAL_INF_BOUNDS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ ((creal_le @ V1) @ V3)) @ ((creal_le @ V3) @ V0))))))) @ ((creal_le @ V1) @ (cinf @ V2))))))))))
(TREAL_INF_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((c/__caret__ @ ((creal_le @ V0) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((creal_le @ V1) @ V4))))))) @ ((creal_le @ (cinf @ V2)) @ V3)))))))))))
(TCONNECTED_REAL_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_le @ V0) @ V1)) @ ((c/__caret__ @ ((cIN @ (V3 @ V0)) @ V2)) @ ((c/__caret__ @ ((cIN @ (V3 @ V1)) @ V4)) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((creal_le @ V0) @ V6)) @ ((c/__caret__ @ ((creal_le @ V6) @ V1)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)))) @ (c? @ (^[V7]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V7)) @ (c! @ (^[V8]: ((c==> @ ((creal_lt @ (creal_abs @ ((creal_sub @ V8) @ V6))) @ V7)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V3 @ V8)) @ (V3 @ V6)))) @ V5))))))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ (c? @ (^[V6]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V6)) @ (c! @ (^[V7]: ((c==> @ ((creal_lt @ (cdistance @ ((c__comma__ @ V7) @ V5))) @ V6)) @ ((cIN @ V7) @ V2))))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V4)) @ (c? @ (^[V6]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V6)) @ (c! @ (^[V7]: ((c==> @ ((creal_lt @ (cdistance @ ((c__comma__ @ V7) @ V5))) @ V6)) @ ((cIN @ V7) @ V4))))))))))) @ (c~ @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_le @ V0) @ V5)) @ ((c/__caret__ @ ((creal_le @ V5) @ V1)) @ ((c/__caret__ @ ((cIN @ (V3 @ V5)) @ V2)) @ ((cIN @ (V3 @ V5)) @ V4)))))))))))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_le @ V0) @ V5)) @ ((c/__caret__ @ ((creal_le @ V5) @ V1)) @ ((c/__caret__ @ (c~ @ ((cIN @ (V3 @ V5)) @ V2))) @ (c~ @ ((cIN @ (V3 @ V5)) @ V4)))))))))))))))))))
(TUNIFORM_LIM_BILINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ (cbilinear @ V5)) @ ((c/__caret__ @ ((ceventually @ (^[V10]: (c! @ (^[V11]: ((c==> @ (V2 @ V11)) @ ((creal_le @ (cvector_norm @ (V6 @ V11))) @ V0)))))) @ V9)) @ ((c/__caret__ @ ((ceventually @ (^[V10]: (c! @ (^[V11]: ((c==> @ (V2 @ V11)) @ ((creal_le @ (cvector_norm @ (V7 @ V11))) @ V1)))))) @ V9)) @ ((c/__caret__ @ (c! @ (^[V10]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V10)) @ ((ceventually @ (^[V11]: (c! @ (^[V12]: ((c==> @ (V2 @ V12)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((V3 @ V12) @ V11)) @ (V6 @ V12)))) @ V10)))))) @ V9))))) @ (c! @ (^[V10]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V10)) @ ((ceventually @ (^[V11]: (c! @ (^[V12]: ((c==> @ (V2 @ V12)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((V4 @ V12) @ V11)) @ (V7 @ V12)))) @ V10)))))) @ V9))))))))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V8)) @ ((ceventually @ (^[V10]: (c! @ (^[V11]: ((c==> @ (V2 @ V11)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((V5 @ ((V3 @ V11) @ V10)) @ ((V4 @ V11) @ V10))) @ ((V5 @ (V6 @ V11)) @ (V7 @ V11))))) @ V8)))))) @ V9))))))))))))))))))))))))
(TSEGMENT_SCALAR_MULTIPLE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ (copen_segment @ ((c__comma__ @ ((c% @ V0) @ V2)) @ ((c% @ V1) @ V2)))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c__caret__/ @ ((c/__caret__ @ ((creal_lt @ V0) @ V4)) @ ((creal_lt @ V4) @ V1))) @ ((c/__caret__ @ ((creal_lt @ V1) @ V4)) @ ((creal_lt @ V4) @ V0)))) @ ((c% @ V4) @ V2)))))))))))))))
(TSEGMENT_SCALAR_MULTIPLE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ ((c% @ V0) @ V2)) @ ((c% @ V1) @ V2))) @ cNIL))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c__caret__/ @ ((c/__caret__ @ ((creal_le @ V0) @ V4)) @ ((creal_le @ V4) @ V1))) @ ((c/__caret__ @ ((creal_le @ V1) @ V4)) @ ((creal_le @ V4) @ V0)))) @ ((c% @ V4) @ V2))))))))))))))
(TREAL_LE_HAUSDIST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V4) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V5) @ cEMPTY))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V4)) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V6) @ cEMPTY)) @ V5))) @ V0))))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V5)) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V6) @ cEMPTY)) @ V4))) @ V1))))) @ ((c__caret__/ @ ((c/__caret__ @ ((cIN @ V2) @ V4)) @ ((creal_le @ V3) @ (csetdist @ ((c__comma__ @ ((cINSERT @ V2) @ cEMPTY)) @ V5))))) @ ((c/__caret__ @ ((cIN @ V2) @ V5)) @ ((creal_le @ V3) @ (csetdist @ ((c__comma__ @ ((cINSERT @ V2) @ cEMPTY)) @ V4)))))))))) @ ((creal_le @ V3) @ (chausdist @ ((c__comma__ @ V4) @ V5)))))))))))))))))
(TNORM_CROSS_MULTIPLY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ ((c% @ V0) @ V2)) @ ((c% @ V1) @ V3))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)))) @ ((c= @ ((c% @ (cvector_norm @ V3)) @ V2)) @ ((c% @ (cvector_norm @ V2)) @ V3))))))))))))
(TVECTOR_MUL_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((c% @ V0) @ V2)) @ ((c% @ V1) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))))))))))
(TVECTOR_SUB_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c% @ ((creal_sub @ V0) @ V1)) @ V2)) @ ((cvector_sub @ ((c% @ V0) @ V2)) @ ((c% @ V1) @ V2))))))))))
(TVECTOR_ADD_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c% @ ((creal_add @ V0) @ V1)) @ V2)) @ ((cvector_add @ ((c% @ V0) @ V2)) @ ((c% @ V1) @ V2))))))))))
(TVECTOR_MUL_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c% @ V0) @ ((c% @ V1) @ V2))) @ ((c% @ ((creal_mul @ V0) @ V1)) @ V2)))))))))
(TMATRIX_CMUL_SUB_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c%% @ ((creal_sub @ V0) @ V1)) @ V2)) @ ((cmatrix_sub @ ((c%% @ V0) @ V2)) @ ((c%% @ V1) @ V2))))))))))
(TMATRIX_CMUL_ADD_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c%% @ ((creal_add @ V0) @ V1)) @ V2)) @ ((cmatrix_add @ ((c%% @ V0) @ V2)) @ ((c%% @ V1) @ V2))))))))))
(TMATRIX_CMUL_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c%% @ V0) @ ((c%% @ V1) @ V2))) @ ((c%% @ ((creal_mul @ V0) @ V1)) @ V2)))))))))
(TPOW_POS_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_pow @ V0) @ (cSUC @ V1)))))))))
(TREAL_POW_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_pow @ V0) @ V1))))))))
(TPOW_PLUS1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_le @ ((creal_add @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ (creal_of_num @ V1)) @ V0))) @ ((creal_pow @ ((creal_add @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ V1))))))))
(TREAL_POW_LE_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_pow @ V0) @ V1))))))))
(TREAL_POW_LBOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_le @ ((creal_add @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ (creal_of_num @ V1)) @ V0))) @ ((creal_pow @ ((creal_add @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ V1))))))))
(TPOW_POS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_pow @ V0) @ V1))))))))
(TLEMMA_2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_add @ ((creal_sub @ ((creal_pow @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_add @ (creal_of_num @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0))) @ (creal_of_num @ V1)))))))))
(TREAL_POW_1_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_le @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((creal_le @ ((creal_pow @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TREAL_POS_ABS_MIDDLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ (creal_abs @ ((creal_sub @ V0) @ (creal_of_num @ V1)))) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((c__caret__/ @ ((c= @ V0) @ ((creal_add @ (creal_of_num @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((c= @ V0) @ ((creal_add @ (creal_of_num @ V1)) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))))
(TREAL_POW_LT_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_pow @ V0) @ V1))))))))
(TREAL_POW_1_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_lt @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((creal_lt @ ((creal_pow @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TPOW_INV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (creal_inv @ ((creal_pow @ V0) @ V1))) @ ((creal_pow @ (creal_inv @ V0)) @ V1))))))))
(TPOW_NZ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ (c~ @ ((c= @ ((creal_pow @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))
(TRATIONAL_POW,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (crational @ V0)) @ (crational @ ((creal_pow @ V0) @ V1))))))))
(TRADICAL_RULES_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cradical @ V0)) @ (cradical @ ((creal_pow @ V0) @ V1))))))))
(TINTEGER_POW,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cinteger @ V0)) @ (cinteger @ ((creal_pow @ V0) @ V1))))))))
(TREAL_INTEGER_CLOSURES_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c? @ (^[V2]: ((c= @ (creal_abs @ V0)) @ (creal_of_num @ V2))))) @ (c? @ (^[V2]: ((c= @ (creal_abs @ ((creal_pow @ V0) @ V1))) @ (creal_of_num @ V2))))))))))
(TREAL_POW_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_pow @ (creal_neg @ V0)) @ V1)) @ (((cCOND @ (cEVEN @ V1)) @ ((creal_pow @ V0) @ V1)) @ (creal_neg @ ((creal_pow @ V0) @ V1)))))))))
(TREAL_POW_INV,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_pow @ (creal_inv @ V0)) @ V1)) @ (creal_inv @ ((creal_pow @ V0) @ V1))))))))
(TPOW_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_pow @ (creal_abs @ V0)) @ V1)) @ (creal_abs @ ((creal_pow @ V0) @ V1))))))))
(TREAL_POLY_CLAUSES_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_pow @ V0) @ (cSUC @ V1))) @ ((creal_mul @ V0) @ ((creal_pow @ V0) @ V1))))))))
(TSUM_GP_BASIC,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_mul @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V1)) @ (^[V2]: ((creal_pow @ V0) @ V2))))) @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_pow @ V0) @ (cSUC @ V1)))))))))
(TLEMMA_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_add @ ((creal_sub @ ((creal_pow @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_add @ (creal_of_num @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0))) @ (creal_of_num @ V1))) @ ((creal_mul @ ((creal_pow @ ((creal_sub @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ (^[V2]: ((creal_mul @ (creal_of_num @ V2)) @ ((creal_pow @ V0) @ ((c- @ V1) @ V2))))))))))))
(TPRODUCT_CONST_NUMSEG_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ (^[V2]: V0))) @ ((creal_pow @ V0) @ V1)))))))
(TREAL_INV_POW,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (creal_inv @ ((creal_pow @ V0) @ V1))) @ ((creal_pow @ (creal_inv @ V0)) @ V1)))))))
(TREAL_ABS_POW,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (creal_abs @ ((creal_pow @ V0) @ V1))) @ ((creal_pow @ (creal_abs @ V0)) @ V1)))))))
(TREAL_POW_EQ_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((creal_pow @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ (creal_abs @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c==> @ ((creal_lt @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (cEVEN @ V1)))) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
(TREAL_POW_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((creal_pow @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0))))))))))
(TPOLYFUN_N_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: ((c= @ V0) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V1)) @ (^[V4]: ((creal_mul @ (V2 @ V4)) @ ((creal_pow @ V3) @ V4))))))))))))))
(TPOWREV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ (cSUC @ V1))) @ (^[V3]: ((creal_mul @ ((creal_pow @ V0) @ V3)) @ ((creal_pow @ V2) @ ((c- @ V1) @ V3)))))) @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ (cSUC @ V1))) @ (^[V3]: ((creal_mul @ ((creal_pow @ V0) @ ((c- @ V1) @ V3))) @ ((creal_pow @ V2) @ V3))))))))))))
(TREAL_DIV_POW2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((creal_div @ ((creal_pow @ V0) @ V2)) @ ((creal_pow @ V0) @ V1))) @ (((cCOND @ ((c<= @ V1) @ V2)) @ ((creal_pow @ V0) @ ((c- @ V2) @ V1))) @ (creal_inv @ ((creal_pow @ V0) @ ((c- @ V1) @ V2)))))))))))))
(TREAL_DIV_POW2_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((creal_div @ ((creal_pow @ V0) @ V2)) @ ((creal_pow @ V0) @ V1))) @ (((cCOND @ ((c< @ V1) @ V2)) @ ((creal_pow @ V0) @ ((c- @ V2) @ V1))) @ (creal_inv @ ((creal_pow @ V0) @ ((c- @ V1) @ V2)))))))))))))
(TREAL_POW_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_pow @ ((creal_pow @ V0) @ V1)) @ V2)) @ ((creal_pow @ V0) @ ((c* @ V1) @ V2))))))))))
(TPRODUCT_CONST_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cproduct @ ((c.. @ V2) @ V1)) @ (^[V3]: V0))) @ ((creal_pow @ V0) @ ((c- @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2))))))))))
(TSUM_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cpsum @ ((c__comma__ @ V1) @ V2)) @ (^[V4]: ((creal_mul @ V0) @ (V3 @ V4))))) @ ((creal_mul @ V0) @ ((cpsum @ ((c__comma__ @ V1) @ V2)) @ V3))))))))))))
(TVSUM_CMUL_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cvsum @ ((c.. @ V1) @ V2)) @ (^[V4]: ((c% @ V0) @ (V3 @ V4))))) @ ((c% @ V0) @ ((cvsum @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(Tpoly_diff_aux_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpoly_diff_aux @ V1) @ ((cCONS @ V0) @ V2))) @ ((cCONS @ ((creal_mul @ (creal_of_num @ V1)) @ V0)) @ ((cpoly_diff_aux @ (cSUC @ V1)) @ V2))))))))))
(TREAL_POLYFUN_EQ_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c= @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V1)) @ (^[V4]: ((creal_mul @ (V2 @ V4)) @ ((creal_pow @ V3) @ V4))))) @ V0)))) @ ((c/__caret__ @ ((c= @ (V2 @ (cNUMERAL @ c_0))) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1))) @ ((c= @ (V2 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))
(TEQUIINTEGRABLE_ON_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cequiintegrable_on @ V2) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((c$ @ V6) @ V1)) @ V0)) @ V6)))))))) @ ((c/__caret__ @ ((cequiintegrable_on @ V2) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_ge @ ((c$ @ V6) @ V1)) @ V0)) @ V6)))))))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))))) @ ((cequiintegrable_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))
(THAS_INTEGRAL_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V2) @ V3) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL))) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_le @ ((c$ @ V8) @ V1)) @ V0)) @ V8)))))))) @ ((c/__caret__ @ (((chas_integral @ V2) @ V4) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL))) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_ge @ ((c$ @ V8) @ V1)) @ V0)) @ V8)))))))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))))) @ (((chas_integral @ V2) @ ((cvector_add @ V3) @ V4)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL)))))))))))))))))))
(TGRADE_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cgrade @ V1) @ ((c% @ V0) @ V2))) @ ((c% @ V0) @ ((cgrade @ V1) @ V2))))))))))
(TDET_ROW_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdet @ (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V1)) @ ((c% @ V0) @ V2)) @ (V3 @ V4)))))) @ ((creal_mul @ V0) @ (cdet @ (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V1)) @ V2) @ (V3 @ V4)))))))))))))))))
(TPOLY_MUL_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpoly_mul @ ((cCONS @ V0) @ cNIL)) @ V1)) @ ((cpoly_cmul @ V0) @ V1)))))))
(TPOLY_NEG_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpoly_neg @ ((cCONS @ V0) @ V1))) @ ((cCONS @ (creal_neg @ V0)) @ (cpoly_neg @ V1))))))))
(TPOLY_DIFF_CLAUSES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpoly_diff @ ((cCONS @ V0) @ V1))) @ ((cpoly_diff_aux @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)))))))
(TPROFORMA_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((cALL @ (^[V3]: ((creal_lt @ V3) @ V2))) @ ((cCONS @ V0) @ V1))))) @ cT))))))
(TPROFORMA_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((cALL @ (^[V3]: ((creal_lt @ V2) @ V3))) @ ((cCONS @ V0) @ V1))))) @ cT))))))
(TPOLY_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpoly @ ((cpoly_cmul @ V0) @ V1)) @ V2)) @ ((creal_mul @ V0) @ ((cpoly @ V1) @ V2))))))))))
(Tpoly_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpoly @ ((cCONS @ V0) @ V1)) @ V2)) @ ((creal_add @ V0) @ ((creal_mul @ V2) @ ((cpoly @ V1) @ V2)))))))))))
(TMINL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMINL @ ((cCONS @ V0) @ V1)) @ V2)) @ ((creal_min @ V0) @ ((cMINL @ V1) @ V2))))))))))
(TMAXL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMAXL @ ((cCONS @ V0) @ V1)) @ V2)) @ ((creal_max @ V0) @ ((cMAXL @ V1) @ V2))))))))))
(TALL_GT_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cALL @ (^[V3]: ((creal_lt @ V0) @ V3))) @ ((cCONS @ V2) @ V1))) @ ((creal_lt @ V0) @ ((cMINL @ V1) @ V2))))))))))
(TPROFORMA_BOTH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (c? @ (^[V4]: ((c/__caret__ @ ((cALL @ (^[V5]: ((creal_lt @ V5) @ V4))) @ ((cCONS @ V2) @ V3))) @ ((cALL @ (^[V5]: ((creal_lt @ V4) @ V5))) @ ((cCONS @ V0) @ V1)))))) @ ((cALL @ (^[V4]: ((cALL @ (^[V5]: ((creal_lt @ V4) @ V5))) @ ((cCONS @ V0) @ V1)))) @ ((cCONS @ V2) @ V3))))))))))))
(Tpoly_mul_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpoly_mul @ ((cCONS @ V0) @ V1)) @ V2)) @ (((cCOND @ ((c= @ V1) @ cNIL)) @ ((cpoly_cmul @ V0) @ V2)) @ ((cpoly_add @ ((cpoly_cmul @ V0) @ V2)) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cpoly_mul @ V1) @ V2))))))))))))
(Tpoly_add_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpoly_add @ ((cCONS @ V0) @ V1)) @ V2)) @ (((cCOND @ ((c= @ V2) @ cNIL)) @ ((cCONS @ V0) @ V1)) @ ((cCONS @ ((creal_add @ V0) @ (cHD @ V2))) @ ((cpoly_add @ V1) @ (cTL @ V2))))))))))))
(TPOLYFUN_N_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c? @ (^[V3]: (c! @ (^[V4]: ((c= @ (V1 @ V4)) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V5]: ((creal_mul @ (V3 @ V5)) @ ((creal_pow @ V4) @ V5)))))))))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c= @ ((creal_mul @ V0) @ (V1 @ V4))) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V5]: ((creal_mul @ (V3 @ V5)) @ ((creal_pow @ V4) @ V5)))))))))))))))))
(TREAL_LE_INF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((creal_le @ V0) @ V2)))))) @ ((creal_le @ V0) @ (cinf @ V1))))))))
(TREAL_SUP_UBOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c? @ (^[V2]: (V1 @ V2)))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ ((creal_lt @ V3) @ V2)))))))) @ ((c==> @ (V1 @ V0)) @ ((creal_le @ V0) @ (csup @ V1)))))))))
(TREAL_SUP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c? @ (^[V2]: (V1 @ V2)))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ ((creal_lt @ V3) @ V2)))))))) @ ((c= @ (c? @ (^[V2]: ((c/__caret__ @ (V1 @ V2)) @ ((creal_lt @ V0) @ V2))))) @ ((creal_lt @ V0) @ (csup @ V1)))))))))
(TREAL_SUP_UBOUND_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c? @ (^[V2]: (V1 @ V2)))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ ((creal_le @ V3) @ V2)))))))) @ ((c==> @ (V1 @ V0)) @ ((creal_le @ V0) @ (csup @ V1)))))))))
(TREAL_SUP_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c? @ (^[V2]: (V1 @ V2)))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ ((creal_le @ V3) @ V2)))))))) @ ((c= @ (c? @ (^[V2]: ((c/__caret__ @ (V1 @ V2)) @ ((creal_lt @ V0) @ V2))))) @ ((creal_lt @ V0) @ (csup @ V1)))))))))
(TSUP_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cbounded @ ((cIMAGE @ clift) @ V1))) @ ((c= @ (csup @ ((cINSERT @ V0) @ V1))) @ (((cCOND @ ((c= @ V1) @ cEMPTY)) @ V0) @ ((creal_max @ V0) @ (csup @ V1))))))))))
(TINF_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cbounded @ ((cIMAGE @ clift) @ V1))) @ ((c= @ (cinf @ ((cINSERT @ V0) @ V1))) @ (((cCOND @ ((c= @ V1) @ cEMPTY)) @ V0) @ ((creal_min @ V0) @ (cinf @ V1))))))))))
(TSUP_INSERT_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ ((c= @ (csup @ ((cINSERT @ V0) @ V1))) @ (((cCOND @ ((c= @ V1) @ cEMPTY)) @ V0) @ ((creal_max @ V0) @ (csup @ V1))))))))))
(TINF_INSERT_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ ((c= @ (cinf @ ((cINSERT @ V0) @ V1))) @ (((cCOND @ ((c= @ V1) @ cEMPTY)) @ V0) @ ((creal_min @ V0) @ (cinf @ V1))))))))))
(TLIFT_IN_IMAGE_LIFT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ (clift @ V0)) @ ((cIMAGE @ clift) @ V1))) @ ((cIN @ V0) @ V1)))))))
(TREAL_SUP_BOUNDS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((creal_le @ V0) @ V3)) @ ((creal_le @ V3) @ V2))))))) @ ((creal_le @ (csup @ V1)) @ V2)))))))))
(TREAL_INF_BOUNDS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((creal_le @ V0) @ V3)) @ ((creal_le @ V3) @ V2))))))) @ ((creal_le @ (cinf @ V1)) @ V2)))))))))
(TCONVERGENT_BOUNDED_MONOTONE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((creal_le @ (creal_abs @ (V1 @ V2))) @ V0)))) @ ((c__caret__/ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V2) @ V3)) @ ((creal_le @ (V1 @ V2)) @ (V1 @ V3)))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V2) @ V3)) @ ((creal_le @ (V1 @ V3)) @ (V1 @ V2)))))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c<= @ V4) @ V5)) @ ((creal_lt @ (creal_abs @ ((creal_sub @ (V1 @ V5)) @ V2))) @ V3)))))))))))))))))
(TCONVERGENT_BOUNDED_INCREASING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V2) @ V3)) @ ((creal_le @ (V1 @ V2)) @ (V1 @ V3)))))))) @ (c! @ (^[V2]: ((creal_le @ (creal_abs @ (V1 @ V2))) @ V0))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c<= @ V4) @ V5)) @ ((creal_lt @ (creal_abs @ ((creal_sub @ (V1 @ V5)) @ V2))) @ V3)))))))))))))))))
(TCOMPACT_REAL_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((creal_le @ (creal_abs @ (V1 @ V2))) @ V0)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c< @ V4) @ V5)) @ ((c< @ (V3 @ V4)) @ (V3 @ V5)))))))) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c<= @ V5) @ V6)) @ ((creal_lt @ (creal_abs @ ((creal_sub @ (V1 @ (V3 @ V6))) @ V2))) @ V4))))))))))))))))))))
(THAS_MEASURE_NESTED_UNIONS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (cmeasurable @ (V1 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((creal_le @ (cmeasure @ (V1 @ V2))) @ V0)))) @ (c! @ (^[V2]: ((cSUBSET @ (V1 @ V2)) @ (V1 @ (cSUC @ V2)))))))) @ (((c--> @ (^[V2]: (clift @ (cmeasure @ (V1 @ V2))))) @ (clift @ (cmeasure @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (V1 @ V3)))))))))) @ csequentially)))))))
(TMEASURABLE_NESTED_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (cmeasurable @ (V1 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((creal_le @ (cmeasure @ (V1 @ V2))) @ V0)))) @ (c! @ (^[V2]: ((cSUBSET @ (V1 @ V2)) @ (V1 @ (cSUC @ V2)))))))) @ (cmeasurable @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (V1 @ V3))))))))))))))
(THAS_MEASURE_COUNTABLE_NEGLIGIBLE_UNIONS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (cmeasurable @ (V1 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c~ @ ((c= @ V2) @ V3))) @ (cnegligible @ ((cINTER @ (V1 @ V2)) @ (V1 @ V3))))))))) @ (c! @ (^[V2]: ((creal_le @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V3]: (cmeasure @ (V1 @ V3))))) @ V0)))))) @ (((csums @ (^[V2]: (clift @ (cmeasure @ (V1 @ V2))))) @ (clift @ (cmeasure @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (V1 @ V3)))))))))) @ (cfrom @ (cNUMERAL @ c_0)))))))))
(THAS_MEASURE_COUNTABLE_NEGLIGIBLE_UNIONS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (cmeasurable @ (V1 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c~ @ ((c= @ V2) @ V3))) @ (cnegligible @ ((cINTER @ (V1 @ V2)) @ (V1 @ V3))))))))) @ (c! @ (^[V2]: ((creal_le @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V3]: (cmeasure @ (V1 @ V3))))) @ V0)))))) @ (cmeasurable @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (V1 @ V3))))))))))))))
(TMEASURABLE_COUNTABLE_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (cmeasurable @ (V1 @ V2))))) @ (c! @ (^[V2]: ((creal_le @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V3]: (cmeasure @ (V1 @ V3))))) @ V0))))) @ (cmeasurable @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (V1 @ V3))))))))))))))
(TMEASURABLE_COUNTABLE_UNIONS_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (cmeasurable @ (V1 @ V2))))) @ (c! @ (^[V2]: ((creal_le @ (cmeasure @ (cUNIONS @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c<= @ V4) @ V2)) @ (V1 @ V4))))))))) @ V0))))) @ (cmeasurable @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (V1 @ V3))))))))))))))
(TSCHNIRELMANN_LBOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((creal_le @ V0) @ ((creal_div @ (creal_of_num @ ((ccount @ V1) @ V2))) @ (creal_of_num @ V2))))))) @ ((creal_le @ V0) @ (cschnirelmann @ V1))))))))
(TINFSUM_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((csummable @ V1) @ V2)) @ ((c= @ ((cinfsum @ V1) @ (^[V3]: ((c% @ V0) @ (V2 @ V3))))) @ ((c% @ V0) @ ((cinfsum @ V1) @ V2)))))))))))
(TPRODUCT_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((((cProduct @ V1) @ V2) @ ((c% @ V0) @ V3)) @ V4)) @ ((c% @ V0) @ ((((cProduct @ V1) @ V2) @ V3) @ V4))))))))))))))
(TPRODUCT_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((((cProduct @ V1) @ V2) @ V3) @ ((c% @ V0) @ V4))) @ ((c% @ V0) @ ((((cProduct @ V1) @ V2) @ V3) @ V4))))))))))))))
(TMEASURE_COUNTABLE_UNIONS_LE_GEN_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (cmeasurable @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ (cFINITE @ V2))) @ ((creal_le @ ((csum @ V2) @ (^[V3]: (cmeasure @ V3)))) @ V0))))))) @ (cmeasurable @ (cUNIONS @ V1))))))))
(TMEASURE_COUNTABLE_UNIONS_LE_STRONG_GEN_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (cmeasurable @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ (cFINITE @ V2))) @ ((creal_le @ (cmeasure @ (cUNIONS @ V2))) @ V0))))))) @ (cmeasurable @ (cUNIONS @ V1))))))))
(TMEASURE_COUNTABLE_UNIONS_APPROACHABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (cmeasurable @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V1)) @ (cFINITE @ V3))) @ ((creal_le @ (cmeasure @ (cUNIONS @ V3))) @ V0))))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ V1)) @ ((c/__caret__ @ (cFINITE @ V3)) @ ((creal_lt @ ((creal_sub @ (cmeasure @ (cUNIONS @ V1))) @ V2)) @ (cmeasure @ (cUNIONS @ V3)))))))))))))))
(TCELL_COMPLEX_SUBDIVISION_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (cpolytope @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cint_le @ (caff_dim @ V3)) @ V2))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((cIN @ V4) @ V1))) @ ((c/__caret__ @ ((cface_of @ ((cINTER @ V3) @ V4)) @ V3)) @ ((cface_of @ ((cINTER @ V3) @ V4)) @ V4)))))))))))) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((creal_lt @ (cdiameter @ V4)) @ V0))))) @ ((c/__caret__ @ ((c= @ (cUNIONS @ V3)) @ (cUNIONS @ V1))) @ ((c/__caret__ @ (cFINITE @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ (cpolytope @ V4))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((cint_le @ (caff_dim @ V4)) @ V2))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V3)) @ ((cIN @ V5) @ V3))) @ ((c/__caret__ @ ((cface_of @ ((cINTER @ V4) @ V5)) @ V4)) @ ((cface_of @ ((cINTER @ V4) @ V5)) @ V5))))))))))))))))))))))
(TEQUIINTEGRABLE_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cequiintegrable_on @ V1) @ V2)) @ ((cequiintegrable_on @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((creal_le @ (creal_abs @ V4)) @ V0)) @ ((cIN @ V5) @ V1))) @ (^[V6]: ((c% @ V4) @ (V5 @ V6))))))))))) @ V2)))))))))
(THAS_BOUNDED_SETVARIATION_ON_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chas_bounded_setvariation_on @ V1) @ V2)) @ ((chas_bounded_setvariation_on @ (^[V3]: ((c% @ V0) @ (V1 @ V3)))) @ V2)))))))))
(TINTEGRABLE_DECREASING_PRODUCT_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V2) @ cUNIV)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))) @ ((creal_le @ (V1 @ V4)) @ (V1 @ V3)))))))) @ (c! @ (^[V3]: ((creal_le @ (creal_abs @ (V1 @ V3))) @ V0)))))) @ ((cintegrable_on @ (^[V3]: ((c% @ (V1 @ V3)) @ (V2 @ V3)))) @ cUNIV)))))))))
(TINTEGRABLE_INCREASING_PRODUCT_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V2) @ cUNIV)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))) @ ((creal_le @ (V1 @ V3)) @ (V1 @ V4)))))))) @ (c! @ (^[V3]: ((creal_le @ (creal_abs @ (V1 @ V3))) @ V0)))))) @ ((cintegrable_on @ (^[V3]: ((c% @ (V1 @ V3)) @ (V2 @ V3)))) @ cUNIV)))))))))
(TCONTINUOUS_ON_CASES_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V3)) @ ((creal_le @ (cdrop @ V5)) @ V0))) @ V5))))))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V3)) @ ((creal_le @ V0) @ (cdrop @ V5)))) @ V5))))))) @ ((c==> @ ((cIN @ (clift @ V0)) @ V3)) @ ((c= @ (V1 @ (clift @ V0))) @ (V2 @ (clift @ V0))))))) @ ((ccontinuous_on @ (^[V4]: (((cCOND @ ((creal_le @ (cdrop @ V4)) @ V0)) @ (V1 @ V4)) @ (V2 @ V4)))) @ V3)))))))))))
(THAS_BOUNDED_VARIATION_ON_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chas_bounded_variation_on @ V1) @ V2)) @ ((chas_bounded_variation_on @ (^[V3]: ((c% @ V0) @ (V1 @ V3)))) @ V2)))))))))
(THAS_VECTOR_DERIVATIVE_TRANSFORM_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((creal_lt @ (cdistance @ ((c__comma__ @ V5) @ V4))) @ V0)) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))) @ (((chas_vector_derivative @ V1) @ V3) @ (cat @ V4))))) @ (((chas_vector_derivative @ V2) @ V3) @ (cat @ V4))))))))))))))
(THAS_VECTOR_DERIVATIVE_TRANSFORM_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V5)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V5)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V6) @ V4))) @ V0))) @ ((c= @ (V1 @ V6)) @ (V2 @ V6)))))) @ (((chas_vector_derivative @ V1) @ V3) @ ((cwithin @ (cat @ V4)) @ V5)))))) @ (((chas_vector_derivative @ V2) @ V3) @ ((cwithin @ (cat @ V4)) @ V5))))))))))))))))
(THAS_VECTOR_DERIVATIVE_CMUL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (((chas_vector_derivative @ (^[V4]: ((c% @ V0) @ (V1 @ V4)))) @ ((c% @ V0) @ V2)) @ V3)) @ (((chas_vector_derivative @ V1) @ V2) @ V3))))))))))))
(TIN_IMAGE_LIFT_DROP_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ ((cIMAGE @ cdrop) @ V1))) @ ((cIN @ (clift @ V0)) @ V1)))))))
(TCONVEX_ON_BOUNDED_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ ((cconvex_on @ V1) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ (creal_abs @ (V1 @ V3))) @ V0))))))) @ ((ccontinuous_on @ ((co @ clift) @ V1)) @ V2)))))))))
(TDROP_DIFFERENTIAL_NEG_AT_MAXIMUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ (cconvex @ V2)) @ ((c/__caret__ @ (((chas_derivative @ V1) @ V3) @ ((cwithin @ (cat @ V5)) @ V2))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ ((cINTER @ V2) @ (cball @ ((c__comma__ @ V5) @ V0))))) @ ((creal_le @ (cdrop @ (V1 @ V6))) @ (cdrop @ (V1 @ V5))))))))))) @ ((c==> @ ((cIN @ V4) @ V2)) @ ((creal_le @ (cdrop @ (V3 @ ((cvector_sub @ V4) @ V5)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))))))))
(TDROP_DIFFERENTIAL_POS_AT_MINIMUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ (cconvex @ V2)) @ ((c/__caret__ @ (((chas_derivative @ V1) @ V3) @ ((cwithin @ (cat @ V5)) @ V2))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ ((cINTER @ V2) @ (cball @ ((c__comma__ @ V5) @ V0))))) @ ((creal_le @ (cdrop @ (V1 @ V5))) @ (cdrop @ (V1 @ V6))))))))))) @ ((c==> @ ((cIN @ V4) @ V2)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ (V3 @ ((cvector_sub @ V4) @ V5)))))))))))))))))))
(TNEGLIGIBLE_LIPSCHITZ_IMAGE_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cnegligible @ V2)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((creal_le @ (cvector_norm @ ((cvector_sub @ (V1 @ V3)) @ (V1 @ V4)))) @ ((creal_mul @ V0) @ (cvector_norm @ ((cvector_sub @ V3) @ V4)))))))))) @ (cnegligible @ ((cIMAGE @ V1) @ V2))))))))))
(TDISCRETE_BOUNDED_IMP_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V3) @ V2))) @ V0)))) @ ((c= @ V3) @ V2))))))) @ (cbounded @ V1)))) @ (cFINITE @ V1)))))))
(TDISCRETE_IMP_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V3) @ V2))) @ V0)))) @ ((c= @ V3) @ V2)))))))) @ (cclosed @ V1)))))))
(TOPEN_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ (copen @ V1))) @ (copen @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TCONVEX_INNER_POLYTOPE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V1)) @ ((c/__caret__ @ (cconvex @ V1)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ (cpolytope @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((c/__caret__ @ ((creal_lt @ (chausdist @ ((c__comma__ @ V2) @ V1))) @ V0)) @ ((c==> @ ((c= @ V2) @ cEMPTY)) @ ((c= @ V1) @ cEMPTY)))))))))))))
(TCONVEX_INNER_APPROXIMATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V1)) @ ((c/__caret__ @ (cconvex @ V1)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((chull @ cconvex) @ V2)) @ V1)) @ ((c/__caret__ @ ((creal_lt @ (chausdist @ ((c__comma__ @ ((chull @ cconvex) @ V2)) @ V1))) @ V0)) @ ((c==> @ ((c= @ V2) @ cEMPTY)) @ ((c= @ V1) @ cEMPTY)))))))))))))
(THOMEOMORPHIC_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((chomeomorphic @ V1) @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TPOLYTOPE_SCALING_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (cpolytope @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))) @ (cpolytope @ V1))))))))
(TMEASURABLE_SCALING_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (cmeasurable @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))) @ (cmeasurable @ V1))))))))
(TPOLYTOPE_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cpolytope @ V1)) @ (cpolytope @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TPATH_CONNECTED_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cpath_connected @ V1)) @ (cpath_connected @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TMEASURE_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V1)) @ ((c= @ (cmeasure @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))) @ ((creal_mul @ ((creal_pow @ (creal_abs @ V0)) @ (cdimindex @ cUNIV))) @ (cmeasure @ V1)))))))))
(TMEASURABLE_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V1)) @ (cmeasurable @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TIS_INTERVAL_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cis_interval @ V1)) @ (cis_interval @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TCONNECTED_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cconnected @ V1)) @ (cconnected @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TCOMPACT_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (ccompact @ V1)) @ (ccompact @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TCLOSED_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cclosed @ V1)) @ (cclosed @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TCONVEX_HULL_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ cconvex) @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))) @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ ((chull @ cconvex) @ V1))))))))
(TIS_INTERVAL_SCALING_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cis_interval @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (cis_interval @ V1))))))))
(THAS_MEASURE_SCALING_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((chas_measure @ ((cIMAGE @ (^[V3]: ((c% @ V0) @ V3))) @ V1)) @ ((creal_mul @ ((creal_pow @ (creal_abs @ V0)) @ (cdimindex @ cUNIV))) @ V2))) @ ((chas_measure @ V1) @ V2))))))))))
(TBANACH_FIX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccomplete @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c/__caret__ @ ((creal_lt @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V1)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((cIN @ V4) @ V1))) @ ((creal_le @ (cdistance @ ((c__comma__ @ (V2 @ V3)) @ (V2 @ V4)))) @ ((creal_mul @ V0) @ (cdistance @ ((c__comma__ @ V3) @ V4))))))))))))))) @ (c?! @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ V3))))))))))))
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(TMEASURABLE_ON_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cmeasurable_on @ V1) @ V2)) @ ((cmeasurable_on @ (^[V3]: ((c% @ V0) @ (V1 @ V3)))) @ V2)))))))))
(TINTEGRABLE_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cintegrable_on @ V1) @ V2)) @ ((cintegrable_on @ (^[V3]: ((c% @ V0) @ (V1 @ V3)))) @ V2)))))))))
(TCOMPLETE_ISOMETRIC_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c/__caret__ @ (csubspace @ V2)) @ ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_ge @ (cvector_norm @ (V1 @ V3))) @ ((creal_mul @ V0) @ (cvector_norm @ V3))))))) @ (ccomplete @ V2)))))) @ (ccomplete @ ((cIMAGE @ V1) @ V2))))))))))
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(TDIFFERENTIAL_COMPONENT_POS_AT_MINIMUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V6)) @ ((c/__caret__ @ ((c<= @ V6) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ (cconvex @ V2)) @ ((c/__caret__ @ (((chas_derivative @ V1) @ V3) @ ((cwithin @ (cat @ V5)) @ V2))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ ((cINTER @ V2) @ (cball @ ((c__comma__ @ V5) @ V0))))) @ ((creal_le @ ((c$ @ (V1 @ V5)) @ V6)) @ ((c$ @ (V1 @ V7)) @ V6)))))))))))) @ ((c==> @ ((cIN @ V4) @ V2)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ (V3 @ ((cvector_sub @ V4) @ V5))) @ V6)))))))))))))))))))
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(TSET_VARIATION_LBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V2) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cdivision_of @ V3) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V1)) @ ((creal_le @ V0) @ ((csum @ V3) @ (^[V5]: (cvector_norm @ (V2 @ V5))))))))))))) @ ((creal_le @ V0) @ ((cset_variation @ V1) @ V2))))))))))
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(THAS_MEASURE_IMP_MEASURABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_measure @ V1) @ V0)) @ (cmeasurable @ V1)))))))
(Thas_measure,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_measure @ V1) @ V0)) @ (((chas_integral @ (^[V2]: (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (clift @ V0)) @ V1)))))))
(TABSOLUTELY_INTEGRABLE_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cabsolutely_integrable_on @ V1) @ V2)) @ ((cabsolutely_integrable_on @ (^[V3]: ((c% @ V0) @ (V1 @ V3)))) @ V2)))))))))
(TDIFFERENTIABLE_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cdifferentiable @ V1) @ V2)) @ ((cdifferentiable @ (^[V3]: ((c% @ V0) @ (V1 @ V3)))) @ V2)))))))))
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(THAS_DERIVATIVE_TRANSFORM_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((creal_lt @ (cdistance @ ((c__comma__ @ V5) @ V4))) @ V0)) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))) @ (((chas_derivative @ V1) @ V3) @ (cat @ V4))))) @ (((chas_derivative @ V2) @ V3) @ (cat @ V4))))))))))))))
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(TCONVEX_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cconvex @ V1)) @ (cconvex @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TCONVEX_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cconvex_on @ V1) @ V2))) @ ((cconvex_on @ (^[V3]: ((creal_mul @ V0) @ (V1 @ V3)))) @ V2)))))))))
(TAFFINE_SCALING_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (caffine @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))) @ (caffine @ V1))))))))
(TAFFINE_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (caffine @ V1)) @ (caffine @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
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(TBOUNDED_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cbounded @ V1)) @ (cbounded @ ((cIMAGE @ (^[V2]: ((c% @ V0) @ V2))) @ V1))))))))
(TLIM_TRANSFORM_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdistance @ ((c__comma__ @ V5) @ V4)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V5) @ V4))) @ V0))) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))) @ (((c--> @ V1) @ V3) @ (cat @ V4))))) @ (((c--> @ V2) @ V3) @ (cat @ V4))))))))))))))
(TLIM_TRANSFORM_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V5)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdistance @ ((c__comma__ @ V6) @ V4)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V6) @ V4))) @ V0)))) @ ((c= @ (V1 @ V6)) @ (V2 @ V6)))))) @ (((c--> @ V1) @ V3) @ ((cwithin @ (cat @ V4)) @ V5))))) @ (((c--> @ V2) @ V3) @ ((cwithin @ (cat @ V4)) @ V5))))))))))))))))
(TBILINEAR_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cbilinear @ V1)) @ ((c= @ ((V1 @ V2) @ ((c% @ V0) @ V3))) @ ((c% @ V0) @ ((V1 @ V2) @ V3)))))))))))))
(TBILINEAR_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cbilinear @ V1)) @ ((c= @ ((V1 @ ((c% @ V0) @ V2)) @ V3)) @ ((c% @ V0) @ ((V1 @ V2) @ V3)))))))))))))
(TLINEAR_COMPOSE_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V1)) @ (clinear @ (^[V2]: ((c% @ V0) @ (V1 @ V2))))))))))
(TLIM_NULL_VMUL_BOUNDED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((c--> @ ((co @ clift) @ V1)) @ (cvec @ (cNUMERAL @ c_0))) @ V3)) @ ((ceventually @ (^[V4]: ((c__caret__/ @ ((c= @ (V1 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_le @ (cvector_norm @ (V2 @ V4))) @ V0)))) @ V3))) @ (((c--> @ (^[V4]: ((c% @ (V1 @ V4)) @ (V2 @ V4)))) @ (cvec @ (cNUMERAL @ c_0))) @ V3)))))))))))
(TLIM_NULL_CMUL_BOUNDED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ceventually @ (^[V4]: ((c__caret__/ @ ((c= @ (V2 @ V4)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((creal_le @ (creal_abs @ (V1 @ V4))) @ V0)))) @ V3)) @ (((c--> @ V2) @ (cvec @ (cNUMERAL @ c_0))) @ V3))) @ (((c--> @ (^[V4]: ((c% @ (V1 @ V4)) @ (V2 @ V4)))) @ (cvec @ (cNUMERAL @ c_0))) @ V3)))))))))))
(TSUM_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((csum @ V1) @ (^[V3]: ((creal_mul @ V0) @ (V2 @ V3))))) @ ((creal_mul @ V0) @ ((csum @ V1) @ V2))))))))))
(TMSUM_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cmsum @ V1) @ (^[V3]: ((c%% @ V0) @ (V2 @ V3))))) @ ((c%% @ V0) @ ((cmsum @ V1) @ V2)))))))))))
(TCONTINUOUS_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous @ V1) @ V2)) @ ((ccontinuous @ (^[V3]: ((c% @ V0) @ (V1 @ V3)))) @ V2)))))))))
(TLIM_NULL_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c--> @ V1) @ (cvec @ (cNUMERAL @ c_0))) @ V2)) @ (((c--> @ (^[V3]: ((c% @ V0) @ (V1 @ V3)))) @ (cvec @ (cNUMERAL @ c_0))) @ V2)))))))))
(TLIM_NULL_CMUL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (((c--> @ (^[V3]: ((c% @ V0) @ (V1 @ V3)))) @ (cvec @ (cNUMERAL @ c_0))) @ V2)) @ (((c--> @ V1) @ (cvec @ (cNUMERAL @ c_0))) @ V2))))))))))
(TLIM_CMUL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (((c--> @ (^[V4]: ((c% @ V0) @ (V1 @ V4)))) @ ((c% @ V0) @ V2)) @ V3)) @ (((c--> @ V1) @ V2) @ V3))))))))))))
(TVSUM_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvsum @ V1) @ (^[V3]: ((c% @ V0) @ (V2 @ V3))))) @ ((c% @ V0) @ ((cvsum @ V1) @ V2))))))))))
(TPRODUCT_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cproduct @ V1) @ (^[V2]: V0))) @ ((creal_pow @ V0) @ (cCARD @ V1)))))))))
(TMULTIVECTOR_MUL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$$ @ ((c% @ V0) @ V1)) @ V2)) @ ((creal_mul @ V0) @ ((c$$ @ V1) @ V2)))))))))))
(TINNER_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cinner @ ((c% @ V0) @ V1)) @ V2)) @ ((c% @ V0) @ ((cinner @ V1) @ V2))))))))))
(TINNER_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cinner @ V1) @ ((c% @ V0) @ V2))) @ ((c% @ V0) @ ((cinner @ V1) @ V2))))))))))
(TOUTER_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((couter @ ((c% @ V0) @ V1)) @ V2)) @ ((c% @ V0) @ ((couter @ V1) @ V2))))))))))
(TOUTER_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((couter @ V1) @ ((c% @ V0) @ V2))) @ ((c% @ V0) @ ((couter @ V1) @ V2))))))))))
(TGEOM_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cgeom_mul @ ((c% @ V0) @ V1)) @ V2)) @ ((c% @ V0) @ ((cgeom_mul @ V1) @ V2))))))))))
(TGEOM_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cgeom_mul @ V1) @ ((c% @ V0) @ V2))) @ ((c% @ V0) @ ((cgeom_mul @ V1) @ V2))))))))))
(TSNDCART_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csndcart @ ((c% @ V0) @ V1))) @ ((c% @ V0) @ (csndcart @ V1))))))))
(TFSTCART_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cfstcart @ ((c% @ V0) @ V1))) @ ((c% @ V0) @ (cfstcart @ V1))))))))
(TCROSS_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccross @ ((c% @ V0) @ V1)) @ V2)) @ ((c% @ V0) @ ((ccross @ V1) @ V2))))))))))
(TCROSS_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccross @ V1) @ ((c% @ V0) @ V2))) @ ((c% @ V0) @ ((ccross @ V1) @ V2))))))))))
(TTHALES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c= @ (clength @ ((c__comma__ @ V2) @ V1))) @ V0)) @ ((c/__caret__ @ ((c= @ (clength @ ((c__comma__ @ V4) @ V1))) @ V0)) @ ((c/__caret__ @ ((c= @ (clength @ ((c__comma__ @ V3) @ V1))) @ V0)) @ ((cbetween @ V1) @ ((c__comma__ @ V2) @ V4)))))) @ ((corthogonal @ ((cvector_sub @ V3) @ V2)) @ ((cvector_sub @ V3) @ V4))))))))))))))
(TDROP_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdrop @ ((c% @ V0) @ V1))) @ ((creal_mul @ V0) @ (cdrop @ V1))))))))
(TVECTOR_VARIATION_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cvector_variation @ V2) @ (^[V4]: (V3 @ ((cvector_add @ ((c% @ V0) @ V4)) @ V1))))) @ (((cCOND @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cvector_variation @ ((cIMAGE @ (^[V4]: ((cvector_add @ ((c% @ V0) @ V4)) @ V1))) @ V2)) @ V3))))))))))))
(TSUBPATH_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csubpath @ V1) @ V2) @ ((co @ (^[V4]: ((creal_add @ V0) @ V4))) @ V3))) @ ((co @ (^[V4]: ((creal_add @ V0) @ V4))) @ (((csubpath @ V1) @ V2) @ V3))))))))))))
(TSPHERE_RETRACT_OF_PUNCTURED_UNIVERSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cretract_of @ (csphere @ ((c__comma__ @ V1) @ V0))) @ ((cDELETE @ cUNIV) @ V1))))))))
(TPATH_CONNECTED_PUNCTURED_BALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (cpath_connected @ ((cDELETE @ (cball @ ((c__comma__ @ V1) @ V0))) @ V1))))))))
(TCONNECTED_PUNCTURED_BALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (cconnected @ ((cDELETE @ (cball @ ((c__comma__ @ V1) @ V0))) @ V1))))))))
(TINFNORM_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinfnorm @ ((c% @ V0) @ V1))) @ ((creal_mul @ (creal_abs @ V0)) @ (cinfnorm @ V1))))))))
(Tvector_mul,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c% @ V0) @ V1)) @ (clambda @ (^[V2]: ((creal_mul @ V0) @ ((c$ @ V1) @ V2))))))))))
(TAFFINE_HULL_FINITE_STEP_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ ((csum @ cEMPTY) @ V2)) @ V0)) @ ((c= @ ((cvsum @ cEMPTY) @ (^[V3]: ((c% @ (V2 @ V3)) @ V3)))) @ V1))))) @ ((c/__caret__ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))))))))
(TCONVEX_HULL_FINITE_STEP_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ cEMPTY)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V2 @ V3)))))) @ ((c/__caret__ @ ((c= @ ((csum @ cEMPTY) @ V2)) @ V0)) @ ((c= @ ((cvsum @ cEMPTY) @ (^[V3]: ((c% @ (V2 @ V3)) @ V3)))) @ V1)))))) @ ((c/__caret__ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))))))))
(TCONVEX_BOUNDS_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V3) @ (ccball @ ((c__comma__ @ V4) @ V0)))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (ccball @ ((c__comma__ @ V4) @ V0)))) @ ((creal_le @ (V3 @ V5)) @ V2)))))) @ ((c==> @ ((cIN @ V1) @ (ccball @ ((c__comma__ @ V4) @ V0)))) @ ((creal_le @ (creal_abs @ (V3 @ V1))) @ ((creal_add @ V2) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_abs @ (V3 @ V4))))))))))))))))))
(TVECTOR_MUL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c$ @ ((c% @ V0) @ V1)) @ V2)) @ ((creal_mul @ V0) @ ((c$ @ V1) @ V2))))))))))
(TCONVEX_CONE_HULL_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cIN @ V1) @ ((chull @ cconvex_cone) @ V2)))) @ ((cIN @ ((c% @ V0) @ V1)) @ ((chull @ cconvex_cone) @ V2))))))))))
(TSPAN_MUL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((cIN @ ((c% @ V0) @ V1)) @ (cspan @ V2))) @ ((cIN @ V1) @ (cspan @ V2)))))))))))
(TSPAN_SPECIAL_SCALE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cspan @ ((cINSERT @ ((c% @ V0) @ V1)) @ V2))) @ (((cCOND @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (cspan @ V2)) @ (cspan @ ((cINSERT @ V1) @ V2)))))))))))
(TREFLECT_ALONG_SCALE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((creflect_along @ ((c% @ V0) @ V1)) @ V2)) @ ((creflect_along @ V1) @ V2))))))))))
(TREFLECT_ALONG_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creflect_along @ V1) @ ((c% @ V0) @ V2))) @ ((c% @ V0) @ ((creflect_along @ V1) @ V2))))))))))
(TORTHOGONAL_MUL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((corthogonal @ ((c% @ V0) @ V1)) @ V2)) @ ((c__caret__/ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((corthogonal @ V1) @ V2))))))))))
(TORTHOGONAL_MUL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((corthogonal @ V1) @ ((c% @ V0) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((corthogonal @ V1) @ V2))))))))))
(TIN_RELATIVE_INTERIOR_CLOSURE_CONVEX_SHRINK,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconvex @ V3)) @ ((c/__caret__ @ ((cIN @ V2) @ (crelative_interior @ V3))) @ ((c/__caret__ @ ((cIN @ V1) @ (cclosure @ V3))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_le @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((cIN @ ((cvector_sub @ V1) @ ((c% @ V0) @ ((cvector_sub @ V1) @ V2)))) @ (crelative_interior @ V3))))))))))))
(TIN_RELATIVE_INTERIOR_CONVEX_SHRINK,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconvex @ V3)) @ ((c/__caret__ @ ((cIN @ V2) @ (crelative_interior @ V3))) @ ((c/__caret__ @ ((cIN @ V1) @ V3)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_le @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((cIN @ ((cvector_sub @ V1) @ ((c% @ V0) @ ((cvector_sub @ V1) @ V2)))) @ (crelative_interior @ V3))))))))))))
(TIN_INTERIOR_CLOSURE_CONVEX_SHRINK,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconvex @ V3)) @ ((c/__caret__ @ ((cIN @ V2) @ (cinterior @ V3))) @ ((c/__caret__ @ ((cIN @ V1) @ (cclosure @ V3))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_le @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((cIN @ ((cvector_sub @ V1) @ ((c% @ V0) @ ((cvector_sub @ V1) @ V2)))) @ (cinterior @ V3))))))))))))
(TIN_INTERIOR_CONVEX_SHRINK,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconvex @ V3)) @ ((c/__caret__ @ ((cIN @ V2) @ (cinterior @ V3))) @ ((c/__caret__ @ ((cIN @ V1) @ V3)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((creal_le @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((cIN @ ((cvector_sub @ V1) @ ((c% @ V0) @ ((cvector_sub @ V1) @ V2)))) @ (cinterior @ V3))))))))))))
(TIN_AFFINE_MUL_DIFF_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (caffine @ V4)) @ ((c/__caret__ @ ((cIN @ V1) @ V4)) @ ((c/__caret__ @ ((cIN @ V2) @ V4)) @ ((cIN @ V3) @ V4))))) @ ((cIN @ ((cvector_add @ ((c% @ V0) @ ((cvector_sub @ V1) @ V2))) @ V3)) @ V4)))))))))))))
(TSET_VARIATION_LBOUND_ON_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cdivision_of @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_le @ V0) @ ((csum @ V4) @ (^[V5]: (cvector_norm @ (V3 @ V5)))))))))) @ ((creal_le @ V0) @ ((cset_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V3))))))))))))
(TINTEGRAL_COMPONENT_LBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ (cdimindex @ cUNIV))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_le @ V0) @ ((c$ @ (V3 @ V5)) @ V4))))))))) @ ((creal_le @ ((creal_mul @ V0) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))) @ ((c$ @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V3)) @ V4))))))))))))))
(TINTERVAL_IMAGE_AFFINITY_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c= @ ((cIMAGE @ (^[V6]: ((cvector_add @ ((c% @ V0) @ V6)) @ V1))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))))))))))))))
(TCONVEX_CONE_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex_cone @ V2)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cIN @ V1) @ V2)))) @ ((cIN @ ((c% @ V0) @ V1)) @ V2)))))))))
(TAFFINITY_INVERSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((co @ (^[V2]: ((cvector_add @ ((c% @ (creal_inv @ V0)) @ V2)) @ (cvector_neg @ ((c% @ (creal_inv @ V0)) @ V1))))) @ (^[V2]: ((cvector_add @ ((c% @ V0) @ V2)) @ V1)))) @ cI)))))))
(TAFFINITY_INVERSES_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((co @ (^[V2]: ((cvector_add @ ((c% @ V0) @ V2)) @ V1))) @ (^[V2]: ((cvector_add @ ((c% @ (creal_inv @ V0)) @ V2)) @ (cvector_neg @ ((c% @ (creal_inv @ V0)) @ V1)))))) @ cI)))))))
(TSPHERE_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ (csphere @ ((c__comma__ @ V1) @ V0))) @ ((cINSERT @ V1) @ cEMPTY))))))))
(TCBALL_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ (ccball @ ((c__comma__ @ V1) @ V0))) @ ((cINSERT @ V1) @ cEMPTY))))))))
(TCBALL_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ (ccball @ ((c__comma__ @ ((c% @ V0) @ V1)) @ ((creal_mul @ V0) @ V2)))) @ ((cIMAGE @ (^[V3]: ((c% @ V0) @ V3))) @ (ccball @ ((c__comma__ @ V1) @ V2))))))))))))
(TBALL_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ (cball @ ((c__comma__ @ ((c% @ V0) @ V1)) @ ((creal_mul @ V0) @ V2)))) @ ((cIMAGE @ (^[V3]: ((c% @ V0) @ V3))) @ (cball @ ((c__comma__ @ V1) @ V2))))))))))))
(TCBALL_MIN_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (ccball @ ((c__comma__ @ V1) @ ((creal_min @ V0) @ V2)))) @ ((cINTER @ (ccball @ ((c__comma__ @ V1) @ V0))) @ (ccball @ ((c__comma__ @ V1) @ V2)))))))))))
(TCBALL_MAX_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (ccball @ ((c__comma__ @ V1) @ ((creal_max @ V0) @ V2)))) @ ((cUNION @ (ccball @ ((c__comma__ @ V1) @ V0))) @ (ccball @ ((c__comma__ @ V1) @ V2)))))))))))
(TBALL_MIN_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cball @ ((c__comma__ @ V1) @ ((creal_min @ V0) @ V2)))) @ ((cINTER @ (cball @ ((c__comma__ @ V1) @ V0))) @ (cball @ ((c__comma__ @ V1) @ V2)))))))))))
(TBALL_MAX_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cball @ ((c__comma__ @ V1) @ ((creal_max @ V0) @ V2)))) @ ((cUNION @ (cball @ ((c__comma__ @ V1) @ V0))) @ (cball @ ((c__comma__ @ V1) @ V2)))))))))))
(TSUBSET_CBALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((creal_le @ V0) @ V2)) @ ((cSUBSET @ (ccball @ ((c__comma__ @ V1) @ V0))) @ (ccball @ ((c__comma__ @ V1) @ V2)))))))))))
(TSUBSET_BALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((creal_le @ V0) @ V2)) @ ((cSUBSET @ (cball @ ((c__comma__ @ V1) @ V0))) @ (cball @ ((c__comma__ @ V1) @ V2)))))))))))
(TINFNORM_MUL_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cinfnorm @ ((c% @ V0) @ V1))) @ ((creal_mul @ (creal_abs @ V0)) @ (cinfnorm @ V1))))))))
(TSPAN_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V1) @ (cspan @ V2))) @ ((cIN @ ((c% @ V0) @ V1)) @ (cspan @ V2))))))))))
(TSUBSPACE_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (csubspace @ V2)) @ ((cIN @ V1) @ V2))) @ ((cIN @ ((c% @ V0) @ V1)) @ V2)))))))))
(TPASTECART_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpastecart @ ((c% @ V0) @ V1)) @ ((c% @ V0) @ V2))) @ ((c% @ V0) @ ((cpastecart @ V1) @ V2))))))))))
(TDIST_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cdistance @ ((c__comma__ @ ((c% @ V0) @ V1)) @ ((c% @ V0) @ V2)))) @ ((creal_mul @ (creal_abs @ V0)) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))))))))
(TVECTOR_MUL_LCANCEL_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((c% @ V0) @ V1)) @ ((c% @ V0) @ V2)))) @ ((c= @ V1) @ V2)))))))))
(TVECTOR_MUL_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((c% @ V0) @ V1)) @ ((c% @ V0) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ V2))))))))))
(TVECTOR_MUL_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c% @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))))))))
(TNORM_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cvector_norm @ ((c% @ V0) @ V1))) @ ((creal_mul @ (creal_abs @ V0)) @ (cvector_norm @ V1))))))))
(TDOT_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ V1) @ ((c% @ V0) @ V2))) @ ((creal_mul @ V0) @ ((cdot @ V1) @ V2))))))))))
(TDOT_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ ((c% @ V0) @ V1)) @ V2)) @ ((creal_mul @ V0) @ ((cdot @ V1) @ V2))))))))))
(TVECTOR_MUL_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c% @ V0) @ (cvector_neg @ V1))) @ (cvector_neg @ ((c% @ V0) @ V1))))))))
(TVECTOR_MUL_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c% @ (creal_neg @ V0)) @ V1)) @ (cvector_neg @ ((c% @ V0) @ V1))))))))
(TDET_OPEN_MAP_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((creal_lt @ (creal_abs @ ((creal_sub @ ((c$ @ ((c$ @ V2) @ V3)) @ V4)) @ ((c$ @ ((c$ @ V1) @ V3)) @ V4)))) @ V0)))))) @ ((creal_lt @ (cdet @ V2)) @ (cdet @ V1)))))))))))
(TDET_OPEN_MAP_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((creal_lt @ (creal_abs @ ((creal_sub @ ((c$ @ ((c$ @ V2) @ V3)) @ V4)) @ ((c$ @ ((c$ @ V1) @ V3)) @ V4)))) @ V0)))))) @ ((creal_gt @ (cdet @ V2)) @ (cdet @ V1)))))))))))
(TDET_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdet @ ((c%% @ V0) @ V1))) @ ((creal_mul @ ((creal_pow @ V0) @ (cdimindex @ cUNIV))) @ (cdet @ V1))))))))
(TCOFACTOR_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccofactor @ ((c%% @ V0) @ V1))) @ ((c%% @ ((creal_pow @ V0) @ ((c- @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (ccofactor @ V1))))))))
(TMATRIX_CMUL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c$ @ ((c$ @ ((c%% @ V0) @ V1)) @ V2)) @ V3)) @ ((creal_mul @ V0) @ ((c$ @ ((c$ @ V1) @ V2)) @ V3))))))))))))
(TMATRIX_MUL_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_mul @ ((c%% @ V0) @ V1)) @ V2)) @ ((c%% @ V0) @ ((cmatrix_mul @ V1) @ V2))))))))))
(TMATRIX_MUL_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_mul @ V1) @ ((c%% @ V0) @ V2))) @ ((c%% @ V0) @ ((cmatrix_mul @ V1) @ V2))))))))))
(TTRANSP_MATRIX_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctransp @ ((c%% @ V0) @ V1))) @ ((c%% @ V0) @ (ctransp @ V1))))))))
(TMATRIX_CMUL_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c%% @ V0) @ V1)) @ (cmat @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cmat @ (cNUMERAL @ c_0))))))))))
(TMATRIX_VECTOR_MUL_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_vector_mul @ V1) @ ((c% @ V0) @ V2))) @ ((c% @ V0) @ ((cmatrix_vector_mul @ V1) @ V2))))))))))
(TQLE_REFL,(c! @ (^[V0]: ((c<<= @ V0) @ V0))))
(Tqjoin,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c&& @ V1) @ V0)) @ (((cCOND @ ((c<<= @ V1) @ V0)) @ V0) @ (((cCOND @ ((c<<= @ V0) @ V1)) @ V1) @ cTOP))))))))
(Tqle,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<<= @ V0) @ V1)) @ ((c__caret__/ @ ((c= @ V0) @ cX)) @ ((c__caret__/ @ ((c= @ V1) @ cTOP)) @ ((c= @ V0) @ V1)))))))))
(TQLE_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<<= @ V1) @ V0)) @ ((c<<= @ V0) @ V2))) @ ((c<<= @ V1) @ V2)))))))))
(TQLE_LJOIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c<<= @ ((c&& @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((c<<= @ V0) @ V2)) @ ((c<<= @ V1) @ V2))))))))))
(TRACONV_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cRACONV @ V1) @ V0)) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ ((c__comma__ @ ((cVar @ V2) @ V3)) @ ((cVar @ V4) @ V5)))) @ ((cALPHAVARS @ V1) @ ((c__comma__ @ ((cVar @ V2) @ V3)) @ ((cVar @ V4) @ V5))))))))))))) @ ((c__caret__/ @ (c? @ (^[V2]: ((c= @ V0) @ ((c__comma__ @ (cEqual @ V2)) @ (cEqual @ V2)))))) @ ((c__caret__/ @ (c? @ (^[V2]: ((c= @ V0) @ ((c__comma__ @ (cSelect @ V2)) @ (cSelect @ V2)))))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ ((c__comma__ @ ((cComb @ V2) @ V3)) @ ((cComb @ V4) @ V5)))) @ ((c/__caret__ @ ((cRACONV @ V1) @ ((c__comma__ @ V2) @ V4))) @ ((cRACONV @ V1) @ ((c__comma__ @ V3) @ V5))))))))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (c? @ (^[V7]: ((c/__caret__ @ ((c= @ V0) @ ((c__comma__ @ (((cAbs @ V2) @ V3) @ V4)) @ (((cAbs @ V5) @ V6) @ V7)))) @ ((c/__caret__ @ ((c= @ V3) @ V6)) @ ((cRACONV @ ((cCONS @ ((c__comma__ @ ((cVar @ V2) @ V3)) @ ((cVar @ V5) @ V6))) @ V1)) @ ((c__comma__ @ V4) @ V7))))))))))))))))))))))))))
(TVFREE_IN_RACONV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cRACONV @ V3) @ V0)) @ ((c= @ ((c/__caret__ @ ((cVFREE_IN @ ((cVar @ V1) @ V2)) @ (cFST @ V0))) @ (c~ @ (c? @ (^[V4]: ((cMEM @ ((c__comma__ @ ((cVar @ V1) @ V2)) @ V4)) @ V3)))))) @ ((c/__caret__ @ ((cVFREE_IN @ ((cVar @ V1) @ V2)) @ (cSND @ V0))) @ (c~ @ (c? @ (^[V4]: ((cMEM @ ((c__comma__ @ V4) @ ((cVar @ V1) @ V2))) @ V3))))))))))))))))
(Tv_tybij_conjunct1,(c! @ (^[V0]: ((c= @ ((cIN @ V0) @ cuniverse)) @ ((c= @ (cdest_V @ (cmk_V @ V0))) @ V0)))))
(TBOUNDED_FUNCTIONS_BIJECTIONS_1_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ V5) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V8)) @ ((c<= @ V8) @ V2))) @ ((cIN @ (V7 @ V8)) @ V1))))) @ (c! @ (^[V8]: ((c==> @ (c~ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V8)) @ ((c<= @ V8) @ V2)))) @ ((c= @ (V7 @ V8)) @ V8)))))) @ V7)))))))) @ ((c__comma__ @ V4) @ V5)))))))))) @ ((cIN @ ((cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ (^[V6]: (((cCOND @ ((c= @ V6) @ (cSUC @ V2))) @ V4) @ (V5 @ V6)))))))))) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cSUC @ V2)))) @ ((cIN @ (V4 @ V5)) @ V1))))) @ (c! @ (^[V5]: ((c==> @ (c~ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cSUC @ V2))))) @ ((c= @ (V4 @ V5)) @ V5)))))) @ V4))))))))))))))
(TTREAL_LE_REFL,(c! @ (^[V0]: ((ctreal_le @ V0) @ V0))))
(TTREAL_MUL_LID,(c! @ (^[V0]: ((ctreal_eq @ ((ctreal_mul @ (ctreal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ V0))))
(TTREAL_ADD_LID,(c! @ (^[V0]: ((ctreal_eq @ ((ctreal_add @ (ctreal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ V0))))
(TTREAL_ADD_LINV,(c! @ (^[V0]: ((ctreal_eq @ ((ctreal_add @ (ctreal_neg @ V0)) @ V0)) @ (ctreal_of_num @ (cNUMERAL @ c_0))))))
(TTREAL_EQ_REFL,(c! @ (^[V0]: ((ctreal_eq @ V0) @ V0))))
(TTREAL_MUL_LINV,(c! @ (^[V0]: ((c==> @ (c~ @ ((ctreal_eq @ V0) @ (ctreal_of_num @ (cNUMERAL @ c_0))))) @ ((ctreal_eq @ ((ctreal_mul @ (ctreal_inv @ V0)) @ V0)) @ (ctreal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(Treal_neg_th,(c! @ (^[V0]: ((c= @ (cmk_real @ (ctreal_eq @ (ctreal_neg @ V0)))) @ (creal_neg @ (cmk_real @ (ctreal_eq @ V0)))))))
(Treal_inv_th,(c! @ (^[V0]: ((c= @ (cmk_real @ (ctreal_eq @ (ctreal_inv @ V0)))) @ (creal_inv @ (cmk_real @ (ctreal_eq @ V0)))))))
(TTREAL_MUL_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((ctreal_eq @ ((ctreal_mul @ V1) @ V0)) @ ((ctreal_mul @ V0) @ V1)))))))
(TTREAL_ADD_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((ctreal_eq @ ((ctreal_add @ V1) @ V0)) @ ((ctreal_add @ V0) @ V1)))))))
(TTREAL_LE_TOTAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((ctreal_le @ V1) @ V0)) @ ((ctreal_le @ V0) @ V1)))))))
(TTREAL_EQ_IMP_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ctreal_eq @ V0) @ V1)) @ ((ctreal_le @ V0) @ V1)))))))
(TTREAL_NEG_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ctreal_eq @ V0) @ V1)) @ ((ctreal_eq @ (ctreal_neg @ V0)) @ (ctreal_neg @ V1))))))))
(TTREAL_INV_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ctreal_eq @ V0) @ V1)) @ ((ctreal_eq @ (ctreal_inv @ V0)) @ (ctreal_inv @ V1))))))))
(TTREAL_EQ_AP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ V0) @ V1)) @ ((ctreal_eq @ V0) @ V1)))))))
(TTREAL_LE_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ctreal_le @ (ctreal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((ctreal_le @ (ctreal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((ctreal_le @ (ctreal_of_num @ (cNUMERAL @ c_0))) @ ((ctreal_mul @ V0) @ V1))))))))
(Treal_mul_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmk_real @ (ctreal_eq @ ((ctreal_mul @ V0) @ V1)))) @ ((creal_mul @ (cmk_real @ (ctreal_eq @ V0))) @ (cmk_real @ (ctreal_eq @ V1)))))))))
(Treal_add_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmk_real @ (ctreal_eq @ ((ctreal_add @ V0) @ V1)))) @ ((creal_add @ (cmk_real @ (ctreal_eq @ V0))) @ (cmk_real @ (ctreal_eq @ V1)))))))))
(TTREAL_MUL_SYM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ctreal_mul @ V1) @ V0)) @ ((ctreal_mul @ V0) @ V1)))))))
(TTREAL_ADD_SYM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ctreal_add @ V1) @ V0)) @ ((ctreal_add @ V0) @ V1)))))))
(Treal_le_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ctreal_le @ V0) @ V1)) @ ((creal_le @ (cmk_real @ (ctreal_eq @ V0))) @ (cmk_real @ (ctreal_eq @ V1)))))))))
(TTREAL_EQ_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ctreal_eq @ V1) @ V0)) @ ((ctreal_eq @ V0) @ V1)))))))
(TTREAL_LE_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((ctreal_le @ V0) @ V1)) @ ((ctreal_le @ V1) @ V0))) @ ((ctreal_eq @ V0) @ V1)))))))
(TTREAL_ADD_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((ctreal_eq @ ((ctreal_mul @ V1) @ ((ctreal_add @ V0) @ V2))) @ ((ctreal_add @ ((ctreal_mul @ V1) @ V0)) @ ((ctreal_mul @ V1) @ V2))))))))))
(TTREAL_MUL_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((ctreal_eq @ ((ctreal_mul @ V0) @ ((ctreal_mul @ V1) @ V2))) @ ((ctreal_mul @ ((ctreal_mul @ V0) @ V1)) @ V2)))))))))
(TTREAL_ADD_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((ctreal_eq @ ((ctreal_add @ V0) @ ((ctreal_add @ V1) @ V2))) @ ((ctreal_add @ ((ctreal_add @ V0) @ V1)) @ V2)))))))))
(TTREAL_LE_LADD_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ctreal_le @ V0) @ V2)) @ ((ctreal_le @ ((ctreal_add @ V1) @ V0)) @ ((ctreal_add @ V1) @ V2))))))))))
(TTREAL_MUL_WELLDEFR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ctreal_eq @ V0) @ V1)) @ ((ctreal_eq @ ((ctreal_mul @ V0) @ V2)) @ ((ctreal_mul @ V1) @ V2))))))))))
(TTREAL_ADD_WELLDEFR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ctreal_eq @ V0) @ V1)) @ ((ctreal_eq @ ((ctreal_add @ V0) @ V2)) @ ((ctreal_add @ V1) @ V2))))))))))
(TTREAL_LE_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ctreal_le @ V1) @ V0)) @ ((ctreal_le @ V0) @ V2))) @ ((ctreal_le @ V1) @ V2)))))))))
(TTREAL_EQ_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ctreal_eq @ V1) @ V0)) @ ((ctreal_eq @ V0) @ V2))) @ ((ctreal_eq @ V1) @ V2)))))))))
(TTREAL_MUL_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ctreal_eq @ V0) @ V2)) @ ((ctreal_eq @ V1) @ V3))) @ ((ctreal_eq @ ((ctreal_mul @ V0) @ V1)) @ ((ctreal_mul @ V2) @ V3))))))))))))
(TTREAL_ADD_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ctreal_eq @ V0) @ V2)) @ ((ctreal_eq @ V1) @ V3))) @ ((ctreal_eq @ ((ctreal_add @ V0) @ V1)) @ ((ctreal_add @ V2) @ V3))))))))))))
(TTREAL_LE_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ctreal_eq @ V0) @ V2)) @ ((ctreal_eq @ V1) @ V3))) @ ((c= @ ((ctreal_le @ V0) @ V1)) @ ((ctreal_le @ V2) @ V3))))))))))))
(TCASEWISE_DEF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((cCASEWISE @ ((cCONS @ V0) @ V1)) @ V2) @ V3)) @ (((cCOND @ (c? @ (^[V4]: ((c= @ ((cFST @ V0) @ V4)) @ V3)))) @ (((cSND @ V0) @ V2) @ (c__at__ @ (^[V4]: ((c= @ ((cFST @ V0) @ V4)) @ V3))))) @ (((cCASEWISE @ V1) @ V2) @ V3))))))))))))
(Teulerian_RULES_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ (cvertices @ V0))) @ ((c= @ (cedges @ V0)) @ cEMPTY))) @ (((ceulerian @ V0) @ cNIL) @ ((c__comma__ @ V1) @ V1))))))))
(Teulerian_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ (cedges @ V0))) @ ((c/__caret__ @ (((cconnects @ V0) @ V4) @ ((c__comma__ @ V1) @ V2))) @ (((ceulerian @ ((cdelete_edge @ V4) @ V0)) @ V5) @ ((c__comma__ @ V2) @ V3))))) @ (((ceulerian @ V0) @ ((cCONS @ V4) @ V5)) @ ((c__comma__ @ V1) @ V3))))))))))))))))
(Tdegree,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdegree @ V0) @ V1)) @ ((cnsum @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ (cedges @ V0))) @ ((cIN @ V1) @ ((ctermini @ V0) @ V3)))) @ V3)))))) @ ((clocaldegree @ V0) @ V1))))))))
(Tlocally_finite,(c! @ (^[V0]: ((c= @ (clocally_finite @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ (cvertices @ V0))) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ (cedges @ V0))) @ ((cIN @ V1) @ ((ctermini @ V0) @ V3)))) @ V3)))))))))))))
(Tconnects,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((cconnects @ V0) @ V1) @ ((c__comma__ @ V2) @ V3))) @ ((c= @ ((ctermini @ V0) @ V1)) @ ((cINSERT @ V2) @ ((cINSERT @ V3) @ cEMPTY)))))))))))))
(Tgraph,(c! @ (^[V0]: ((c= @ (cgraph @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ (cedges @ V0))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V2) @ (cvertices @ V0))) @ ((c/__caret__ @ ((cIN @ V3) @ (cvertices @ V0))) @ ((c= @ ((ctermini @ V0) @ V1)) @ ((cINSERT @ V2) @ ((cINSERT @ V3) @ cEMPTY))))))))))))))))
(TI_PAIR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cI_PAIR @ V0)) @ (cI_PAIR @ V1))) @ ((c= @ V0) @ V1)))))))
(TPAIR,(c! @ (^[V0]: ((c= @ ((c__comma__ @ (cFST @ V0)) @ (cSND @ V0))) @ V0))))
(Tprod_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (cABS_prod @ (cREP_prod @ V0))) @ V0))))
(TSND_DEF,(c! @ (^[V0]: ((c= @ (cSND @ V0)) @ (c__at__ @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ ((c__comma__ @ V2) @ V1))))))))))
(TFST_DEF,(c! @ (^[V0]: ((c= @ (cFST @ V0)) @ (c__at__ @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ ((c__comma__ @ V1) @ V2))))))))))
(TPAIR_SURJECTIVE,(c! @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ ((c__comma__ @ V1) @ V2)))))))))
(TALPHAVARS_conjunct0,(c! @ (^[V0]: ((c= @ ((cALPHAVARS @ cNIL) @ V0)) @ ((c= @ (cFST @ V0)) @ (cSND @ V0))))))
(TALPHAVARS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cALPHAVARS @ ((cCONS @ V0) @ V1)) @ V2)) @ ((c__caret__/ @ ((c= @ V2) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ (cFST @ V0)) @ (cFST @ V2)))) @ ((c/__caret__ @ (c~ @ ((c= @ (cSND @ V0)) @ (cSND @ V2)))) @ ((cALPHAVARS @ V1) @ V2))))))))))))
(TASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cASSOC @ V1) @ ((cCONS @ V0) @ V2))) @ (((cCOND @ ((c= @ (cFST @ V0)) @ V1)) @ (cSND @ V0)) @ ((cASSOC @ V1) @ V2))))))))))
(Tpoint_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (cmk_point @ (cdest_point @ V0))) @ V0))))
(Thomop_conjunct1,(c! @ (^[V0]: ((c= @ V0) @ (cprojp @ (chomop @ V0))))))
(Thomop_def,(c! @ (^[V0]: ((c= @ (chomop @ V0)) @ (chomol @ (cdest_point @ V0))))))
(Thomop_conjunct0,(c! @ (^[V0]: (c~ @ ((c= @ (chomop @ V0)) @ (cvec @ (cNUMERAL @ c_0)))))))
(TPROJP_TOTAL,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V0) @ (cprojp @ V1))))))))
(TAXIOM_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((con @ V0) @ V2)) @ ((c/__caret__ @ ((con @ V1) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((con @ V0) @ V3)) @ ((con @ V1) @ V3))) @ ((c= @ V3) @ V2))))))))))))))
(TPOINT_CLAUSES_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ ((c= @ (cdest_point @ V0)) @ (cdest_point @ V1))))))))
(Ton,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((con @ V0) @ V1)) @ ((cperpl @ (cdest_point @ V0)) @ V1)))))))
(TEXP_10_CONG_3,(c! @ (^[V0]: (((c== @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))))
(TREAL_LT_POW2,(c! @ (^[V0]: ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))))
(TREAL_POW2_CLAUSES_conjunct3,(c! @ (^[V0]: ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))))))
(TPOW_2_LT,(c! @ (^[V0]: ((creal_lt @ (creal_of_num @ V0)) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))))
(TREAL_POW2_CLAUSES_conjunct5,(c! @ (^[V0]: ((creal_le @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TREAL_LE_SUC_POW2,(c! @ (^[V0]: ((creal_le @ ((creal_add @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cSUC @ V0))))))
(TPOW_2_LE1,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))))
(TREAL_POW2_CLAUSES_conjunct9,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_sub @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TREAL_POW2_CLAUSES_conjunct8,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))))))
(TREAL_POW2_CLAUSES_conjunct0,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))))
(TREAL_POS,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_of_num @ V0)))))
(TREAL_POW2_CLAUSES_conjunct2,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))))))
(TREAL_POW2_CLAUSES_conjunct4,(c! @ (^[V0]: ((creal_le @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TDIVIDES_1,(c! @ (^[V0]: ((cnum_divides @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0))))
(TDIVIDES_0,(c! @ (^[V0]: ((cnum_divides @ V0) @ (cNUMERAL @ c_0)))))
(TDIVIDES_REFL,(c! @ (^[V0]: ((cnum_divides @ V0) @ V0))))
(TTAG_INVOLUTION,(c! @ (^[V0]: ((cinvolution @ ctag) @ (czset @ V0)))))
(TINT_LT_POW2,(c! @ (^[V0]: ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_pow @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))))
(TINT_LE_POW2,(c! @ (^[V0]: ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cint_pow @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))))
(TINT_POS,(c! @ (^[V0]: ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_of_num @ V0)))))
(TLESS_0_CASES,(c! @ (^[V0]: ((c__caret__/ @ ((c= @ (cNUMERAL @ c_0)) @ V0)) @ ((c< @ (cNUMERAL @ c_0)) @ V0)))))
(Tnum_CASES,(c! @ (^[V0]: ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ (c? @ (^[V1]: ((c= @ V0) @ (cSUC @ V1))))))))
(TEVEN_OR_ODD,(c! @ (^[V0]: ((c__caret__/ @ (cEVEN @ V0)) @ (cODD @ V0)))))
(THAS_SIZE_NUMSEG_1,(c! @ (^[V0]: ((cHAS_SIZE @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ V0))))
(THAS_SIZE_NUMSEG_LE,(c! @ (^[V0]: ((cHAS_SIZE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c<= @ V2) @ V0)) @ V2)))))) @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(THAS_SIZE_NUMSEG_LT,(c! @ (^[V0]: ((cHAS_SIZE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c< @ V2) @ V0)) @ V2)))))) @ V0))))
(TFINITE_NUMBER_SEGMENT,(c! @ (^[V0]: ((cHAS_SIZE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c< @ V2) @ V0))) @ V2)))))) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TARITH_GE_conjunct5,(c! @ (^[V0]: ((c>= @ (cBIT1 @ V0)) @ c_0))))
(TARITH_GE_conjunct4,(c! @ (^[V0]: ((c>= @ (cBIT0 @ V0)) @ c_0))))
(TGE_REFL,(c! @ (^[V0]: ((c>= @ V0) @ V0))))
(TARITH_GT_conjunct5,(c! @ (^[V0]: ((c> @ (cBIT1 @ V0)) @ c_0))))
(TSWAPSEQ_IDENTITY_EVEN,(c! @ (^[V0]: ((c==> @ ((cswapseq @ V0) @ cI)) @ (cEVEN @ V0)))))
(THAS_SIZE_CART_UNIV,(c! @ (^[V0]: ((c==> @ ((cHAS_SIZE @ cUNIV) @ V0)) @ ((cHAS_SIZE @ cUNIV) @ ((cEXP @ V0) @ (cdimindex @ cUNIV)))))))
(TDIMINDEX_UNIQUE,(c! @ (^[V0]: ((c==> @ ((cHAS_SIZE @ cUNIV) @ V0)) @ ((c= @ (cdimindex @ cUNIV)) @ V0)))))
(TPHI_LOWERBOUND_2,(c! @ (^[V0]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))) @ V0)) @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cphi @ V0))))))
(TNOT_CONG_MINUS1,(c! @ (^[V0]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))) @ V0)) @ (c~ @ (((c== @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V0)))))))
(TEVEN_PHI,(c! @ (^[V0]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))) @ V0)) @ (cEVEN @ (cphi @ V0))))))
(TPHI_LOWERBOUND_1_STRONG,(c! @ (^[V0]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cphi @ V0))))))
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(TCONG_MINUS1_SQUARE,(c! @ (^[V0]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ (((c== @ ((c* @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V0))))))
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(TPRIMEPOW_FACTOR,(c! @ (^[V0]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (cprime @ V1)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V1) @ V3))) @ ((c= @ V0) @ ((c* @ ((cEXP @ V1) @ V2)) @ V3)))))))))))))))
(TDIM_SUBSTANDARD,(c! @ (^[V0]: ((c==> @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c= @ (cdim @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ V0) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ V2) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ V2))))))) @ V0)))))
(TSIGMA_LBOUND,(c! @ (^[V0]: ((c==> @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (csigma @ V0))))))
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(TNORM_BASIS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((c= @ (cvector_norm @ (cbasis @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TDIM_SPECIAL_HYPERPLANE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdim @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c= @ ((c$ @ V2) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V2))))))) @ ((c- @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TSPECIAL_HYPERPLANE_SPAN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((c= @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c= @ ((c$ @ V2) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V2)))))) @ (cspan @ ((cIMAGE @ cbasis) @ ((cDELETE @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ V0))))))))
(TMATRIX_REFLECT_ALONG_BASIS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((c= @ (cmatrix @ (creflect_along @ (cbasis @ V0)))) @ (clambda @ (^[V1]: (clambda @ (^[V2]: (((cCOND @ ((c/__caret__ @ ((c= @ V1) @ V0)) @ ((c= @ V2) @ V0))) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (((cCOND @ ((c= @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))
(TBASIS_NONZERO,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ (c~ @ ((c= @ (cbasis @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))))
(TPERFECT_EULER,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cEVEN @ V0)) @ (cperfect @ V0))) @ (c? @ (^[V1]: ((c/__caret__ @ (cprime @ ((c- @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ V0) @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c- @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))
(TPHI_ANOTHER,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cphi @ V0)) @ (cCARD @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c/__caret__ @ ((c< @ V2) @ V0)) @ (cnum_coprime @ ((c__comma__ @ V2) @ V0))))) @ V2)))))))))))
(TPHI_LIMIT_STRONG,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c<= @ (cphi @ V0)) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TPRIME_FACTOR,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c? @ (^[V1]: ((c/__caret__ @ (cprime @ V1)) @ ((cnum_divides @ V1) @ V0))))))))
(TREAL_NZ_IMP_LT,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_of_num @ V0))))))
(TMOD_0,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ (cNUMERAL @ c_0)) @ V0)) @ (cNUMERAL @ c_0))))))
(TDIV_0,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cDIV @ (cNUMERAL @ c_0)) @ V0)) @ (cNUMERAL @ c_0))))))
(TDIV_REFL,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cDIV @ V0) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TLE_1_conjunct1,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)))))
(TLE_1_conjunct0,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c< @ (cNUMERAL @ c_0)) @ V0)))))
(TCOPRIME_MINUS1,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (cnum_coprime @ ((c__comma__ @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))))
(TODD_POW2_MINUS1,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (cODD @ ((c- @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TFINITE_DIVISORS,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cnum_divides @ V2) @ V0)) @ V2))))))))))
(TFTA,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (c?! @ (^[V1]: ((c/__caret__ @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c~ @ ((c= @ (V1 @ V3)) @ (cNUMERAL @ c_0)))) @ V3))))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ (V1 @ V2)) @ (cNUMERAL @ c_0)))) @ (cprime @ V2))))) @ ((c= @ V0) @ ((cnproduct @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c~ @ ((c= @ (V1 @ V3)) @ (cNUMERAL @ c_0)))) @ V3)))))) @ (^[V2]: ((cEXP @ V2) @ (V1 @ V2)))))))))))))
(TEVEN_ODD_DECOMP,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cODD @ V2)) @ ((c= @ V0) @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ V2)))))))))))
(TPRIMEFACT,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (c? @ (^[V1]: ((cprimefact @ V1) @ V0)))))))
(TEVEN_EXISTS_LEMMA_conjunct1,(c! @ (^[V0]: ((c==> @ (c~ @ (cEVEN @ V0))) @ (c? @ (^[V1]: ((c= @ V0) @ (cSUC @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)))))))))
(TPERFECT_EUCLID,(c! @ (^[V0]: ((c==> @ (cprime @ ((c- @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cperfect @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c- @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TZAG_INVOLUTION,(c! @ (^[V0]: ((c==> @ (cprime @ V0)) @ ((cinvolution @ czag) @ (czset @ V0))))))
(TPRIME_ODD,(c! @ (^[V0]: ((c==> @ (cprime @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cODD @ V0))))))
(TSIGMA_PRIME,(c! @ (^[V0]: ((c==> @ (cprime @ V0)) @ ((c= @ (csigma @ V0)) @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TPHI_PRIME,(c! @ (^[V0]: ((c==> @ (cprime @ V0)) @ ((c= @ (cphi @ V0)) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TPRIME_GE_2,(c! @ (^[V0]: ((c==> @ (cprime @ V0)) @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)))))
(TPRIME_IMP_NZ,(c! @ (^[V0]: ((c==> @ (cprime @ V0)) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))))))
(TZSET_FINITE,(c! @ (^[V0]: ((c==> @ (cprime @ V0)) @ (cFINITE @ (czset @ V0))))))
(TODD_SQUARE,(c! @ (^[V0]: ((c==> @ (cODD @ V0)) @ (c? @ (^[V1]: ((c= @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TSQRT_EVEN_POW2,(c! @ (^[V0]: ((c==> @ (cEVEN @ V0)) @ ((c= @ (csqrt @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cDIV @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))
(TEVEN_SQUARE,(c! @ (^[V0]: ((c==> @ (cEVEN @ V0)) @ (c? @ (^[V1]: ((c= @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))))))))
(TEVEN_EXISTS_LEMMA_conjunct0,(c! @ (^[V0]: ((c==> @ (cEVEN @ V0)) @ (c? @ (^[V1]: ((c= @ V0) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))))))))
(TAUBREY_THM_4,(c! @ (^[V0]: ((c==> @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c= @ ((creal_add @ ((creal_pow @ ((creal_div @ (creal_of_num @ V2)) @ (creal_of_num @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ ((creal_div @ (creal_of_num @ V3)) @ (creal_of_num @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ ((creal_div @ (creal_of_num @ V4)) @ (creal_of_num @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ ((creal_div @ (creal_of_num @ V5)) @ (creal_of_num @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ V0)))))))))))))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ ((creal_add @ ((creal_pow @ (creal_of_num @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ (creal_of_num @ V2)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ (creal_of_num @ V3)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (creal_of_num @ V4)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ V0))))))))))))))
(TTRIANGLE_FINITE_SUM,(c! @ (^[V0]: ((c= @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ (^[V1]: ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (ctriangle @ V1)))))) @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ (creal_of_num @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TSUM_NUMBERS,(c! @ (^[V0]: ((c= @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V1]: (creal_of_num @ V1)))) @ ((creal_div @ ((creal_mul @ (creal_of_num @ V0)) @ ((creal_add @ (creal_of_num @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))
(TREAL_POW_ONE,(c! @ (^[V0]: ((c= @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TPOW_0,(c! @ (^[V0]: ((c= @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cSUC @ V0))) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TREAL_POW_ZERO,(c! @ (^[V0]: ((c= @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TPOW_MINUS1,(c! @ (^[V0]: ((c= @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TREAL_OF_NUM_SUC,(c! @ (^[V0]: ((c= @ ((creal_add @ (creal_of_num @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cSUC @ V0))))))
(TREAL_TRIANGLE,(c! @ (^[V0]: ((c= @ (creal_of_num @ (ctriangle @ V0))) @ ((creal_div @ ((creal_mul @ (creal_of_num @ V0)) @ ((creal_add @ (creal_of_num @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))
(TREAL,(c! @ (^[V0]: ((c= @ (creal_of_num @ (cSUC @ V0))) @ ((creal_add @ (creal_of_num @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(Treal_of_num,(c! @ (^[V0]: ((c= @ (creal_of_num @ V0)) @ (cmk_real @ (^[V1]: ((ctreal_eq @ (ctreal_of_num @ V0)) @ V1)))))))
(Tint_of_num_th,(c! @ (^[V0]: ((c= @ (creal_of_int @ (cint_of_num @ V0))) @ (creal_of_num @ V0)))))
(TPOW_M1,(c! @ (^[V0]: ((c= @ (creal_abs @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TABS_N,(c! @ (^[V0]: ((c= @ (creal_abs @ (creal_of_num @ V0))) @ (creal_of_num @ V0)))))
(Treal_of_num_th,(c! @ (^[V0]: ((c= @ (cmk_real @ (ctreal_eq @ (ctreal_of_num @ V0)))) @ (creal_of_num @ V0)))))
(TFRAC_NUM,(c! @ (^[V0]: ((c= @ (cfrac @ (creal_of_num @ V0))) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TFLOOR_NUM,(c! @ (^[V0]: ((c= @ (cfloor @ (creal_of_num @ V0))) @ (creal_of_num @ V0)))))
(TDROP_VEC,(c! @ (^[V0]: ((c= @ (cdrop @ (cvec @ V0))) @ (creal_of_num @ V0)))))
(Ttreal_of_num,(c! @ (^[V0]: ((c= @ (ctreal_of_num @ V0)) @ ((c__comma__ @ (chreal_of_num @ V0)) @ (chreal_of_num @ (cNUMERAL @ c_0)))))))
(TCOUNT_UNIV,(c! @ (^[V0]: ((c= @ ((ccount @ cUNIV) @ V0)) @ V0))))
(TMOD_1,(c! @ (^[V0]: ((c= @ ((cMOD @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ c_0)))))
(TEXP_ONE,(c! @ (^[V0]: ((c= @ ((cEXP @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TEXP_0,(c! @ (^[V0]: ((c= @ ((cEXP @ (cNUMERAL @ c_0)) @ (cSUC @ V0))) @ (cNUMERAL @ c_0)))))
(TEXP_ZERO,(c! @ (^[V0]: ((c= @ ((cEXP @ (cNUMERAL @ c_0)) @ V0)) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ c_0))))))
(TARITH_EXP_conjunct3,(c! @ (^[V0]: ((c= @ ((cEXP @ (cBIT1 @ V0)) @ c_0)) @ (cBIT1 @ c_0)))))
(TARITH_EXP_conjunct2,(c! @ (^[V0]: ((c= @ ((cEXP @ (cBIT0 @ V0)) @ c_0)) @ (cBIT1 @ c_0)))))
(TARITH_EXP_conjunct7,(c! @ (^[V0]: ((c= @ ((cEXP @ c_0) @ (cBIT1 @ V0))) @ c_0))))
(TARITH_EXP_conjunct4,(c! @ (^[V0]: ((c= @ ((cEXP @ c_0) @ (cBIT0 @ V0))) @ ((c* @ ((cEXP @ c_0) @ V0)) @ ((cEXP @ c_0) @ V0))))))
(TEXP_1,(c! @ (^[V0]: ((c= @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))
(TEXP_2,(c! @ (^[V0]: ((c= @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ V0) @ V0)))))
(TEXP_4,(c! @ (^[V0]: ((c= @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((cEXP @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))
(TEXP_conjunct0,(c! @ (^[V0]: ((c= @ ((cEXP @ V0) @ (cNUMERAL @ c_0))) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TDIV_1,(c! @ (^[V0]: ((c= @ ((cDIV @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))
(TSUC_SUB1,(c! @ (^[V0]: ((c= @ ((c- @ (cSUC @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))
(TSUB_0_conjunct0,(c! @ (^[V0]: ((c= @ ((c- @ (cNUMERAL @ c_0)) @ V0)) @ (cNUMERAL @ c_0)))))
(TARITH_SUB_conjunct5,(c! @ (^[V0]: ((c= @ ((c- @ (cBIT1 @ V0)) @ c_0)) @ (cBIT1 @ V0)))))
(TARITH_SUB_conjunct4,(c! @ (^[V0]: ((c= @ ((c- @ (cBIT0 @ V0)) @ c_0)) @ (cBIT0 @ V0)))))
(TARITH_SUB_conjunct3,(c! @ (^[V0]: ((c= @ ((c- @ c_0) @ (cBIT1 @ V0))) @ c_0))))
(TARITH_SUB_conjunct2,(c! @ (^[V0]: ((c= @ ((c- @ c_0) @ (cBIT0 @ V0))) @ c_0))))
(TSUB_0_conjunct1,(c! @ (^[V0]: ((c= @ ((c- @ V0) @ (cNUMERAL @ c_0))) @ V0))))
(TSUB_EQUAL_0,(c! @ (^[V0]: ((c= @ ((c- @ V0) @ V0)) @ (cNUMERAL @ c_0)))))
(TADD_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((c+ @ (cNUMERAL @ c_0)) @ V0)) @ V0))))
(TARITH_ADD_conjunct5,(c! @ (^[V0]: ((c= @ ((c+ @ (cBIT1 @ V0)) @ c_0)) @ (cBIT1 @ V0)))))
(TARITH_ADD_conjunct4,(c! @ (^[V0]: ((c= @ ((c+ @ (cBIT0 @ V0)) @ c_0)) @ (cBIT0 @ V0)))))
(TARITH_ADD_conjunct3,(c! @ (^[V0]: ((c= @ ((c+ @ c_0) @ (cBIT1 @ V0))) @ (cBIT1 @ V0)))))
(TARITH_ADD_conjunct2,(c! @ (^[V0]: ((c= @ ((c+ @ c_0) @ (cBIT0 @ V0))) @ (cBIT0 @ V0)))))
(TADD_0,(c! @ (^[V0]: ((c= @ ((c+ @ V0) @ (cNUMERAL @ c_0))) @ V0))))
(TMULT_CLAUSES_conjunct2,(c! @ (^[V0]: ((c= @ ((c* @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ V0))))
(TMULT_2,(c! @ (^[V0]: ((c= @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ ((c+ @ V0) @ V0)))))
(TMULT_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((c* @ (cNUMERAL @ c_0)) @ V0)) @ (cNUMERAL @ c_0)))))
(TARITH_MULT_conjunct5,(c! @ (^[V0]: ((c= @ ((c* @ (cBIT1 @ V0)) @ c_0)) @ c_0))))
(TARITH_MULT_conjunct4,(c! @ (^[V0]: ((c= @ ((c* @ (cBIT0 @ V0)) @ c_0)) @ c_0))))
(TARITH_MULT_conjunct3,(c! @ (^[V0]: ((c= @ ((c* @ c_0) @ (cBIT1 @ V0))) @ c_0))))
(TARITH_MULT_conjunct2,(c! @ (^[V0]: ((c= @ ((c* @ c_0) @ (cBIT0 @ V0))) @ c_0))))
(TMULT_CLAUSES_conjunct3,(c! @ (^[V0]: ((c= @ ((c* @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))
(TMULT_0,(c! @ (^[V0]: ((c= @ ((c* @ V0) @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)))))
(Ttriangle,(c! @ (^[V0]: ((c= @ (ctriangle @ V0)) @ ((cDIV @ ((c* @ V0) @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))
(Ttau,(c! @ (^[V0]: ((c= @ (ctau @ V0)) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)) @ (cCARD @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cnum_divides @ V2) @ V0)) @ V2)))))))))))
(TSIGMA_POW2,(c! @ (^[V0]: ((c= @ (csigma @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))) @ ((c- @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(Tsigma,(c! @ (^[V0]: ((c= @ (csigma @ V0)) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)) @ ((cnsum @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cnum_divides @ V2) @ V0)) @ V2)))))) @ (^[V1]: V1)))))))
(Tphi,(c! @ (^[V0]: ((c= @ (cphi @ V0)) @ (cCARD @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ V0)) @ (cnum_coprime @ ((c__comma__ @ V2) @ V0))))) @ V2))))))))))
(TPHI_ALT,(c! @ (^[V0]: ((c= @ (cphi @ V0)) @ (cCARD @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V2) @ V0))) @ ((c< @ V2) @ V0))) @ V2))))))))))
(Toddpart,(c! @ (^[V0]: ((c= @ (coddpart @ V0)) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)) @ (((cCOND @ (cODD @ V0)) @ V0) @ (coddpart @ ((cDIV @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TNUMBER_DENUMBER_conjunct1,(c! @ (^[V0]: ((c= @ (cnumber @ (cdenumber @ V0))) @ V0))))
(Tnumber,(c! @ (^[V0]: ((c= @ (cnumber @ V0)) @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ ((cDIV @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c- @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((cMOD @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))
(TNUM_OF_INT_OF_NUM,(c! @ (^[V0]: ((c= @ (cnum_of_int @ (cint_of_num @ V0))) @ V0))))
(TGCD_1_conjunct0,(c! @ (^[V0]: ((c= @ (cnum_gcd @ ((c__comma__ @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0))) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TGCD_0_conjunct0,(c! @ (^[V0]: ((c= @ (cnum_gcd @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0))) @ V0))))
(TGCD_1_conjunct1,(c! @ (^[V0]: ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TGCD_0_conjunct1,(c! @ (^[V0]: ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ (cNUMERAL @ c_0)))) @ V0))))
(TGCD_REFL,(c! @ (^[V0]: ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ V0))) @ V0))))
(TLCM_1_conjunct0,(c! @ (^[V0]: ((c= @ (clcm @ ((c__comma__ @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0))) @ V0))))
(TLCM_0_conjunct0,(c! @ (^[V0]: ((c= @ (clcm @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0))) @ (cNUMERAL @ c_0)))))
(TLCM_1_conjunct1,(c! @ (^[V0]: ((c= @ (clcm @ ((c__comma__ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0))))
(TLCM_0_conjunct1,(c! @ (^[V0]: ((c= @ (clcm @ ((c__comma__ @ V0) @ (cNUMERAL @ c_0)))) @ (cNUMERAL @ c_0)))))
(TLCM_REFL,(c! @ (^[V0]: ((c= @ (clcm @ ((c__comma__ @ V0) @ V0))) @ V0))))
(Tindex,(c! @ (^[V0]: ((c= @ (cindex @ V0)) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)) @ (((cCOND @ (cODD @ V0)) @ (cNUMERAL @ c_0)) @ (cSUC @ (cindex @ ((cDIV @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TDIST_LZERO,(c! @ (^[V0]: ((c= @ (cdist @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0))) @ V0))))
(TDIST_RZERO,(c! @ (^[V0]: ((c= @ (cdist @ ((c__comma__ @ V0) @ (cNUMERAL @ c_0)))) @ V0))))
(TNUMBER_DENUMBER_conjunct0,(c! @ (^[V0]: ((c= @ (cdenumber @ (cnumber @ V0))) @ V0))))
(TBINOM_PENULT,(c! @ (^[V0]: ((c= @ (cbinom @ ((c__comma__ @ (cSUC @ V0)) @ V0))) @ (cSUC @ V0)))))
(Tbinom_conjunct1,(c! @ (^[V0]: ((c= @ (cbinom @ ((c__comma__ @ (cNUMERAL @ c_0)) @ (cSUC @ V0)))) @ (cNUMERAL @ c_0)))))
(TBINOM_1,(c! @ (^[V0]: ((c= @ (cbinom @ ((c__comma__ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0))))
(Tbinom_conjunct0,(c! @ (^[V0]: ((c= @ (cbinom @ ((c__comma__ @ V0) @ (cNUMERAL @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TBINOM_REFL,(c! @ (^[V0]: ((c= @ (cbinom @ ((c__comma__ @ V0) @ V0))) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TBINARYSUM_BITSET,(c! @ (^[V0]: ((c= @ (cbinarysum @ (cbitset @ V0))) @ V0))))
(TARITH_SUC_conjunct0,(c! @ (^[V0]: ((c= @ (cSUC @ (cNUMERAL @ V0))) @ (cNUMERAL @ (cSUC @ V0))))))
(TARITH_SUC_conjunct3,(c! @ (^[V0]: ((c= @ (cSUC @ (cBIT1 @ V0))) @ (cBIT0 @ (cSUC @ V0))))))
(TARITH_SUC_conjunct2,(c! @ (^[V0]: ((c= @ (cSUC @ (cBIT0 @ V0))) @ (cBIT1 @ V0)))))
(TADD1,(c! @ (^[V0]: ((c= @ (cSUC @ V0)) @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TSUC_DEF,(c! @ (^[V0]: ((c= @ (cSUC @ V0)) @ (cmk_num @ (cIND_SUC @ (cdest_num @ V0)))))))
(TPRE_conjunct1,(c! @ (^[V0]: ((c= @ (cPRE @ (cSUC @ V0))) @ V0))))
(TARITH_PRE_conjunct0,(c! @ (^[V0]: ((c= @ (cPRE @ (cNUMERAL @ V0))) @ (cNUMERAL @ (cPRE @ V0))))))
(TARITH_PRE_conjunct3,(c! @ (^[V0]: ((c= @ (cPRE @ (cBIT1 @ V0))) @ (cBIT0 @ V0)))))
(TARITH_PRE_conjunct2,(c! @ (^[V0]: ((c= @ (cPRE @ (cBIT0 @ V0))) @ (((cCOND @ ((c= @ V0) @ c_0)) @ c_0) @ (cBIT1 @ (cPRE @ V0)))))))
(TBIT1_THM,(c! @ (^[V0]: ((c= @ (cNUMERAL @ (cBIT1 @ V0))) @ (cSUC @ ((c+ @ (cNUMERAL @ V0)) @ (cNUMERAL @ V0)))))))
(TBIT0_THM,(c! @ (^[V0]: ((c= @ (cNUMERAL @ (cBIT0 @ V0))) @ ((c+ @ (cNUMERAL @ V0)) @ (cNUMERAL @ V0))))))
(TNUMERAL,(c! @ (^[V0]: ((c= @ (cNUMERAL @ V0)) @ V0))))
(TISQRT_SUC,(c! @ (^[V0]: ((c= @ (cISQRT @ (cSUC @ V0))) @ (((cCOND @ (c? @ (^[V1]: ((c= @ (cSUC @ V0)) @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ (cSUC @ (cISQRT @ V0))) @ (cISQRT @ V0))))))
(TISQRT,(c! @ (^[V0]: ((c= @ (cISQRT @ V0)) @ (c__at__ @ (^[V1]: ((c/__caret__ @ ((c<= @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ ((c< @ V0) @ ((cEXP @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TFACT_conjunct1,(c! @ (^[V0]: ((c= @ (cFACT @ (cSUC @ V0))) @ ((c* @ (cSUC @ V0)) @ (cFACT @ V0))))))
(TCARD_NUMSEG_1,(c! @ (^[V0]: ((c= @ (cCARD @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0))) @ V0))))
(TCARD_NUMSEG_LE,(c! @ (^[V0]: ((c= @ (cCARD @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c<= @ V2) @ V0)) @ V2))))))) @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TCARD_NUMSEG_LT,(c! @ (^[V0]: ((c= @ (cCARD @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c< @ V2) @ V0)) @ V2))))))) @ V0))))
(TBIT1,(c! @ (^[V0]: ((c= @ (cBIT1 @ V0)) @ (cSUC @ ((c+ @ V0) @ V0))))))
(TBIT1_DEF,(c! @ (^[V0]: ((c= @ (cBIT1 @ V0)) @ (cSUC @ (cBIT0 @ V0))))))
(TBIT0_DEF_conjunct1,(c! @ (^[V0]: ((c= @ (cBIT0 @ (cSUC @ V0))) @ (cSUC @ (cSUC @ (cBIT0 @ V0)))))))
(TBIT0,(c! @ (^[V0]: ((c= @ (cBIT0 @ V0)) @ ((c+ @ V0) @ V0)))))
(TINDEX_ODDPART_DECOMPOSITION,(c! @ (^[V0]: ((c= @ V0) @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cindex @ V0))) @ (coddpart @ V0))))))
(Tnadd_of_num,(c! @ (^[V0]: ((c= @ (cnadd_of_num @ V0)) @ (cmk_nadd @ (^[V1]: ((c* @ V0) @ V1)))))))
(Tpoly_diff_aux_conjunct0,(c! @ (^[V0]: ((c= @ ((cpoly_diff_aux @ V0) @ cNIL)) @ cNIL))))
(TDELETE1_REVPERM,(c! @ (^[V0]: ((c= @ ((cDELETE1 @ V0) @ (cREVPERM @ (cSUC @ V0)))) @ (cREVPERM @ V0)))))
(TREVPERM_conjunct1,(c! @ (^[V0]: ((c= @ (cREVPERM @ (cSUC @ V0))) @ ((cCONS @ V0) @ (cREVPERM @ V0))))))
(TINT_POW_ONE,(c! @ (^[V0]: ((c= @ ((cint_pow @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TINT_POW_ZERO,(c! @ (^[V0]: ((c= @ ((cint_pow @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_OF_NUM_SUC,(c! @ (^[V0]: ((c= @ ((cint_add @ (cint_of_num @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cint_of_num @ (cSUC @ V0))))))
(Tint_of_num,(c! @ (^[V0]: ((c= @ (cint_of_num @ V0)) @ (cint_of_real @ (creal_of_num @ V0))))))
(TINT_ABS_NUM,(c! @ (^[V0]: ((c= @ (cint_abs @ (cint_of_num @ V0))) @ (cint_of_num @ V0)))))
(Threal_of_num_th,(c! @ (^[V0]: ((c= @ (cmk_hreal @ (cnadd_eq @ (cnadd_of_num @ V0)))) @ (chreal_of_num @ V0)))))
(Threal_of_num,(c! @ (^[V0]: ((c= @ (chreal_of_num @ V0)) @ (cmk_hreal @ (^[V1]: ((cnadd_eq @ (cnadd_of_num @ V0)) @ V1)))))))
(Tzset,(c! @ (^[V0]: ((c= @ (czset @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V1) @ ((c= @ ((c+ @ ((cEXP @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ V3) @ V4)))) @ V0)) @ ((c__comma__ @ V2) @ ((c__comma__ @ V3) @ V4)))))))))))))))
(TNADD_OF_NUM,(c! @ (^[V0]: ((c= @ (cdest_nadd @ (cnadd_of_num @ V0))) @ (^[V1]: ((c* @ V0) @ V1))))))
(TINJN,(c! @ (^[V0]: ((c= @ (cINJN @ V0)) @ (^[V1]: (^[V2]: ((c= @ V1) @ V0)))))))
(TNUMSEG_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((c.. @ V0) @ (cNUMERAL @ c_0))) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((cINSERT @ (cNUMERAL @ c_0)) @ cEMPTY)) @ cEMPTY)))))
(TNUMSEG_SING,(c! @ (^[V0]: ((c= @ ((c.. @ V0) @ V0)) @ ((cINSERT @ V0) @ cEMPTY)))))
(TSET_OF_LIST_REVPERM,(c! @ (^[V0]: ((c= @ (cset_of_list @ (cREVPERM @ V0))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c< @ V2) @ V0)) @ V2)))))))))
(Tfrom,(c! @ (^[V0]: ((c= @ (cfrom @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c<= @ V0) @ V2)) @ V2)))))))))
(Tcodeset,(c! @ (^[V0]: ((c= @ (ccodeset @ V0)) @ ((cIMAGE @ cSUC) @ (cbitset @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TBITSET_STEP_conjunct1,(c! @ (^[V0]: ((c= @ (cbitset @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cINSERT @ (cNUMERAL @ c_0)) @ ((cIMAGE @ cSUC) @ (cbitset @ V0)))))))
(TBITSET_STEP_conjunct0,(c! @ (^[V0]: ((c= @ (cbitset @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))) @ ((cIMAGE @ cSUC) @ (cbitset @ V0))))))
(Tbitset,(c! @ (^[V0]: ((c= @ (cbitset @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (cODD @ ((cDIV @ V0) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)))) @ V2)))))))))
(TNUMSEG_LE,(c! @ (^[V0]: ((c= @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c<= @ V2) @ V0)) @ V2)))))) @ ((c.. @ (cNUMERAL @ c_0)) @ V0)))))
(TNUMSEG_LT,(c! @ (^[V0]: ((c= @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c< @ V2) @ V0)) @ V2)))))) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ cEMPTY) @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TOUTER_ACI_conjunct3,(c! @ (^[V0]: ((c= @ ((couter @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY))) @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY)))) @ (cvec @ (cNUMERAL @ c_0))))))
(TOUTER_MBASIS_REFL,(c! @ (^[V0]: ((c= @ ((couter @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY))) @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY)))) @ (cvec @ (cNUMERAL @ c_0))))))
(TPASTECART_VEC,(c! @ (^[V0]: ((c= @ ((cpastecart @ (cvec @ V0)) @ (cvec @ V0))) @ (cvec @ V0)))))
(TLIFT_NUM,(c! @ (^[V0]: ((c= @ (clift @ (creal_of_num @ V0))) @ (cvec @ V0)))))
(Tvec,(c! @ (^[V0]: ((c= @ (cvec @ V0)) @ (clambda @ (^[V1]: (creal_of_num @ V0)))))))
(TSNDCART_VEC,(c! @ (^[V0]: ((c= @ (csndcart @ (cvec @ V0))) @ (cvec @ V0)))))
(TFSTCART_VEC,(c! @ (^[V0]: ((c= @ (cfstcart @ (cvec @ V0))) @ (cvec @ V0)))))
(Tbasis,(c! @ (^[V0]: ((c= @ (cbasis @ V0)) @ (clambda @ (^[V1]: (((cCOND @ ((c= @ V1) @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(Tmat,(c! @ (^[V0]: ((c= @ (cmat @ V0)) @ (clambda @ (^[V1]: (clambda @ (^[V2]: (((cCOND @ ((c= @ V1) @ V2)) @ (creal_of_num @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))
(TTRANSP_MAT,(c! @ (^[V0]: ((c= @ (ctransp @ (cmat @ V0))) @ (cmat @ V0)))))
(TREAL_LT_1_POW2,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))))))
(TREAL_POW2_CLAUSES_conjunct10,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))))) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))))))
(TDIVIDES_2,(c! @ (^[V0]: ((c= @ ((cnum_divides @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ (cEVEN @ V0)))))
(TDIVIDES_ZERO,(c! @ (^[V0]: ((c= @ ((cnum_divides @ (cNUMERAL @ c_0)) @ V0)) @ ((c= @ V0) @ (cNUMERAL @ c_0))))))
(TDIVIDES_ONE,(c! @ (^[V0]: ((c= @ ((cnum_divides @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(Tfinite_sum_tybij_conjunct1,(c! @ (^[V0]: ((c= @ ((cIN @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c+ @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))))) @ ((c= @ (cdest_finite_sum @ (cmk_finite_sum @ V0))) @ V0)))))
(Tfinite_image_tybij_conjunct1,(c! @ (^[V0]: ((c= @ ((cIN @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdest_finite_image @ (cfinite_index @ V0))) @ V0)))))
(Tind_model_tybij_conjunct1,(c! @ (^[V0]: ((c= @ ((cIN @ V0) @ (c__at__ @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (cFINITE @ V1)))))) @ ((c= @ (cdest_ind @ (cmk_ind @ V0))) @ V0)))))
(Tinacc_tybij_conjunct1,(c! @ (^[V0]: ((c= @ ((cIN @ V0) @ cUNIV)) @ ((c= @ (cdest_I @ (cmk_I @ V0))) @ V0)))))
(TARITH_GE_conjunct2,(c! @ (^[V0]: ((c= @ ((c>= @ c_0) @ (cBIT0 @ V0))) @ ((c>= @ c_0) @ V0)))))
(TARITH_GT_conjunct4,(c! @ (^[V0]: ((c= @ ((c> @ (cBIT0 @ V0)) @ c_0)) @ ((c> @ V0) @ c_0)))))
(TARITH_EQ_conjunct3,(c! @ (^[V0]: ((c= @ ((c= @ (cBIT1 @ V0)) @ c_0)) @ cF))))
(TARITH_EQ_conjunct2,(c! @ (^[V0]: ((c= @ ((c= @ (cBIT0 @ V0)) @ c_0)) @ ((c= @ V0) @ c_0)))))
(TARITH_EQ_conjunct5,(c! @ (^[V0]: ((c= @ ((c= @ c_0) @ (cBIT1 @ V0))) @ cF))))
(TARITH_EQ_conjunct4,(c! @ (^[V0]: ((c= @ ((c= @ c_0) @ (cBIT0 @ V0))) @ ((c= @ c_0) @ V0)))))
(TBITSET_EQ_EMPTY,(c! @ (^[V0]: ((c= @ ((c= @ (cbitset @ V0)) @ cEMPTY)) @ ((c= @ V0) @ (cNUMERAL @ c_0))))))
(TBASIS_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cbasis @ V0)) @ (cvec @ (cNUMERAL @ c_0)))) @ (c~ @ ((cIN @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))))))
(TARITH_LE_conjunct3,(c! @ (^[V0]: ((c= @ ((c<= @ (cBIT1 @ V0)) @ c_0)) @ cF))))
(TARITH_LE_conjunct2,(c! @ (^[V0]: ((c= @ ((c<= @ (cBIT0 @ V0)) @ c_0)) @ ((c<= @ V0) @ c_0)))))
(TARITH_LE_conjunct5,(c! @ (^[V0]: ((c= @ ((c<= @ c_0) @ (cBIT1 @ V0))) @ cT))))
(TARITH_LE_conjunct4,(c! @ (^[V0]: ((c= @ ((c<= @ c_0) @ (cBIT0 @ V0))) @ cT))))
(TLESS_EQ_0,(c! @ (^[V0]: ((c= @ ((c<= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V0) @ (cNUMERAL @ c_0))))))
(TLT_NZ,(c! @ (^[V0]: ((c= @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))))))
(TARITH_LT_conjunct3,(c! @ (^[V0]: ((c= @ ((c< @ (cBIT1 @ V0)) @ c_0)) @ cF))))
(TARITH_LT_conjunct2,(c! @ (^[V0]: ((c= @ ((c< @ (cBIT0 @ V0)) @ c_0)) @ cF))))
(TARITH_LT_conjunct5,(c! @ (^[V0]: ((c= @ ((c< @ c_0) @ (cBIT1 @ V0))) @ cT))))
(TARITH_LT_conjunct4,(c! @ (^[V0]: ((c= @ ((c< @ c_0) @ (cBIT0 @ V0))) @ ((c< @ c_0) @ V0)))))
(TLT_conjunct0,(c! @ (^[V0]: ((c= @ ((c< @ V0) @ (cNUMERAL @ c_0))) @ cF))))
(TPHI_PRIME_EQ,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ ((c= @ (cphi @ V0)) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (cprime @ V0)))))
(TREAL_LT_NZ,(c! @ (^[V0]: ((c= @ (c~ @ ((c= @ (creal_of_num @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_of_num @ V0))))))
(TNOT_ODD,(c! @ (^[V0]: ((c= @ (c~ @ (cODD @ V0))) @ (cEVEN @ V0)))))
(TNOT_EVEN,(c! @ (^[V0]: ((c= @ (c~ @ (cEVEN @ V0))) @ (cODD @ V0)))))
(TSIGMA_PRIME_EQ,(c! @ (^[V0]: ((c= @ (cprime @ V0)) @ ((c= @ (csigma @ V0)) @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(Tprime_DELTA,(c! @ (^[V0]: ((c= @ (cprime @ V0)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c< @ V1) @ V0)) @ ((c==> @ ((cnum_divides @ V1) @ V0)) @ ((c= @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))
(Tprime,(c! @ (^[V0]: ((c= @ (cprime @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V1]: ((c==> @ ((cnum_divides @ V1) @ V0)) @ ((c__caret__/ @ ((c= @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ V1) @ V0))))))))))
(TPRIME_DIVISOR_SQRT,(c! @ (^[V0]: ((c= @ (cprime @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V1) @ V0)) @ ((c<= @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))) @ ((c= @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TPRIME_PRIME_FACTOR,(c! @ (^[V0]: ((c= @ (cprime @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ ((cnum_divides @ V1) @ V0))) @ ((c= @ V1) @ V0)))))))))
(TPRIME_PRIME_FACTOR_SQRT,(c! @ (^[V0]: ((c= @ (cprime @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c~ @ (c? @ (^[V1]: ((c/__caret__ @ (cprime @ V1)) @ ((c/__caret__ @ ((cnum_divides @ V1) @ V0)) @ ((c<= @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))))))))))))
(TPRIME,(c! @ (^[V0]: ((c= @ (cprime @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V1)) @ ((c< @ V1) @ V0))) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1)))))))))))
(Tperfect,(c! @ (^[V0]: ((c= @ (cperfect @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ (csigma @ V0)) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)))))))
(TCOPRIME_2_conjunct0,(c! @ (^[V0]: ((c= @ (cnum_coprime @ ((c__comma__ @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))) @ (cODD @ V0)))))
(TCOPRIME_0_conjunct1,(c! @ (^[V0]: ((c= @ (cnum_coprime @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0))) @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TCOPRIME_2_conjunct1,(c! @ (^[V0]: ((c= @ (cnum_coprime @ ((c__comma__ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cODD @ V0)))))
(TCOPRIME_0_conjunct0,(c! @ (^[V0]: ((c= @ (cnum_coprime @ ((c__comma__ @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TCOPRIME_REFL,(c! @ (^[V0]: ((c= @ (cnum_coprime @ ((c__comma__ @ V0) @ V0))) @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TMULTIPLICATIVE_CONST,(c! @ (^[V0]: ((c= @ (cmultiplicative @ (^[V1]: V0))) @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TTERM,(c! @ (^[V0]: ((c= @ (cTERM @ V0)) @ (((cRTC @ cTERM1) @ (cNUMERAL @ c_0)) @ ((cNPAIR @ V0) @ (cNUMERAL @ c_0)))))))
(TODD_PHI_EQ,(c! @ (^[V0]: ((c= @ (cODD @ (cphi @ V0))) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))
(TODD_ODDPART,(c! @ (^[V0]: ((c= @ (cODD @ (coddpart @ V0))) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))))))
(TODD_conjunct1,(c! @ (^[V0]: ((c= @ (cODD @ (cSUC @ V0))) @ (c~ @ (cODD @ V0))))))
(TARITH_ODD_conjunct0,(c! @ (^[V0]: ((c= @ (cODD @ (cNUMERAL @ V0))) @ (cODD @ V0)))))
(TARITH_ODD_conjunct3,(c! @ (^[V0]: ((c= @ (cODD @ (cBIT1 @ V0))) @ cT))))
(TARITH_ODD_conjunct2,(c! @ (^[V0]: ((c= @ (cODD @ (cBIT0 @ V0))) @ cF))))
(TODD_MOD_2,(c! @ (^[V0]: ((c= @ (cODD @ V0)) @ (((c== @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))
(TODD_MOD,(c! @ (^[V0]: ((c= @ (cODD @ V0)) @ ((c= @ ((cMOD @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TODD_EXISTS,(c! @ (^[V0]: ((c= @ (cODD @ V0)) @ (c? @ (^[V1]: ((c= @ V0) @ (cSUC @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)))))))))
(TEVEN_PHI_EQ,(c! @ (^[V0]: ((c= @ (cEVEN @ (cphi @ V0))) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c<= @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))) @ V0))))))
(TEVEN_conjunct1,(c! @ (^[V0]: ((c= @ (cEVEN @ (cSUC @ V0))) @ (c~ @ (cEVEN @ V0))))))
(TARITH_EVEN_conjunct0,(c! @ (^[V0]: ((c= @ (cEVEN @ (cNUMERAL @ V0))) @ (cEVEN @ V0)))))
(TARITH_EVEN_conjunct3,(c! @ (^[V0]: ((c= @ (cEVEN @ (cBIT1 @ V0))) @ cF))))
(TARITH_EVEN_conjunct2,(c! @ (^[V0]: ((c= @ (cEVEN @ (cBIT0 @ V0))) @ cT))))
(TEVEN_MOD_2,(c! @ (^[V0]: ((c= @ (cEVEN @ V0)) @ (((c== @ V0) @ (cNUMERAL @ c_0)) @ (cnum_mod @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))
(TEVEN_MOD,(c! @ (^[V0]: ((c= @ (cEVEN @ V0)) @ ((c= @ ((cMOD @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ c_0))))))
(TEVEN_DIV,(c! @ (^[V0]: ((c= @ (cEVEN @ V0)) @ ((c= @ V0) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ ((cDIV @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))
(TEVEN_EXISTS,(c! @ (^[V0]: ((c= @ (cEVEN @ V0)) @ (c? @ (^[V1]: ((c= @ V0) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))))))))
(TEVEN_ODD_DECOMPOSITION,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cODD @ V2)) @ ((c= @ V0) @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ V2)))))))) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))))))
(TFNIL,(c! @ (^[V0]: ((c= @ (cFNIL @ V0)) @ (c__at__ @ (^[V1]: cT))))))
(TISQRT_WORKS_conjunct0,(c! @ (^[V0]: ((c<= @ ((cEXP @ (cISQRT @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))))
(TPHI_LIMIT,(c! @ (^[V0]: ((c<= @ (cphi @ V0)) @ V0))))
(TODDPART_LE,(c! @ (^[V0]: ((c<= @ (coddpart @ V0)) @ V0))))
(TFACT_LE,(c! @ (^[V0]: ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cFACT @ V0)))))
(TLE_0,(c! @ (^[V0]: ((c<= @ (cNUMERAL @ c_0)) @ V0))))
(TLE_SQUARE_REFL,(c! @ (^[V0]: ((c<= @ V0) @ ((c* @ V0) @ V0)))))
(TLESS_EQ_SUC_REFL,(c! @ (^[V0]: ((c<= @ V0) @ (cSUC @ V0)))))
(TFACT_LE_REFL,(c! @ (^[V0]: ((c<= @ V0) @ (cFACT @ V0)))))
(TLESS_EQ_REFL,(c! @ (^[V0]: ((c<= @ V0) @ V0))))
(TLESS_0,(c! @ (^[V0]: ((c< @ (cNUMERAL @ c_0)) @ (cSUC @ V0)))))
(TFACT_LESS,(c! @ (^[V0]: ((c< @ (cNUMERAL @ c_0)) @ (cFACT @ V0)))))
(TISQRT_WORKS_conjunct1,(c! @ (^[V0]: ((c< @ V0) @ ((cEXP @ ((c+ @ (cISQRT @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))
(TLT_POW2_REFL,(c! @ (^[V0]: ((c< @ V0) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)))))
(TLESS_SUC_REFL,(c! @ (^[V0]: ((c< @ V0) @ (cSUC @ V0)))))
(TARITH_GE_conjunct3,(c! @ (^[V0]: (c~ @ ((c>= @ c_0) @ (cBIT1 @ V0))))))
(TARITH_GT_conjunct3,(c! @ (^[V0]: (c~ @ ((c> @ c_0) @ (cBIT1 @ V0))))))
(TARITH_GT_conjunct2,(c! @ (^[V0]: (c~ @ ((c> @ c_0) @ (cBIT0 @ V0))))))
(TREAL_FACT_NZ,(c! @ (^[V0]: (c~ @ ((c= @ (creal_of_num @ (cFACT @ V0))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TNOT_SUC,(c! @ (^[V0]: (c~ @ ((c= @ (cSUC @ V0)) @ (cNUMERAL @ c_0))))))
(TSUC_NOT,(c! @ (^[V0]: (c~ @ ((c= @ (cNUMERAL @ c_0)) @ (cSUC @ V0))))))
(TFACT_NZ,(c! @ (^[V0]: (c~ @ ((c= @ (cFACT @ V0)) @ (cNUMERAL @ c_0))))))
(TNOT_LESS_0,(c! @ (^[V0]: (c~ @ ((c< @ V0) @ (cNUMERAL @ c_0))))))
(TLESS_REFL,(c! @ (^[V0]: (c~ @ ((c< @ V0) @ V0)))))
(TEVEN_AND_ODD,(c! @ (^[V0]: (c~ @ ((c/__caret__ @ (cEVEN @ V0)) @ (cODD @ V0))))))
(TPRIME_4X,(c! @ (^[V0]: (c~ @ (cprime @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0))))))
(TPRIME_SQUARE,(c! @ (^[V0]: (c~ @ (cprime @ ((c* @ V0) @ V0))))))
(TSUBSPACE_SPECIAL_HYPERPLANE,(c! @ (^[V0]: (csubspace @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c= @ ((c$ @ V2) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V2)))))))))
(TSUBSPACE_SUBSTANDARD,(c! @ (^[V0]: (csubspace @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ V0) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ V2) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ V2)))))))))
(TRATIONAL_NUM,(c! @ (^[V0]: (crational @ (creal_of_num @ V0)))))
(TRADICAL_RULES_conjunct0,(c! @ (^[V0]: (cradical @ (creal_of_num @ V0)))))
(TCOPRIME_PLUS1,(c! @ (^[V0]: (cnum_coprime @ ((c__comma__ @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)))))
(TCOPRIME_1,(c! @ (^[V0]: (cnum_coprime @ ((c__comma__ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TMULTIPLICATIVE_POWERSUM,(c! @ (^[V0]: (cmultiplicative @ (^[V1]: ((cnsum @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cnum_divides @ V3) @ V1)) @ V3)))))) @ (^[V2]: ((cEXP @ V2) @ V0))))))))
(TMULTIPLICATIVE_GCD,(c! @ (^[V0]: (cmultiplicative @ (^[V1]: (cnum_gcd @ ((c__comma__ @ V0) @ V1)))))))
(TLINEAR_LIFT_COMPONENT,(c! @ (^[V0]: (clinear @ (^[V1]: (clift @ ((c$ @ V1) @ V0)))))))
(TINTEGRAL_VECTOR_STDBASIS,(c! @ (^[V0]: (cintegral_vector @ (cbasis @ V0)))))
(TINTEGRAL_VECTOR_VEC,(c! @ (^[V0]: (cintegral_vector @ (cvec @ V0)))))
(TINTEGER_CLOSED_conjunct0,(c! @ (^[V0]: (cinteger @ (creal_of_num @ V0)))))
(TCLOSED_SUBSTANDARD,(c! @ (^[V0]: (cclosed @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ V0) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ V2) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ V2)))))))))
(TODD_DOUBLE,(c! @ (^[V0]: (cODD @ (cSUC @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))))))
(TLIST_UNIQ_REVPERM,(c! @ (^[V0]: (cLIST_UNIQ @ (cREVPERM @ V0)))))
(TINFINITE_FROM,(c! @ (^[V0]: (cINFINITE @ (cfrom @ V0)))))
(TFINITE_BITSET,(c! @ (^[V0]: (cFINITE @ (cbitset @ V0)))))
(TFINITE_NUMSEG_LE,(c! @ (^[V0]: (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c<= @ V2) @ V0)) @ V2)))))))))
(TFINITE_NUMSEG_LT,(c! @ (^[V0]: (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c< @ V2) @ V0)) @ V2)))))))))
(TPHI_FINITE_LEMMA,(c! @ (^[V0]: (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V2) @ V0))) @ ((c< @ V2) @ V0))) @ V2)))))))))
(TEVEN_DOUBLE,(c! @ (^[V0]: (cEVEN @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)))))
(TREAL_INTEGER_CLOSURES_conjunct0,(c! @ (^[V0]: (c? @ (^[V1]: ((c= @ (creal_abs @ (creal_of_num @ V0))) @ (creal_of_num @ V1)))))))
(TNUMBER_SURJ,(c! @ (^[V0]: (c? @ (^[V1]: ((c= @ (cnumber @ V1)) @ V0))))))
(TFINITE_INDEX_INRANGE_2,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c= @ ((c$ @ V2) @ V0)) @ ((c$ @ V2) @ V1))))) @ (c! @ (^[V2]: ((c= @ ((c$ @ V2) @ V0)) @ ((c$ @ V2) @ V1))))))))))))
(TFINITE_INDEX_INRANGE,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ (c! @ (^[V2]: ((c= @ ((c$ @ V2) @ V0)) @ ((c$ @ V2) @ V1)))))))))))
(TEUCLID,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (cprime @ V1)) @ ((c> @ V1) @ V0)))))))
(TEUCLID_BOUND,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (cprime @ V1)) @ ((c/__caret__ @ ((c< @ V0) @ V1)) @ ((c<= @ V1) @ (cSUC @ (cFACT @ V0))))))))))
(TLAGRANGE_REAL_NUM,(c! @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ (creal_of_num @ V0)) @ ((creal_add @ ((creal_pow @ (creal_of_num @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ (creal_of_num @ V2)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ (creal_of_num @ V3)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (creal_of_num @ V4)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))))))
(TLAGRANGE_NUM,(c! @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V0) @ ((c+ @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c+ @ ((cEXP @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c+ @ ((cEXP @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cEXP @ V4) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))))))
(TINT_EUCLID_BOUND,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (cint_prime @ V1)) @ ((c/__caret__ @ ((cint_lt @ (cint_of_num @ V0)) @ V1)) @ ((cint_le @ V1) @ ((cint_add @ (cint_of_num @ (cFACT @ V0))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))
(TREAL_SUB_POW_R1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c= @ ((creal_sub @ ((creal_pow @ V1) @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ V1) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (^[V2]: ((creal_pow @ V1) @ V2)))))))))))
(TREAL_SUB_POW_L1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c= @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_pow @ V1) @ V0))) @ ((creal_mul @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (^[V2]: ((creal_pow @ V1) @ V2)))))))))))
(TREAL_LT_FRACTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c= @ ((creal_lt @ ((creal_div @ V1) @ (creal_of_num @ V0))) @ V1)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))))))))
(TREAL_LT_MULTIPLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c= @ ((creal_lt @ V1) @ ((creal_mul @ (creal_of_num @ V0)) @ V1))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))))))))
(TNEGLIGIBLE_STANDARD_HYPERPLANE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ (cnegligible @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((c$ @ V3) @ V0)) @ V1)) @ V3))))))))))))
(TREAL_POW_EQ_1_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((creal_pow @ V1) @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c= @ (creal_abs @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TREAL_LT_FRACTION_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_div @ V1) @ (creal_of_num @ V0)))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))))))))
(TREAL_ABS_LEMMA1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_mul @ (creal_of_num @ V0)) @ (creal_abs @ V1))) @ (creal_abs @ ((creal_mul @ (creal_of_num @ V0)) @ V1))))))))
(TSUM_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0)) @ (^[V2]: V1))) @ ((creal_mul @ (creal_of_num @ V0)) @ V1)))))))
(TINTERIOR_HALFSPACE_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinterior @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_le @ ((c$ @ V3) @ V0)) @ V1)) @ V3))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_lt @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TINTERIOR_HALFSPACE_COMPONENT_GE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinterior @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_ge @ ((c$ @ V3) @ V0)) @ V1)) @ V3))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_gt @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TINTERIOR_STANDARD_HYPERPLANE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinterior @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((c$ @ V3) @ V0)) @ V1)) @ V3))))))) @ cEMPTY))))))
(TCLOSURE_HALFSPACE_COMPONENT_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cclosure @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_lt @ ((c$ @ V3) @ V0)) @ V1)) @ V3))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_le @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TCLOSURE_HALFSPACE_COMPONENT_GT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cclosure @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_gt @ ((c$ @ V3) @ V0)) @ V1)) @ V3))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_ge @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TUNBOUNDED_HALFSPACE_COMPONENT_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_lt @ ((c$ @ V3) @ V0)) @ V1)) @ V3))))))))))))
(TUNBOUNDED_HALFSPACE_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_le @ ((c$ @ V3) @ V0)) @ V1)) @ V3))))))))))))
(TUNBOUNDED_HALFSPACE_COMPONENT_GT,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_gt @ ((c$ @ V3) @ V0)) @ V1)) @ V3))))))))))))
(TUNBOUNDED_HALFSPACE_COMPONENT_GE,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_ge @ ((c$ @ V3) @ V0)) @ V1)) @ V3))))))))))))
(TOPEN_HALFSPACE_COMPONENT_LT,(c! @ (^[V0]: (c! @ (^[V1]: (copen @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_lt @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TOPEN_HALFSPACE_COMPONENT_GT,(c! @ (^[V0]: (c! @ (^[V1]: (copen @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_gt @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TCONVEX_HALFSPACE_COMPONENT_LT,(c! @ (^[V0]: (c! @ (^[V1]: (cconvex @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_lt @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TCONVEX_HALFSPACE_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (cconvex @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_le @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TCONVEX_HALFSPACE_COMPONENT_GT,(c! @ (^[V0]: (c! @ (^[V1]: (cconvex @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_gt @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TCONVEX_HALFSPACE_COMPONENT_GE,(c! @ (^[V0]: (c! @ (^[V1]: (cconvex @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_ge @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TCONVEX_STANDARD_HYPERPLANE,(c! @ (^[V0]: (c! @ (^[V1]: (cconvex @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TCLOSED_HALFSPACE_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (cclosed @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_le @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TCLOSED_HALFSPACE_COMPONENT_GE,(c! @ (^[V0]: (c! @ (^[V1]: (cclosed @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_ge @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TCLOSED_STANDARD_HYPERPLANE,(c! @ (^[V0]: (c! @ (^[V1]: (cclosed @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TAFFINE_STANDARD_HYPERPLANE,(c! @ (^[V0]: (c! @ (^[V1]: (caffine @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((c$ @ V3) @ V0)) @ V1)) @ V3)))))))))))
(TREAL_POW_LT2_REV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((creal_lt @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V2) @ V0)))) @ ((creal_lt @ V1) @ V2)))))))))
(TREAL_POW_EQ_ABS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V2) @ V0)))) @ ((c= @ (creal_abs @ V1)) @ (creal_abs @ V2))))))))))
(TREAL_POW_LE2_REV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((creal_le @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V2) @ V0))))) @ ((creal_le @ V1) @ V2)))))))))
(TREAL_POW_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c= @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V2) @ V0)))))) @ ((c= @ V1) @ V2)))))))))
(TREAL_POW_EQ_ODD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cODD @ V0)) @ ((c= @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V2) @ V0)))) @ ((c= @ V1) @ V2)))))))))
(TREAL_POW_LT2_ODD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cODD @ V0)) @ ((c= @ ((creal_lt @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V2) @ V0))) @ ((creal_lt @ V1) @ V2))))))))))
(TREAL_POW_LE2_ODD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cODD @ V0)) @ ((c= @ ((creal_le @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V2) @ V0))) @ ((creal_le @ V1) @ V2))))))))))
(TREAL_POW_EQ_ODD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cODD @ V0)) @ ((c= @ ((c= @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V2) @ V0))) @ ((c= @ V1) @ V2))))))))))
(TREAL_POW_EQ_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V2) @ V0))) @ (((cCOND @ (cEVEN @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ (creal_abs @ V1)) @ (creal_abs @ V2)))) @ ((c= @ V1) @ V2))))))))))
(TSUM_GP_MULTIPLIED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V0) @ V2)) @ ((c= @ ((creal_mul @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)) @ ((csum @ ((c.. @ V0) @ V2)) @ (^[V3]: ((creal_pow @ V1) @ V3))))) @ ((creal_sub @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V1) @ (cSUC @ V2))))))))))))
(TREAL_POW_MONO_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)) @ ((c< @ V0) @ V2))) @ ((creal_lt @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V1) @ V2))))))))))
(TREAL_POW_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)) @ ((c<= @ V0) @ V2))) @ ((creal_le @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V1) @ V2))))))))))
(TREAL_POW_MONO_INV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((creal_le @ V1) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c<= @ V2) @ V0)))) @ ((creal_le @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V1) @ V2))))))))))
(TREAL_POW_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c<= @ V2) @ V0))) @ ((c= @ ((creal_pow @ V1) @ ((c- @ V0) @ V2))) @ ((creal_div @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V1) @ V2)))))))))))
(TPOW_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_pow @ V1) @ ((c+ @ V0) @ V2))) @ ((creal_mul @ ((creal_pow @ V1) @ V0)) @ ((creal_pow @ V1) @ V2))))))))))
(TDET_ROW_OPERATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V0) @ V2))))))) @ ((c= @ (cdet @ (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V0)) @ ((cvector_add @ ((crow @ V0) @ V3)) @ ((c% @ V1) @ ((crow @ V2) @ V3)))) @ ((crow @ V4) @ V3)))))) @ (cdet @ V3))))))))))))
(TTAGGED_DIVISION_UNION_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((ctagged_division_of @ V2) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_le @ ((c$ @ V7) @ V0)) @ V1)) @ V7)))))))) @ ((ctagged_division_of @ V3) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_ge @ ((c$ @ V7) @ V0)) @ V1)) @ V7))))))))))) @ ((ctagged_division_of @ ((cUNION @ V2) @ V3)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))))))))))))))))
(TREAL_MUL_RSUM0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_mul @ V1) @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0)) @ V2))) @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0)) @ (^[V3]: ((creal_mul @ V1) @ (V2 @ V3))))))))))))
(TSERIES_RATIO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ V1) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V4]: ((c==> @ ((c>= @ V4) @ V0)) @ ((creal_le @ (cvector_norm @ (V2 @ (cSUC @ V4)))) @ ((creal_mul @ V1) @ (cvector_norm @ (V2 @ V4))))))))) @ (c? @ (^[V4]: (((csums @ V2) @ V4) @ V3)))))))))))))
(THOMEOMORPHIC_STANDARD_HYPERPLANE_HYPERPLANE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV))))) @ ((chomeomorphic @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((c$ @ V5) @ V0)) @ V1)) @ V5)))))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V2) @ V5)) @ V3)) @ V5))))))))))))))))
(TINTERVAL_SPLIT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((c= @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((creal_ge @ ((c$ @ V5) @ V0)) @ V1)) @ V5))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V0)) @ ((creal_max @ ((c$ @ V2) @ V0)) @ V1)) @ ((c$ @ V2) @ V4))))) @ V3)) @ cNIL)))))))))))))
(TDIVISION_POINTS_SUBSET_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV)))) @ ((creal_lt @ ((c$ @ V2) @ V5)) @ ((c$ @ V3) @ V5)))))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V2) @ V0)) @ V1)) @ ((creal_lt @ V1) @ ((c$ @ V3) @ V0)))))))) @ ((cSUBSET @ ((cdivision_points @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((c$ @ V6) @ V0)) @ V1)) @ V6))))))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V4)) @ (c~ @ ((c= @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_le @ ((c$ @ V8) @ V0)) @ V1)) @ V8))))))) @ cEMPTY)))) @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_le @ ((c$ @ V8) @ V0)) @ V1)) @ V8))))))))))))) @ ((cdivision_points @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V4))))))))))))))
(TDIVISION_POINTS_SUBSET_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV)))) @ ((creal_lt @ ((c$ @ V2) @ V5)) @ ((c$ @ V3) @ V5)))))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V2) @ V0)) @ V1)) @ ((creal_lt @ V1) @ ((c$ @ V3) @ V0)))))))) @ ((cSUBSET @ ((cdivision_points @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_ge @ ((c$ @ V6) @ V0)) @ V1)) @ V6))))))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V4)) @ (c~ @ ((c= @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_ge @ ((c$ @ V8) @ V0)) @ V1)) @ V8))))))) @ cEMPTY)))) @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_ge @ ((c$ @ V8) @ V0)) @ V1)) @ V8))))))))))))) @ ((cdivision_points @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V4))))))))))))))
(TDIVISION_POINTS_PSUBSET_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV)))) @ ((creal_lt @ ((c$ @ V2) @ V5)) @ ((c$ @ V3) @ V5)))))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ ((creal_lt @ V1) @ ((c$ @ V3) @ V0))) @ (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V5) @ V4)) @ ((c__caret__/ @ ((c= @ ((c$ @ (cinterval_lowerbound @ V5)) @ V0)) @ V1)) @ ((c= @ ((c$ @ (cinterval_upperbound @ V5)) @ V0)) @ V1)))))))))))) @ ((cPSUBSET @ ((cdivision_points @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((c$ @ V6) @ V0)) @ V1)) @ V6))))))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V4)) @ (c~ @ ((c= @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_le @ ((c$ @ V8) @ V0)) @ V1)) @ V8))))))) @ cEMPTY)))) @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_le @ ((c$ @ V8) @ V0)) @ V1)) @ V8))))))))))))) @ ((cdivision_points @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V4))))))))))))))
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(TINTEGRAL_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV))))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V4)) @ ((cvector_add @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V0)) @ ((creal_min @ ((c$ @ V3) @ V0)) @ V1)) @ ((c$ @ V3) @ V5)))))) @ cNIL))) @ V4)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V0)) @ ((creal_max @ ((c$ @ V2) @ V0)) @ V1)) @ ((c$ @ V2) @ V5))))) @ V3)) @ cNIL))) @ V4)))))))))))))))
(TDIVISION_0,(c! @ (^[V0]: (c! @ (^[V1]: (((cCOND @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ ((c= @ ((cDIV @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ ((c= @ ((cMOD @ V0) @ V1)) @ V0))) @ ((c/__caret__ @ ((c= @ V0) @ ((c+ @ ((c* @ ((cDIV @ V0) @ V1)) @ V1)) @ ((cMOD @ V0) @ V1)))) @ ((c< @ ((cMOD @ V0) @ V1)) @ V1))))))))
(TORDER,(c! @ (^[V0]: (c! @ (^[V1]: (((c== @ ((cEXP @ V0) @ ((corder @ V1) @ V0))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1)))))))
(TTREAL_OF_NUM_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((ctreal_eq @ ((ctreal_mul @ (ctreal_of_num @ V0)) @ (ctreal_of_num @ V1))) @ (ctreal_of_num @ ((c* @ V0) @ V1))))))))
(TTREAL_OF_NUM_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((ctreal_eq @ ((ctreal_add @ (ctreal_of_num @ V0)) @ (ctreal_of_num @ V1))) @ (ctreal_of_num @ ((c+ @ V0) @ V1))))))))
(TDIVIDES_EXP_MINUS1,(c! @ (^[V0]: (c! @ (^[V1]: ((cnum_divides @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c- @ ((cEXP @ V0) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TGCD_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cnum_divides @ (cnum_gcd @ ((c__comma__ @ V1) @ V0))) @ V1))))))
(TGCD_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cnum_divides @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ V1))))))
(TEGCD_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cnum_divides @ (cegcd @ ((c__comma__ @ V1) @ V0))) @ V1))))))
(TEGCD_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cnum_divides @ (cegcd @ ((c__comma__ @ V0) @ V1))) @ V1))))))
(TLCM_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cnum_divides @ V1) @ (clcm @ ((c__comma__ @ V0) @ V1))))))))
(TLCM_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cnum_divides @ V0) @ (clcm @ ((c__comma__ @ V0) @ V1))))))))
(TNADD_OF_NUM_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((cnadd_eq @ ((cnadd_mul @ (cnadd_of_num @ V0)) @ (cnadd_of_num @ V1))) @ (cnadd_of_num @ ((c* @ V0) @ V1))))))))
(TNADD_OF_NUM_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((cnadd_eq @ ((cnadd_add @ (cnadd_of_num @ V0)) @ (cnadd_of_num @ V1))) @ (cnadd_of_num @ ((c+ @ V0) @ V1))))))))
(TLESS_LESS_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((c= @ V1) @ V0)) @ ((c__caret__/ @ ((c< @ V1) @ V0)) @ ((c< @ V0) @ V1))))))))
(TLESS_EQ_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((c<= @ V1) @ V0)) @ ((c<= @ V0) @ V1)))))))
(TLET_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((c<= @ V1) @ V0)) @ ((c< @ V0) @ V1)))))))
(TLESS_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((c< @ V1) @ V0)) @ ((c<= @ V0) @ V1)))))))
(TLT_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((c< @ V0) @ V1)) @ ((c__caret__/ @ ((c< @ V1) @ V0)) @ ((c= @ V0) @ V1))))))))
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(THAS_SIZE_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: ((cHAS_SIZE @ ((c.. @ V1) @ V0)) @ ((c- @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)))))))
(TCONG_1_DIVIDES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (((c== @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V0))) @ ((cnum_divides @ V0) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TDIVIDES_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cnum_divides @ V0) @ V1)) @ ((c__caret__/ @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ ((c__caret__/ @ ((c= @ V1) @ V0)) @ ((c<= @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ V1)))))))))
(TDIVIDES_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cnum_divides @ V0) @ V1)) @ ((c__caret__/ @ ((c<= @ V0) @ V1)) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
(TDIVIDES_LE_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cnum_divides @ V0) @ V1)) @ ((c__caret__/ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ V1))) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
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(TBITSET_BOUND_WEAK,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V0) @ (cbitset @ V1))) @ ((c< @ V0) @ V1)))))))
(TOUTER_ACI_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c> @ V0) @ V1)) @ ((c= @ ((couter @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY))) @ (cmbasis @ ((cINSERT @ V1) @ cEMPTY)))) @ ((c% @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((couter @ (cmbasis @ ((cINSERT @ V1) @ cEMPTY))) @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY)))))))))))
(TTREAL_OF_NUM_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ V0) @ V1)) @ ((ctreal_eq @ (ctreal_of_num @ V0)) @ (ctreal_of_num @ V1))))))))
(TNADD_OF_NUM_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ V0) @ V1)) @ ((cnadd_eq @ (cnadd_of_num @ V0)) @ (cnadd_of_num @ V1))))))))
(TEQ_IMP_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ V0) @ V1)) @ ((c<= @ V0) @ V1)))))))
(TOR_LESS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ (cSUC @ V0)) @ V1)) @ ((c< @ V0) @ V1)))))))
(TCONG_EXP_MINUS1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ (((c== @ ((cEXP @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ (((cCOND @ (cEVEN @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cnum_mod @ V1))))))))
(TREAL_OF_NUM_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V1) @ V0)) @ ((c= @ ((creal_sub @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ (creal_of_num @ ((c- @ V0) @ V1)))))))))
(TADD_SUM_DIFF_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V1) @ V0)) @ ((c= @ ((c- @ ((c+ @ V0) @ V1)) @ ((c- @ V0) @ V1))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))))))))
(TGCD_SUB_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V1) @ V0)) @ ((c= @ (cnum_gcd @ ((c__comma__ @ ((c- @ V0) @ V1)) @ V1))) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1)))))))))
(TINT_OF_NUM_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V1) @ V0)) @ ((c= @ ((cint_sub @ (cint_of_num @ V0)) @ (cint_of_num @ V1))) @ (cint_of_num @ ((c- @ V0) @ V1)))))))))
(TLESS_EQUAL_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V1) @ V0)) @ (c? @ (^[V2]: ((c= @ V0) @ ((c+ @ V1) @ V2))))))))))
(TNUMSEG_REC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V0) @ (cSUC @ V1))) @ ((c= @ ((c.. @ V0) @ (cSUC @ V1))) @ ((cINSERT @ (cSUC @ V1)) @ ((c.. @ V0) @ V1)))))))))
(TREAL_MONO_POW2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V0) @ V1)) @ ((creal_le @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))))))))
(TSUB_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V0) @ V1)) @ ((c= @ ((c+ @ ((c- @ V1) @ V0)) @ V0)) @ V1)))))))
(TADD_SUM_DIFF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V0) @ V1)) @ ((c= @ ((c+ @ ((c+ @ V1) @ V0)) @ ((c- @ V1) @ V0))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))))))))
(TGCD_SUB_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V0) @ V1)) @ ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ ((c- @ V1) @ V0)))) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1)))))))))
(TNUMSEG_RREC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V0) @ V1)) @ ((c= @ ((cINSERT @ V1) @ ((c.. @ V0) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c.. @ V0) @ V1))))))))
(TNUMSEG_LREC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V0) @ V1)) @ ((c= @ ((cINSERT @ V0) @ ((c.. @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1))) @ ((c.. @ V0) @ V1))))))))
(TFACT_MONO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V0) @ V1)) @ ((c<= @ (cFACT @ V0)) @ (cFACT @ V1))))))))
(TLESS_EQ_IMP_LESS_SUC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V0) @ V1)) @ ((c< @ V0) @ (cSUC @ V1))))))))
(TEXP_LE_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V1) @ ((cEXP @ V0) @ V1))))))))
(TMOD_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ V1) @ V0)) @ ((c= @ ((cMOD @ V1) @ V0)) @ V1)))))))
(TLESS_ADD_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ V1) @ V0)) @ (c? @ (^[V2]: ((c= @ V0) @ ((c+ @ V1) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TLESS_LEMMA1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ V0) @ (cSUC @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ V1)) @ ((c< @ V0) @ V1))))))))
(TDIFF_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ V0) @ V1)) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c< @ ((c+ @ V0) @ ((c- @ V1) @ V0))) @ ((c+ @ V0) @ V1)))))))))
(TDIV_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ V0) @ V1)) @ ((c= @ ((cDIV @ V0) @ V1)) @ (cNUMERAL @ c_0))))))))
(TBINOM_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ V0) @ V1)) @ ((c= @ (cbinom @ ((c__comma__ @ V0) @ V1))) @ (cNUMERAL @ c_0))))))))
(TLESS_OR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ V0) @ V1)) @ ((c<= @ (cSUC @ V0)) @ V1)))))))
(TLESS_IMP_LESS_OR_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ V0) @ V1)) @ ((c<= @ V0) @ V1)))))))
(TLESS_SUC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ V0) @ V1)) @ ((c< @ V0) @ (cSUC @ V1))))))))
(THAS_SIZE_FUNSPACE_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ cUNIV) @ V1)) @ ((cHAS_SIZE @ cUNIV) @ V0))) @ ((cHAS_SIZE @ cUNIV) @ ((cEXP @ V0) @ V1))))))))
(TBASIS_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ (cbasis @ V1)) @ V0)) @ (((cCOND @ ((c= @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))
(TDIVIDES_FACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ V1))) @ ((cnum_divides @ V0) @ (cFACT @ V1))))))))
(TDOT_BASIS_BASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))))) @ ((c= @ ((cdot @ (cbasis @ V0)) @ (cbasis @ V1))) @ (((cCOND @ ((c= @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))
(TORTHOGONAL_BASIS_BASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))))) @ ((c= @ ((corthogonal @ (cbasis @ V0)) @ (cbasis @ V1))) @ (c~ @ ((c= @ V0) @ V1)))))))))
(TBASIS_INJ_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))))) @ ((c= @ ((c= @ (cbasis @ V0)) @ (cbasis @ V1))) @ ((c= @ V0) @ V1))))))))
(TBASIS_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c= @ (cbasis @ V0)) @ (cbasis @ V1))))))) @ ((c= @ V0) @ V1)))))))
(TBASIS_NE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V0) @ V1))))))) @ (c~ @ ((c= @ (cbasis @ V0)) @ (cbasis @ V1)))))))))
(TFINITE_INDEX_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))))) @ ((c= @ ((c= @ (cfinite_index @ V0)) @ (cfinite_index @ V1))) @ ((c= @ V0) @ V1))))))))
(TLUCAS_WEAK,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ ((c/__caret__ @ (((c== @ ((cEXP @ V0) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c< @ V2) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (c~ @ (((c== @ ((cEXP @ V0) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1))))))))) @ (cprime @ V1)))))))
(TLUCAS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ ((c/__caret__ @ (((c== @ ((cEXP @ V0) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cprime @ V2)) @ ((cnum_divides @ V2) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (c~ @ (((c== @ ((cEXP @ V0) @ ((cDIV @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1))))))))) @ (cprime @ V1)))))))
(TLESS_EQUAL_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ V0) @ V1)) @ ((c<= @ V1) @ V0))) @ ((c= @ V0) @ V1)))))))
(TSIGMA_MULT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1))) @ ((c<= @ ((c+ @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c+ @ V1) @ ((c* @ V0) @ V1)))) @ (csigma @ ((c* @ V0) @ V1)))))))))
(TDIVIDES_DIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c= @ ((cMOD @ V1) @ V0)) @ (cNUMERAL @ c_0)))) @ ((cnum_divides @ V0) @ V1)))))))
(TDIVIDES_TRIVIAL_UPPERBOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))) @ (c~ @ ((cnum_divides @ ((cEXP @ V0) @ V1)) @ V1))))))))
(TFACTORIZATION_INDEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cnum_divides @ ((cEXP @ V0) @ V2)) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((c< @ V2) @ V3)) @ (c~ @ ((cnum_divides @ ((cEXP @ V0) @ V3)) @ V1))))))))))))))
(TIS_QUADRATIC_RESIDUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ (c~ @ ((cnum_divides @ V1) @ V0)))) @ ((c= @ ((cis_quadratic_residue @ V0) @ (cnum_mod @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c/__caret__ @ ((c< @ V2) @ V1)) @ (((c== @ ((cEXP @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0) @ (cnum_mod @ V1)))))))))))))
(TLESS_CASES_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c< @ V1) @ V0))) @ (c~ @ ((c= @ V1) @ V0)))) @ ((c< @ V0) @ V1)))))))
(TSUM_OF_TWO_SQUARES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ ((c= @ V1) @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ V1) @ ((c+ @ ((cEXP @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cEXP @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))))))
(TPRIME_COPRIME_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c< @ V0) @ V1)))) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))))))))
(TCONG_UNIQUE_INVERSE_PRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c< @ V0) @ V1)))) @ (c?! @ (^[V2]: ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c/__caret__ @ ((c< @ V2) @ V1)) @ (((c== @ ((c* @ V0) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1))))))))))))
(TBEZOUT_PRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ (c~ @ ((cnum_divides @ V1) @ V0)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ ((c* @ V0) @ V2)) @ ((c+ @ ((c* @ V1) @ V3)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))
(TFERMAT_LITTLE_PRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1)))) @ (((c== @ ((cEXP @ V0) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1))))))))
(TIS_QUADRATIC_RESIDUE_COMMON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1)))) @ ((c= @ ((cis_quadratic_residue @ V0) @ (cnum_mod @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c/__caret__ @ ((c< @ V2) @ V1)) @ (((c== @ ((cEXP @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0) @ (cnum_mod @ V1)))))))))))))
(TDISTINCT_PRIME_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cprime @ V0)) @ ((c/__caret__ @ (cprime @ V1)) @ (c~ @ ((c= @ V0) @ V1))))) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))))))))
(TDIVIDES_PRIME_PRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cprime @ V0)) @ (cprime @ V1))) @ ((c= @ ((cnum_divides @ V0) @ V1)) @ ((c= @ V0) @ V1))))))))
(TLAGRANGE_LEMMA_ODD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cprime @ V0)) @ (cODD @ V0))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V4)) @ V0)) @ ((c= @ ((c* @ V2) @ V0)) @ ((c+ @ ((cEXP @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c+ @ ((cEXP @ V4) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))))))))
(TCOPRIME_BEZOUT_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (c~ @ ((c= @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ ((c* @ V0) @ V2)) @ ((c+ @ ((c* @ V1) @ V3)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))
(TCOPRIME_BEZOUT_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ ((c* @ V0) @ V2)) @ ((c+ @ ((c* @ V1) @ V3)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))
(TGCD_COPRIME_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ ((c* @ V2) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))) @ ((c/__caret__ @ ((c= @ V1) @ ((c* @ V3) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))) @ (cnum_coprime @ ((c__comma__ @ V2) @ V3))))))))))))))
(TCONG_MOD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ (((c== @ ((cMOD @ V0) @ V1)) @ V0) @ (cnum_mod @ V1))))))))
(TFLOOR_DIV_DIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ (cfloor @ ((creal_div @ (creal_of_num @ V0)) @ (creal_of_num @ V1)))) @ (creal_of_num @ ((cDIV @ V0) @ V1)))))))))
(TMOD_MOD_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((cMOD @ V0) @ V1)) @ V1)) @ ((cMOD @ V0) @ V1))))))))
(TPLUS_MOD_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((c+ @ V0) @ V1)) @ V1)) @ ((cMOD @ V0) @ V1))))))))
(TMOD_MULT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((c* @ V1) @ V0)) @ V1)) @ (cNUMERAL @ c_0))))))))
(TDIVISION_SIMP_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ ((c+ @ ((c* @ ((cDIV @ V0) @ V1)) @ V1)) @ ((cMOD @ V0) @ V1))) @ V0)))))))
(TDIVISION_SIMP_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ ((c+ @ ((c* @ V1) @ ((cDIV @ V0) @ V1))) @ ((cMOD @ V0) @ V1))) @ V0)))))))
(TDIVISION_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ ((c+ @ ((c* @ ((cDIV @ V0) @ V1)) @ V1)) @ ((cMOD @ V0) @ V1)))))))))
(TDIVIDES_MOD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cnum_divides @ V1) @ V0)) @ ((c= @ ((cMOD @ V0) @ V1)) @ (cNUMERAL @ c_0)))))))))
(TMOD_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ ((c= @ ((cMOD @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ (c? @ (^[V2]: ((c= @ V0) @ ((c* @ V2) @ V1)))))))))))
(TDIV_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ ((c= @ ((cDIV @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ ((c< @ V0) @ V1))))))))
(TCOPRIME_MOD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ (cnum_coprime @ ((c__comma__ @ ((cMOD @ V0) @ V1)) @ V1))) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1)))))))))
(TDIVISION_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c< @ ((cMOD @ V0) @ V1)) @ V1)))))))
(TLESS_ADD_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c< @ V0) @ ((c+ @ V0) @ V1))))))))
(TDIVMOD_EXIST,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ ((c+ @ ((c* @ V2) @ V1)) @ V3))) @ ((c< @ V3) @ V1))))))))))))
(TRATIONAL_LOWEST_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V2) @ V3))) @ ((c= @ ((c* @ V0) @ V3)) @ ((c* @ V2) @ V1))))))))))))))
(TDIV_MULT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cDIV @ ((c* @ V0) @ V1)) @ V0)) @ V1)))))))
(TMOD_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c<= @ ((cMOD @ V1) @ V0)) @ V1)))))))
(TDIV_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c<= @ ((cDIV @ V1) @ V0)) @ V1)))))))
(TBEZOUT_GCD_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ ((c* @ V0) @ V2)) @ ((c+ @ ((c* @ V1) @ V3)) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))))))))))))
(TBEZOUT_ADD_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cnum_divides @ V2) @ V0)) @ ((c/__caret__ @ ((cnum_divides @ V2) @ V1)) @ ((c= @ ((c* @ V0) @ V3)) @ ((c+ @ ((c* @ V1) @ V4)) @ V2))))))))))))))))
(TDOT_BASIS_BASIS_UNEQUAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ V1))) @ ((c= @ ((cdot @ (cbasis @ V0)) @ (cbasis @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TPRIME_POWER_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cprime @ V1)) @ ((c= @ (c? @ (^[V2]: ((c= @ V0) @ ((cEXP @ V1) @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cprime @ V2)) @ ((cnum_divides @ V2) @ V0))) @ ((c= @ V2) @ V1)))))))))))
(TSQUAREMOD_INJ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cprime @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ V1)) @ ((c< @ ((cMOD @ ((c+ @ ((cEXP @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ V1)) @ V1))))))))))
(TSQUAREMOD_INJ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cprime @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ V1)) @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V1)) @ ((c= @ ((cMOD @ ((c+ @ ((cEXP @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ V1)) @ ((cMOD @ ((c+ @ ((cEXP @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ V1))))) @ ((c= @ V2) @ V3))))))))))))
(TPRIME_COPRIME_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cprime @ V0)) @ ((c__caret__/ @ ((cnum_divides @ V0) @ V1)) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1)))))))))
(TPRIME_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cprime @ V0)) @ ((c__caret__/ @ ((c= @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c__caret__/ @ ((cnum_divides @ V0) @ V1)) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))))))))))
(TPHI_PRIMEPOW_SUC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cprime @ V0)) @ ((c= @ (cphi @ ((cEXP @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c- @ ((cEXP @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cEXP @ V0) @ V1)))))))))
(TPHI_PRIMEPOW,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cprime @ V0)) @ ((c= @ (cphi @ ((cEXP @ V0) @ V1))) @ (((cCOND @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c- @ ((cEXP @ V0) @ V1)) @ ((cEXP @ V0) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TDIVIDES_FACT_PRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cprime @ V0)) @ ((c= @ ((cnum_divides @ V0) @ (cFACT @ V1))) @ ((c<= @ V0) @ V1))))))))
(TPRIME_COPRIME_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cprime @ V0)) @ ((c= @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (c~ @ ((cnum_divides @ V0) @ V1)))))))))
(TLAGRANGE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cprime @ V0)) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c<= @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c/__caret__ @ ((c<= @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V4)) @ V0)) @ ((c= @ ((c* @ V2) @ V0)) @ ((c+ @ ((cEXP @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c+ @ ((cEXP @ V4) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1)))))))))))))))))
(TCOPRIME_ORDER_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V1) @ V0))) @ (((c== @ ((cEXP @ V0) @ ((corder @ V1) @ V0))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1))))))))
(TORDER_DIVIDES_PHI,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V1) @ V0))) @ ((cnum_divides @ ((corder @ V1) @ V0)) @ (cphi @ V1))))))))
(TCOPRIME_ORDER_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V1) @ V0))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c< @ V2) @ ((corder @ V1) @ V0)))) @ (c~ @ (((c== @ ((cEXP @ V0) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1))))))))))))
(TFERMAT_LITTLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (((c== @ ((cEXP @ V0) @ (cphi @ V1))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1))))))))
(TCOPRIME_ORDER_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c> @ ((corder @ V0) @ V1)) @ (cNUMERAL @ c_0))))))))
(TSIGMA_MULTIPLICATIVE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c= @ (csigma @ ((c* @ V0) @ V1))) @ ((c* @ (csigma @ V0)) @ (csigma @ V1)))))))))
(TPHI_MULTIPLICATIVE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c= @ (cphi @ ((c* @ V0) @ V1))) @ ((c* @ (cphi @ V0)) @ (cphi @ V1)))))))))
(TCOPRIME_SOS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (cnum_coprime @ ((c__comma__ @ ((c* @ V0) @ V1)) @ ((c+ @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))
(TDIVIDES_EXP_PLUS1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cODD @ V1)) @ ((cnum_divides @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c+ @ ((cEXP @ V0) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TINDEX_ODDPART_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cODD @ V1)) @ ((c= @ (coddpart @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ V1))) @ V1)))))))
(TCOPRIME_ODD_POW2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cODD @ V1)) @ (cnum_coprime @ ((c__comma__ @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ V1))))))))
(TINDEX_ODDPART_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cODD @ V0)) @ ((c= @ (cindex @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ V0))) @ V1)))))))
(TBEZOUT_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c/__caret__ @ ((cnum_divides @ V2) @ V1)) @ ((cnum_divides @ V2) @ V0))) @ ((c__caret__/ @ ((c= @ ((c* @ V1) @ V3)) @ ((c+ @ ((c* @ V0) @ V4)) @ V2))) @ ((c= @ ((c* @ V0) @ V3)) @ ((c+ @ ((c* @ V1) @ V4)) @ V2))))))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c/__caret__ @ ((cnum_divides @ V2) @ V1)) @ ((cnum_divides @ V2) @ ((c+ @ V1) @ V0)))) @ ((c__caret__/ @ ((c= @ ((c* @ V1) @ V3)) @ ((c+ @ ((c* @ ((c+ @ V1) @ V0)) @ V4)) @ V2))) @ ((c= @ ((c* @ ((c+ @ V1) @ V0)) @ V3)) @ ((c+ @ ((c* @ V1) @ V4)) @ V2))))))))))))))))
(TREAL_OF_NUM_POW,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_pow @ (creal_of_num @ V0)) @ V1)) @ (creal_of_num @ ((cEXP @ V0) @ V1))))))))
(TREAL_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_mul @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ (creal_of_num @ ((c* @ V0) @ V1))))))))
(TREAL_OF_NUM_MIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_min @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ (creal_of_num @ ((cMIN @ V0) @ V1))))))))
(TREAL_OF_NUM_MAX,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_max @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ (creal_of_num @ ((cMAX @ V0) @ V1))))))))
(TREAL_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_add @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ (creal_of_num @ ((c+ @ V0) @ V1))))))))
(TSUM_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpsum @ ((c__comma__ @ V0) @ V1)) @ (^[V2]: (creal_of_num @ (cNUMERAL @ c_0))))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TDECIMAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDECIMAL @ V0) @ V1)) @ ((creal_div @ (creal_of_num @ V0)) @ (creal_of_num @ V1))))))))
(TMAT_0_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c$ @ ((c$ @ (cmat @ (cNUMERAL @ c_0))) @ V0)) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TVEC_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c$ @ (cvec @ V1)) @ V0)) @ (creal_of_num @ V1)))))))
(Torder,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((corder @ V1) @ V0)) @ (((cCOND @ (cnum_coprime @ ((c__comma__ @ V1) @ V0))) @ (cminimal @ (^[V2]: ((c/__caret__ @ ((c> @ V2) @ (cNUMERAL @ c_0))) @ (((c== @ ((cEXP @ V0) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1)))))) @ (cNUMERAL @ c_0))))))))
(TNPRODUCT_CONST_NUMSEG_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ (^[V2]: V0))) @ ((cEXP @ V0) @ V1)))))))
(TNUMPAIR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cNUMPAIR @ V0) @ V1)) @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TNPAIR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cNPAIR @ V1) @ V0)) @ ((c+ @ ((cEXP @ ((c+ @ V1) @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TMIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cMIN @ V0) @ V1)) @ (((cCOND @ ((c<= @ V0) @ V1)) @ V0) @ V1)))))))
(TMAX,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cMAX @ V1) @ V0)) @ (((cCOND @ ((c<= @ V1) @ V0)) @ V0) @ V1)))))))
(TARITH_EXP_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cEXP @ (cNUMERAL @ V0)) @ (cNUMERAL @ V1))) @ (cNUMERAL @ ((cEXP @ V0) @ V1))))))))
(TARITH_EXP_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cEXP @ (cBIT1 @ V0)) @ (cBIT1 @ V1))) @ ((c* @ (cBIT1 @ V0)) @ ((c* @ ((cEXP @ (cBIT1 @ V0)) @ V1)) @ ((cEXP @ (cBIT1 @ V0)) @ V1)))))))))
(TARITH_EXP_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cEXP @ (cBIT1 @ V0)) @ (cBIT0 @ V1))) @ ((c* @ ((cEXP @ (cBIT1 @ V0)) @ V1)) @ ((cEXP @ (cBIT1 @ V0)) @ V1))))))))
(TARITH_EXP_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cEXP @ (cBIT0 @ V0)) @ (cBIT1 @ V1))) @ ((c* @ (cBIT0 @ V0)) @ ((c* @ ((cEXP @ (cBIT0 @ V0)) @ V1)) @ ((cEXP @ (cBIT0 @ V0)) @ V1)))))))))
(TARITH_EXP_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cEXP @ (cBIT0 @ V0)) @ (cBIT0 @ V1))) @ ((c* @ ((cEXP @ (cBIT0 @ V0)) @ V1)) @ ((cEXP @ (cBIT0 @ V0)) @ V1))))))))
(TEXP_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cEXP @ V0) @ (cSUC @ V1))) @ ((c* @ V0) @ ((cEXP @ V0) @ V1))))))))
(TCOUNT_REVPERM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cCOUNT @ V0) @ (cREVPERM @ V1))) @ (((cCOND @ ((c< @ V0) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ c_0))))))))
(TDIFF_SQUARE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c* @ ((c+ @ V0) @ V1)) @ ((c- @ V0) @ V1))))))))
(TADD_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ ((c+ @ V1) @ V0)) @ V0)) @ V1))))))
(TADD_SUB2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ ((c+ @ V0) @ V1)) @ V0)) @ V1))))))
(TSUB_MONO_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ (cSUC @ V0)) @ (cSUC @ V1))) @ ((c- @ V0) @ V1)))))))
(TSUB_OLD_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ (cSUC @ V0)) @ V1)) @ (((cCOND @ ((c< @ V0) @ V1)) @ (cNUMERAL @ c_0)) @ (cSUC @ ((c- @ V0) @ V1)))))))))
(TARITH_SUB_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ (cNUMERAL @ V0)) @ (cNUMERAL @ V1))) @ (cNUMERAL @ ((c- @ V0) @ V1))))))))
(TARITH_SUB_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ (cBIT1 @ V0)) @ (cBIT1 @ V1))) @ (cBIT0 @ ((c- @ V0) @ V1))))))))
(TARITH_SUB_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ (cBIT1 @ V0)) @ (cBIT0 @ V1))) @ (((cCOND @ ((c<= @ V1) @ V0)) @ (cBIT1 @ ((c- @ V0) @ V1))) @ c_0)))))))
(TARITH_SUB_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ (cBIT0 @ V0)) @ (cBIT1 @ V1))) @ (cPRE @ (cBIT0 @ ((c- @ V0) @ V1)))))))))
(TARITH_SUB_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ (cBIT0 @ V0)) @ (cBIT0 @ V1))) @ (cBIT0 @ ((c- @ V0) @ V1))))))))
(TADD_SUBR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ V1) @ ((c+ @ V0) @ V1))) @ (cNUMERAL @ c_0)))))))
(TADD_SUBR2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c- @ V0) @ ((c+ @ V0) @ V1))) @ (cNUMERAL @ c_0)))))))
(TADD_CLAUSES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+ @ (cSUC @ V0)) @ V1)) @ (cSUC @ ((c+ @ V0) @ V1))))))))
(TARITH_ADD_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+ @ (cNUMERAL @ V0)) @ (cNUMERAL @ V1))) @ (cNUMERAL @ ((c+ @ V0) @ V1))))))))
(TARITH_ADD_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+ @ (cBIT1 @ V0)) @ (cBIT1 @ V1))) @ (cBIT0 @ (cSUC @ ((c+ @ V0) @ V1)))))))))
(TARITH_ADD_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+ @ (cBIT1 @ V0)) @ (cBIT0 @ V1))) @ (cBIT1 @ ((c+ @ V0) @ V1))))))))
(TARITH_ADD_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+ @ (cBIT0 @ V0)) @ (cBIT1 @ V1))) @ (cBIT1 @ ((c+ @ V0) @ V1))))))))
(TARITH_ADD_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+ @ (cBIT0 @ V0)) @ (cBIT0 @ V1))) @ (cBIT0 @ ((c+ @ V0) @ V1))))))))
(TADD_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+ @ V1) @ V0)) @ ((c+ @ V0) @ V1)))))))
(TADD_SUC,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+ @ V0) @ (cSUC @ V1))) @ (cSUC @ ((c+ @ V0) @ V1))))))))
(TBINOM_TOP_STEP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ ((c- @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)) @ (cbinom @ ((c__comma__ @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)))) @ ((c* @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cbinom @ ((c__comma__ @ V0) @ V1)))))))))
(TBINOM_BOTTOM_STEP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cbinom @ ((c__comma__ @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((c* @ ((c- @ V0) @ V1)) @ (cbinom @ ((c__comma__ @ V0) @ V1)))))))))
(TMULT_CLAUSES_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ (cSUC @ V0)) @ V1)) @ ((c+ @ ((c* @ V0) @ V1)) @ V1)))))))
(TARITH_MULT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ (cNUMERAL @ V0)) @ (cNUMERAL @ V1))) @ (cNUMERAL @ ((c* @ V0) @ V1))))))))
(TBINOM_FACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ (cFACT @ V0)) @ ((c* @ (cFACT @ V1)) @ (cbinom @ ((c__comma__ @ ((c+ @ V0) @ V1)) @ V1))))) @ (cFACT @ ((c+ @ V0) @ V1))))))))
(TARITH_MULT_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ (cBIT1 @ V0)) @ (cBIT1 @ V1))) @ ((c+ @ (cBIT1 @ V0)) @ ((c+ @ (cBIT0 @ V1)) @ (cBIT0 @ (cBIT0 @ ((c* @ V0) @ V1)))))))))))
(TARITH_MULT_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ (cBIT1 @ V0)) @ (cBIT0 @ V1))) @ ((c+ @ (cBIT0 @ V1)) @ (cBIT0 @ (cBIT0 @ ((c* @ V0) @ V1))))))))))
(TARITH_MULT_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ (cBIT0 @ V0)) @ (cBIT1 @ V1))) @ ((c+ @ (cBIT0 @ V0)) @ (cBIT0 @ (cBIT0 @ ((c* @ V0) @ V1))))))))))
(TARITH_MULT_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ (cBIT0 @ V0)) @ (cBIT0 @ V1))) @ (cBIT0 @ (cBIT0 @ ((c* @ V0) @ V1)))))))))
(TMULT_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ V1) @ V0)) @ ((c* @ V0) @ V1)))))))
(TMULT_SUC,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c* @ V0) @ (cSUC @ V1))) @ ((c+ @ V0) @ ((c* @ V0) @ V1))))))))
(TGCD_ADD_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_gcd @ ((c__comma__ @ ((c+ @ V1) @ V0)) @ V1))) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TGCD_ADD_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_gcd @ ((c__comma__ @ ((c+ @ V0) @ V1)) @ V1))) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TGCD_MULTIPLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_gcd @ ((c__comma__ @ V1) @ ((c* @ V0) @ V1)))) @ V1))))))
(TGCD_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_gcd @ ((c__comma__ @ V1) @ V0))) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TGCD_ADD_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ ((c+ @ V1) @ V0)))) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TGCD_ADD_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ ((c+ @ V0) @ V1)))) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))))))
(Tnum_gcd,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ (cnum_of_int @ (cint_gcd @ ((c__comma__ @ (cint_of_num @ V0)) @ (cint_of_num @ V1))))))))))
(TLCM_MULTIPLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (clcm @ ((c__comma__ @ V1) @ ((c* @ V0) @ V1)))) @ ((c* @ V0) @ V1)))))))
(TLCM_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (clcm @ ((c__comma__ @ V1) @ V0))) @ (clcm @ ((c__comma__ @ V0) @ V1))))))))
(Tlcm,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (clcm @ ((c__comma__ @ V0) @ V1))) @ (((cCOND @ ((c= @ ((c* @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)) @ ((cDIV @ ((c* @ V0) @ V1)) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))))))))
(Tegcd,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cegcd @ ((c__comma__ @ V0) @ V1))) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ V1) @ (((cCOND @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ V0) @ (((cCOND @ ((c<= @ V0) @ V1)) @ (cegcd @ ((c__comma__ @ V0) @ ((c- @ V1) @ V0)))) @ (cegcd @ ((c__comma__ @ ((c- @ V0) @ V1)) @ V1)))))))))))
(TEGCD_GCD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cegcd @ ((c__comma__ @ V0) @ V1))) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TDIST_LADD_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdist @ ((c__comma__ @ ((c+ @ V0) @ V1)) @ V0))) @ V1))))))
(TDIST_RADD_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdist @ ((c__comma__ @ V0) @ ((c+ @ V0) @ V1)))) @ V1))))))
(Tbinom_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cbinom @ ((c__comma__ @ (cSUC @ V0)) @ (cSUC @ V1)))) @ ((c+ @ (cbinom @ ((c__comma__ @ V0) @ (cSUC @ V1)))) @ (cbinom @ ((c__comma__ @ V0) @ V1)))))))))
(TBINOM_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cbinom @ ((c__comma__ @ V0) @ V1))) @ (((cCOND @ ((c< @ V0) @ V1)) @ (cNUMERAL @ c_0)) @ ((cDIV @ (cFACT @ V0)) @ ((c* @ (cFACT @ V1)) @ (cFACT @ ((c- @ V0) @ V1)))))))))))
(TSUB_PRESUC,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cPRE @ ((c- @ (cSUC @ V0)) @ V1))) @ ((c- @ V0) @ V1)))))))
(TNUMPAIR_DEST_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cNUMSND @ ((cNUMPAIR @ V0) @ V1))) @ V1))))))
(TNUMPAIR_DEST_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cNUMFST @ ((cNUMPAIR @ V1) @ V0))) @ V1))))))
(TCARD_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cCARD @ ((c.. @ V1) @ V0))) @ ((c- @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)))))))
(TCARD_NUMSEG_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cCARD @ ((c.. @ V0) @ ((c+ @ V0) @ V1)))) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TINT_OF_NUM_POW,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_pow @ (cint_of_num @ V0)) @ V1)) @ (cint_of_num @ ((cEXP @ V0) @ V1))))))))
(TINT_OF_NUM_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_mul @ (cint_of_num @ V0)) @ (cint_of_num @ V1))) @ (cint_of_num @ ((c* @ V0) @ V1))))))))
(TINT_OF_NUM_MIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_min @ (cint_of_num @ V0)) @ (cint_of_num @ V1))) @ (cint_of_num @ ((cMIN @ V0) @ V1))))))))
(TINT_OF_NUM_MAX,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_max @ (cint_of_num @ V0)) @ (cint_of_num @ V1))) @ (cint_of_num @ ((cMAX @ V0) @ V1))))))))
(TINT_OF_NUM_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_add @ (cint_of_num @ V0)) @ (cint_of_num @ V1))) @ (cint_of_num @ ((c+ @ V0) @ V1))))))))
(TNUM_GCD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_of_num @ (cnum_gcd @ ((c__comma__ @ V0) @ V1)))) @ (cint_gcd @ ((c__comma__ @ (cint_of_num @ V0)) @ (cint_of_num @ V1)))))))))
(THREAL_OF_NUM_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chreal_mul @ (chreal_of_num @ V0)) @ (chreal_of_num @ V1))) @ (chreal_of_num @ ((c* @ V0) @ V1))))))))
(THREAL_OF_NUM_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chreal_add @ (chreal_of_num @ V0)) @ (chreal_of_num @ V1))) @ (chreal_of_num @ ((c+ @ V0) @ V1))))))))
(TFROM_INTER_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINTER @ (cfrom @ V0)) @ ((c.. @ (cNUMERAL @ c_0)) @ V1))) @ ((c.. @ V0) @ V1)))))))
(TNUMSEG_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c.. @ V0) @ (cSUC @ V1))) @ (((cCOND @ ((c<= @ V0) @ (cSUC @ V1))) @ ((cINSERT @ (cSUC @ V1)) @ ((c.. @ V0) @ V1))) @ ((c.. @ V0) @ V1))))))))
(Tnumseg,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c.. @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((c<= @ V0) @ V3)) @ ((c<= @ V3) @ V1))) @ V3)))))))))))
(TOUTER_MBASIS_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((couter @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY))) @ (cmbasis @ ((cINSERT @ V1) @ cEMPTY)))) @ (((cCOND @ ((c/__caret__ @ ((cIN @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((cIN @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ (c~ @ ((c= @ V0) @ V1))))) @ (((cCOND @ ((c< @ V0) @ V1)) @ (cmbasis @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))) @ (cvector_neg @ (cmbasis @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TGEOM_MBASIS_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cgeom_mul @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY))) @ (cmbasis @ ((cINSERT @ V1) @ cEMPTY)))) @ (((cCOND @ ((c/__caret__ @ ((cIN @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((cIN @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))) @ (((cCOND @ ((c= @ V0) @ V1)) @ (cmbasis @ cEMPTY)) @ (((cCOND @ ((c< @ V0) @ V1)) @ (cmbasis @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))) @ (cvector_neg @ (cmbasis @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TOUTER_MBASIS_SKEWSYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((couter @ (cmbasis @ ((cINSERT @ V1) @ cEMPTY))) @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY)))) @ (cvector_neg @ ((couter @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY))) @ (cmbasis @ ((cINSERT @ V1) @ cEMPTY))))))))))
(TSEQUENTIALLY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cnetord @ csequentially) @ V0) @ V1)) @ ((c>= @ V0) @ V1)))))))
(TCONG_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((c== @ V1) @ (cNUMERAL @ c_0)) @ (cnum_mod @ V0))) @ ((cnum_divides @ V0) @ V1)))))))
(TCONG_TO_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((c== @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c? @ (^[V2]: ((c= @ V0) @ ((c+ @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c* @ V2) @ V1))))))))))))
(TTREAL_OF_NUM_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ctreal_le @ (ctreal_of_num @ V0)) @ (ctreal_of_num @ V1))) @ ((c<= @ V0) @ V1)))))))
(TTREAL_OF_NUM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ctreal_eq @ (ctreal_of_num @ V0)) @ (ctreal_of_num @ V1))) @ ((c= @ V0) @ V1)))))))
(TREAL_POW2_THM_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_lt @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))) @ ((c< @ V0) @ V1)))))))
(TREAL_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_lt @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ ((c< @ V0) @ V1)))))))
(TREAL_POW2_THM_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_lt @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))) @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))) @ ((c< @ V0) @ V1)))))))
(TREAL_POW2_THM_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_le @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))) @ ((c<= @ V0) @ V1)))))))
(TREAL_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_le @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ ((c<= @ V0) @ V1)))))))
(TREAL_POW2_THM_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_le @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))) @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)))) @ ((c<= @ V0) @ V1)))))))
(TREAL_OF_NUM_GT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_gt @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ ((c> @ V0) @ V1)))))))
(TREAL_OF_NUM_GE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_ge @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ ((c>= @ V0) @ V1)))))))
(Tprimepow_DELTA,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cprimepow @ V1) @ V0)) @ ((c/__caret__ @ (cprime @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (c! @ (^[V2]: ((c==> @ ((c<= @ V2) @ V0)) @ ((c==> @ ((cnum_divides @ V2) @ V0)) @ ((c__caret__/ @ ((c= @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cnum_divides @ V1) @ V2))))))))))))))
(Tprimepow,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cprimepow @ V1) @ V0)) @ ((c/__caret__ @ (cprime @ V1)) @ (c? @ (^[V2]: ((c= @ V0) @ ((cEXP @ V1) @ V2)))))))))))
(Tdivides_DELTA,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnum_divides @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((c<= @ V2) @ V0)) @ ((c= @ V0) @ ((c* @ V1) @ V2)))))))))))
(Tnum_divides,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnum_divides @ V0) @ V1)) @ ((cint_divides @ (cint_of_num @ V0)) @ (cint_of_num @ V1))))))))
(TDIVIDES_DIV_MULT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnum_divides @ V0) @ V1)) @ ((c= @ ((c* @ ((cDIV @ V1) @ V0)) @ V0)) @ V1)))))))
(TPRIMEPOW_DIVISORS_DIVIDES,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnum_divides @ V0) @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cprime @ V2)) @ ((cnum_divides @ ((cEXP @ V2) @ V3)) @ V0))) @ ((cnum_divides @ ((cEXP @ V2) @ V3)) @ V1))))))))))))
(TNADD_OF_NUM_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnadd_le @ (cnadd_of_num @ V0)) @ (cnadd_of_num @ V1))) @ ((c<= @ V0) @ V1)))))))
(TNADD_OF_NUM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnadd_eq @ (cnadd_of_num @ V0)) @ (cnadd_of_num @ V1))) @ ((c= @ V0) @ V1)))))))
(TINT_OF_NUM_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ (cint_of_num @ V0)) @ (cint_of_num @ V1))) @ ((c< @ V0) @ V1)))))))
(TINT_OF_NUM_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ (cint_of_num @ V0)) @ (cint_of_num @ V1))) @ ((c<= @ V0) @ V1)))))))
(TINT_OF_NUM_GT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_gt @ (cint_of_num @ V0)) @ (cint_of_num @ V1))) @ ((c> @ V0) @ V1)))))))
(TINT_OF_NUM_GE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_ge @ (cint_of_num @ V0)) @ (cint_of_num @ V1))) @ ((c>= @ V0) @ V1)))))))
(THREAL_OF_NUM_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chreal_le @ (chreal_of_num @ V0)) @ (chreal_of_num @ V1))) @ ((c<= @ V0) @ V1)))))))
(TTERM1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cTERM1 @ V0) @ V1)) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ V2)) @ ((c= @ V1) @ ((cNPAIR @ ((cNPAIR @ (cNUMERAL @ c_0)) @ V3)) @ V2)))))))) @ ((c__caret__/ @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ V0) @ V2)) @ ((c= @ V1) @ ((cNPAIR @ ((cNPAIR @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ c_0))) @ V2)))))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ ((cNPAIR @ V2) @ V3))) @ ((c= @ V1) @ ((cNPAIR @ ((cNPAIR @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ V3)))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c__caret__/ @ ((c= @ V2) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c= @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((c/__caret__ @ ((c= @ V0) @ ((cNPAIR @ V3) @ ((cNPAIR @ V4) @ V5)))) @ ((c= @ V1) @ ((cNPAIR @ ((cNPAIR @ V2) @ ((cNPAIR @ V3) @ V4))) @ V5)))))))))))))))))))))
(TMEM_REVPERM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cMEM @ V0) @ (cREVPERM @ V1))) @ ((c< @ V0) @ V1)))))))
(TIN_FROM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V1) @ (cfrom @ V0))) @ ((c<= @ V0) @ V1)))))))
(TIN_NUMSEG_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c< @ V0) @ V1))))))))
(TIN_NUMSEG_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ ((c.. @ (cNUMERAL @ c_0)) @ V1))) @ ((c<= @ V0) @ V1)))))))
(TARITH_GE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c>= @ (cNUMERAL @ V1)) @ (cNUMERAL @ V0))) @ ((c>= @ V1) @ V0)))))))
(TARITH_GE_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c>= @ (cBIT1 @ V1)) @ (cBIT1 @ V0))) @ ((c>= @ V1) @ V0)))))))
(TARITH_GE_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c>= @ (cBIT1 @ V1)) @ (cBIT0 @ V0))) @ ((c>= @ V1) @ V0)))))))
(TARITH_GE_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c>= @ (cBIT0 @ V1)) @ (cBIT1 @ V0))) @ ((c> @ V1) @ V0)))))))
(TARITH_GE_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c>= @ (cBIT0 @ V1)) @ (cBIT0 @ V0))) @ ((c>= @ V1) @ V0)))))))
(TGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c>= @ V1) @ V0)) @ ((c<= @ V0) @ V1)))))))
(TARITH_GT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c> @ (cNUMERAL @ V1)) @ (cNUMERAL @ V0))) @ ((c> @ V1) @ V0)))))))
(TARITH_GT_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c> @ (cBIT1 @ V1)) @ (cBIT1 @ V0))) @ ((c> @ V1) @ V0)))))))
(TARITH_GT_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c> @ (cBIT1 @ V1)) @ (cBIT0 @ V0))) @ ((c>= @ V1) @ V0)))))))
(TARITH_GT_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c> @ (cBIT0 @ V1)) @ (cBIT1 @ V0))) @ ((c> @ V1) @ V0)))))))
(TARITH_GT_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c> @ (cBIT0 @ V1)) @ (cBIT0 @ V0))) @ ((c> @ V1) @ V0)))))))
(TGREATER,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c> @ V1) @ V0)) @ ((c< @ V0) @ V1)))))))
(TREAL_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ ((c= @ V0) @ V1)))))))
(TORDER_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((corder @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ (c~ @ (cnum_coprime @ ((c__comma__ @ V0) @ V1)))))))))
(TEXP_EQ_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cEXP @ V0) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
(TEXP_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cEXP @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0))))))))))
(TSUB_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c- @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ ((c<= @ V0) @ V1)))))))
(TSUB_EQ_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c- @ V0) @ V1)) @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
(TEQ_ADD_RCANCEL_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c+ @ V1) @ V0)) @ V0)) @ ((c= @ V1) @ (cNUMERAL @ c_0))))))))
(TADD_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c+ @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
(TEQ_ADD_LCANCEL_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c+ @ V0) @ V1)) @ V0)) @ ((c= @ V1) @ (cNUMERAL @ c_0))))))))
(TCANCEL_TIMES2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))) @ ((c= @ V0) @ V1)))))))
(TMULT_EQ_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c* @ V0) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c/__caret__ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TMULT_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c* @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
(TMULT_FIX,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c* @ V0) @ V1)) @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TNUMBER_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cnumber @ V0)) @ (cnumber @ V1))) @ ((c= @ V0) @ V1)))))))
(TGCD_ZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
(TLCM_ZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (clcm @ ((c__comma__ @ V0) @ V1))) @ (cNUMERAL @ c_0))) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
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(TINV_SUC_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cSUC @ V0)) @ (cSUC @ V1))) @ ((c= @ V0) @ V1)))))))
(TARITH_EQ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cNUMERAL @ V0)) @ (cNUMERAL @ V1))) @ ((c= @ V0) @ V1)))))))
(TISQRT_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cISQRT @ V0)) @ V1)) @ ((c/__caret__ @ ((c<= @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ ((c< @ V0) @ ((cEXP @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TARITH_EQ_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cBIT1 @ V0)) @ (cBIT1 @ V1))) @ ((c= @ V0) @ V1)))))))
(TARITH_EQ_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cBIT1 @ V0)) @ (cBIT0 @ V1))) @ cF))))))
(TARITH_EQ_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cBIT0 @ V0)) @ (cBIT1 @ V1))) @ cF))))))
(TARITH_EQ_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cBIT0 @ V0)) @ (cBIT0 @ V1))) @ ((c= @ V0) @ V1)))))))
(TDIVISORS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ ((cnum_divides @ V2) @ V0)) @ ((cnum_divides @ V2) @ V1))))))))))
(TMULTIPLES_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ ((cnum_divides @ V0) @ V2)) @ ((cnum_divides @ V1) @ V2))))))))))
(TPRIMEPOW_DIVISORS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cprime @ V2)) @ ((c= @ ((cnum_divides @ ((cEXP @ V2) @ V3)) @ V0)) @ ((cnum_divides @ ((cEXP @ V2) @ V3)) @ V1)))))))))))))
(TINT_OF_NUM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cint_of_num @ V0)) @ (cint_of_num @ V1))) @ ((c= @ V0) @ V1)))))))
(THREAL_OF_NUM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (chreal_of_num @ V0)) @ (chreal_of_num @ V1))) @ ((c= @ V0) @ V1)))))))
(TINJN_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cINJN @ V0)) @ (cINJN @ V1))) @ ((c= @ V0) @ V1)))))))
(TNUMSEG_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((c.. @ V1) @ V0)) @ cEMPTY)) @ ((c< @ V0) @ V1)))))))
(TBITSET_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cbitset @ V0)) @ (cbitset @ V1))) @ ((c= @ V0) @ V1)))))))
(TVEC_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cvec @ V0)) @ (cvec @ V1))) @ ((c= @ V0) @ V1)))))))
(TMAT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cmat @ V0)) @ (cmat @ V1))) @ ((c= @ V0) @ V1)))))))
(TLESS_EQ_MONO,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<= @ (cSUC @ V0)) @ (cSUC @ V1))) @ ((c<= @ V0) @ V1)))))))
(TLE_SUC_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<= @ (cSUC @ V0)) @ V1)) @ ((c< @ V0) @ V1)))))))
(TARITH_LE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<= @ (cNUMERAL @ V0)) @ (cNUMERAL @ V1))) @ ((c<= @ V0) @ V1)))))))
(TARITH_LE_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<= @ (cBIT1 @ V0)) @ (cBIT1 @ V1))) @ ((c<= @ V0) @ V1)))))))
(TARITH_LE_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<= @ (cBIT1 @ V0)) @ (cBIT0 @ V1))) @ ((c< @ V0) @ V1)))))))
(TARITH_LE_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<= @ (cBIT0 @ V0)) @ (cBIT1 @ V1))) @ ((c<= @ V0) @ V1)))))))
(TARITH_LE_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<= @ (cBIT0 @ V0)) @ (cBIT0 @ V1))) @ ((c<= @ V0) @ V1)))))))
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(TLE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<= @ V0) @ (cSUC @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ (cSUC @ V1))) @ ((c<= @ V0) @ V1))))))))
(TLESS_OR_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<= @ V0) @ V1)) @ ((c__caret__/ @ ((c< @ V0) @ V1)) @ ((c= @ V0) @ V1))))))))
(TLESS_MONO_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c< @ (cSUC @ V0)) @ (cSUC @ V1))) @ ((c< @ V0) @ V1)))))))
(TEXP_LT_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c< @ (cNUMERAL @ c_0)) @ ((cEXP @ V0) @ V1))) @ ((c__caret__/ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
(TLT_MULT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c< @ (cNUMERAL @ c_0)) @ ((c* @ V0) @ V1))) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c< @ (cNUMERAL @ c_0)) @ V1))))))))
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(TARITH_LT_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c< @ (cBIT0 @ V0)) @ (cBIT1 @ V1))) @ ((c<= @ V0) @ V1)))))))
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(TLT_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c< @ V1) @ V0)) @ (c? @ (^[V2]: ((c= @ V0) @ ((c+ @ V1) @ (cSUC @ V2)))))))))))
(TBITSET_BOUND_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c< @ V0) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (cbitset @ V0))) @ ((c< @ V2) @ V1))))))))))
(TLT_ADDR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c< @ V0) @ ((c+ @ V1) @ V0))) @ ((c< @ (cNUMERAL @ c_0)) @ V1)))))))
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(TLT_SUC_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c< @ V0) @ (cSUC @ V1))) @ ((c<= @ V0) @ V1)))))))
(TLESS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c< @ V0) @ V1)) @ ((c<= @ (cSUC @ V0)) @ V1)))))))
(TLT_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c< @ V0) @ V1)) @ ((c/__caret__ @ ((c<= @ V0) @ V1)) @ (c~ @ ((c= @ V0) @ V1)))))))))
(TDIVIDES_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cnum_divides @ V0) @ V1)) @ ((cnum_divides @ V1) @ V0))) @ ((c= @ V0) @ V1)))))))
(TLE_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((c<= @ V0) @ V1)) @ ((c<= @ V1) @ V0))) @ ((c= @ V0) @ V1)))))))
(TNOT_SUC_LESS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c<= @ (cSUC @ V1)) @ V0))) @ ((c<= @ V0) @ V1)))))))
(TNOT_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c<= @ V1) @ V0))) @ ((c< @ V0) @ V1)))))))
(TNOT_LESS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c< @ V1) @ V0))) @ ((c<= @ V0) @ V1)))))))
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(TCOPRIME_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_coprime @ ((c__comma__ @ V1) @ V0))) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))))))))
(TCOPRIME_BEZOUT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_coprime @ ((c__comma__ @ V1) @ V0))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c__caret__/ @ ((c= @ ((c- @ ((c* @ V1) @ V2)) @ ((c* @ V0) @ V3))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ ((c- @ ((c* @ V0) @ V2)) @ ((c* @ V1) @ V3))) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))
(TCOPRIME_GCD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(Tnum_coprime,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (cint_coprime @ ((c__comma__ @ (cint_of_num @ V0)) @ (cint_of_num @ V1)))))))))
(Tcoprime,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V2) @ V0)) @ ((cnum_divides @ V2) @ V1))) @ ((c= @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))
(TCOPRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (c! @ (^[V2]: ((c= @ ((c/__caret__ @ ((cnum_divides @ V2) @ V0)) @ ((cnum_divides @ V2) @ V1))) @ ((c= @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))
(TCOPRIME_PRIME_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (c! @ (^[V2]: (c~ @ ((c/__caret__ @ (cprime @ V2)) @ ((c/__caret__ @ ((cnum_divides @ V2) @ V0)) @ ((cnum_divides @ V2) @ V1))))))))))))
(TODD_EXP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cODD @ ((cEXP @ V0) @ V1))) @ ((c__caret__/ @ (cODD @ V0)) @ ((c= @ V1) @ (cNUMERAL @ c_0)))))))))
(TODD_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cODD @ ((c- @ V0) @ V1))) @ ((c/__caret__ @ ((c< @ V1) @ V0)) @ (c~ @ ((c= @ (cODD @ V0)) @ (cODD @ V1))))))))))
(TODD_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cODD @ ((c+ @ V0) @ V1))) @ (c~ @ ((c= @ (cODD @ V0)) @ (cODD @ V1)))))))))
(TODD_MULT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cODD @ ((c* @ V0) @ V1))) @ ((c/__caret__ @ (cODD @ V0)) @ (cODD @ V1))))))))
(TPARITY_EXP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cEVEN @ ((cEXP @ V1) @ (cSUC @ V0)))) @ (cEVEN @ V1)))))))
(TEVEN_EXP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cEVEN @ ((cEXP @ V0) @ V1))) @ ((c/__caret__ @ (cEVEN @ V0)) @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0))))))))))
(TEVEN_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cEVEN @ ((c- @ V0) @ V1))) @ ((c__caret__/ @ ((c<= @ V0) @ V1)) @ ((c= @ (cEVEN @ V0)) @ (cEVEN @ V1)))))))))
(TEVEN_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cEVEN @ ((c+ @ V0) @ V1))) @ ((c= @ (cEVEN @ V0)) @ (cEVEN @ V1))))))))
(TEVEN_MULT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cEVEN @ ((c* @ V0) @ V1))) @ ((c__caret__/ @ (cEVEN @ V0)) @ (cEVEN @ V1))))))))
(TMOD_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c= @ V0) @ ((c* @ V1) @ V2))))) @ (((cCOND @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ ((cMOD @ V0) @ V1)) @ (cNUMERAL @ c_0)))))))))
(TBOUNDS_LINEAR_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c<= @ ((c* @ V1) @ V2)) @ V0)))) @ ((c= @ V1) @ (cNUMERAL @ c_0))))))))
(TSUB_LESS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ ((c- @ V1) @ V0)) @ V1))))))
(TDIV_MUL_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ ((c* @ V0) @ ((cDIV @ V1) @ V0))) @ V1))))))
(TDIST_ADDBOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ (cdist @ ((c__comma__ @ V0) @ V1))) @ ((c+ @ V0) @ V1)))))))
(TLE_ADDR,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ V1) @ ((c+ @ V0) @ V1)))))))
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(TZERO_LESS_EXP,(c! @ (^[V0]: (c! @ (^[V1]: ((c< @ (cNUMERAL @ c_0)) @ ((cEXP @ (cSUC @ V0)) @ V1)))))))
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(TNPAIR_LT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c< @ V0) @ ((cNPAIR @ V0) @ V1)))))))
(TLESS_ADD_SUC,(c! @ (^[V0]: (c! @ (^[V1]: ((c< @ V0) @ ((c+ @ V0) @ (cSUC @ V1))))))))
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(TSUM_GP_OFFSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((csum @ ((c.. @ V0) @ ((c+ @ V0) @ V1))) @ (^[V3]: ((creal_pow @ V2) @ V3)))) @ (((cCOND @ ((c= @ V2) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_add @ (creal_of_num @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_pow @ V2) @ V0)) @ ((creal_div @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_pow @ V2) @ (cSUC @ V1)))) @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2))))))))))))
(TSUM_GP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((csum @ ((c.. @ V0) @ V1)) @ (^[V3]: ((creal_pow @ V2) @ V3)))) @ (((cCOND @ ((c< @ V1) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))) @ (((cCOND @ ((c= @ V2) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ ((c- @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))) @ ((creal_div @ ((creal_sub @ ((creal_pow @ V2) @ V0)) @ ((creal_pow @ V2) @ (cSUC @ V1)))) @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2))))))))))))
(TREAL_ABS_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_mul @ ((creal_pow @ (creal_of_num @ V0)) @ V1)) @ (creal_abs @ V2))) @ (creal_abs @ ((creal_mul @ ((creal_pow @ (creal_of_num @ V0)) @ V1)) @ V2))))))))))
(TORDER_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c== @ V0) @ V2) @ (cnum_mod @ V1))) @ ((c= @ ((corder @ V1) @ V0)) @ ((corder @ V1) @ V2))))))))))
(TCONG_DIVIDES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c== @ V0) @ V2) @ (cnum_mod @ V1))) @ ((c= @ ((cnum_divides @ V1) @ V0)) @ ((cnum_divides @ V1) @ V2))))))))))
(TCONG_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c== @ V0) @ V2) @ (cnum_mod @ V1))) @ ((c= @ (cnum_coprime @ ((c__comma__ @ V1) @ V0))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V2)))))))))))
(TDIVIDES_RMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnum_divides @ ((c* @ V1) @ V0)) @ V2)) @ ((cnum_divides @ V1) @ V2)))))))))
(TDIVIDES_LMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnum_divides @ ((c* @ V0) @ V1)) @ V2)) @ ((cnum_divides @ V1) @ V2)))))))))
(TDIVISION_DECOMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnum_divides @ V0) @ ((c* @ V1) @ V2))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((c* @ V3) @ V4))) @ ((c/__caret__ @ ((cnum_divides @ V3) @ V1)) @ ((cnum_divides @ V4) @ V2)))))))))))))))
(TDIVIDES_MUL_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnum_divides @ V0) @ V2)) @ ((cnum_divides @ ((c* @ V1) @ V0)) @ ((c* @ V1) @ V2))))))))))
(TDIVIDES_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnum_divides @ V0) @ V1)) @ ((cnum_divides @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2))))))))))
(TDIVIDES_MUL_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnum_divides @ V0) @ V1)) @ ((cnum_divides @ ((c* @ V0) @ V2)) @ ((c* @ V1) @ V2))))))))))
(TDIVIDES_REXP_SUC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnum_divides @ V0) @ V1)) @ ((cnum_divides @ V0) @ ((cEXP @ V1) @ (cSUC @ V2)))))))))))
(TDIVIDES_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnum_divides @ V0) @ V1)) @ ((cnum_divides @ V0) @ ((c* @ V1) @ V2))))))))))
(TDIVIDES_LCM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c__caret__/ @ ((cnum_divides @ V0) @ V1)) @ ((cnum_divides @ V0) @ V2))) @ ((cnum_divides @ V0) @ (clcm @ ((c__comma__ @ V1) @ V2)))))))))))
(TREAL_RAT_ABS_MIDDLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (creal_abs @ ((creal_sub @ ((creal_div @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ (creal_of_num @ V2)))) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((c__caret__/ @ ((c= @ ((creal_div @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ ((creal_add @ (creal_of_num @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((c= @ ((creal_div @ (creal_of_num @ V0)) @ (creal_of_num @ V1))) @ ((creal_add @ (creal_of_num @ V2)) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))))))
(TZAG_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (czag @ ((c__comma__ @ V2) @ ((c__comma__ @ V1) @ V0)))) @ ((c__comma__ @ V2) @ ((c__comma__ @ V1) @ V0)))) @ ((c= @ V1) @ V2)))))))))
(TADD_IMP_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ ((c+ @ V0) @ V2)) @ V1)) @ ((c= @ V0) @ ((c- @ V1) @ V2))))))))))
(TEQ_IMP_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ V0) @ V1)) @ (((c== @ V0) @ V1) @ (cnum_mod @ V2))))))))))
(TARITHMETIC_PROGRESSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c= @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (^[V3]: ((c+ @ V0) @ ((c* @ V2) @ V3))))) @ ((cDIV @ ((c* @ V1) @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ ((c* @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))
(TDIVIDES_EXP_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ ((c= @ ((cnum_divides @ ((cEXP @ V0) @ V1)) @ ((cEXP @ V0) @ V2))) @ ((c<= @ V1) @ V2))))))))))
(TCONG_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V2) @ V0)) @ ((c= @ (((c== @ V0) @ V2) @ (cnum_mod @ V1))) @ (c? @ (^[V3]: ((c= @ V0) @ ((c+ @ ((c* @ V3) @ V1)) @ V2)))))))))))))
(TSUB_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ ((c= @ ((c- @ V0) @ ((c- @ V2) @ V1))) @ ((c- @ ((c+ @ V0) @ V1)) @ V2))))))))))
(TNUMSEG_ADD_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((c.. @ V0) @ ((c+ @ V1) @ V2))) @ ((cUNION @ ((c.. @ V0) @ V1)) @ ((c.. @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c+ @ V1) @ V2))))))))))))
(TEXP_MONO_LE_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V0) @ V1)) @ ((c<= @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2))))))))))
(TCONG_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c< @ V2) @ V1)) @ ((c= @ (((c== @ V0) @ V2) @ (cnum_mod @ V1))) @ (c? @ (^[V3]: ((c= @ V0) @ ((c+ @ ((c* @ V3) @ V1)) @ V2)))))))))))))
(TCONG_MOD_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c< @ V1) @ V2)) @ ((c= @ ((c= @ ((cMOD @ V0) @ V2)) @ V1)) @ (((c== @ V0) @ V1) @ (cnum_mod @ V2)))))))))))
(TLESS_MONO_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c< @ V0) @ V1)) @ ((c< @ ((c+ @ V0) @ V2)) @ ((c+ @ V1) @ V2))))))))))
(Tnat_mod_lemma,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((c== @ V0) @ V1) @ (cnum_mod @ V2))) @ ((c<= @ V1) @ V0))) @ (c? @ (^[V3]: ((c= @ V0) @ ((c+ @ V1) @ ((c* @ V2) @ V3)))))))))))))
(TDIVIDES_EXP2_REV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ ((cEXP @ V1) @ V0)) @ ((cEXP @ V2) @ V0))) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0))))) @ ((cnum_divides @ V1) @ V2)))))))))
(TDIVIDES_CMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2))) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0))))) @ ((cnum_divides @ V1) @ V2)))))))))
(TGCD_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V2) @ V0)) @ ((cnum_divides @ V2) @ V1))) @ ((cnum_divides @ V2) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1)))))))))))
(TEGCD_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V2) @ V0)) @ ((cnum_divides @ V2) @ V1))) @ ((cnum_divides @ V2) @ (cegcd @ ((c__comma__ @ V0) @ V1)))))))))))
(TCOPRIME_DIVPROD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V1) @ ((c* @ V0) @ V2))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V0)))) @ ((cnum_divides @ V1) @ V2)))))))))
(TDIVIDES_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V1) @ V0)) @ ((cnum_divides @ V0) @ V2))) @ ((cnum_divides @ V1) @ V2)))))))))
(TLCM_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V0) @ V2)) @ ((cnum_divides @ V1) @ V2))) @ ((cnum_divides @ (clcm @ ((c__comma__ @ V0) @ V1))) @ V2)))))))))
(TDIVIDES_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V0) @ V2)) @ ((c/__caret__ @ ((cnum_divides @ V1) @ V2)) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))))) @ ((cnum_divides @ ((c* @ V0) @ V1)) @ V2)))))))))
(TDIVIDES_REXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V0) @ V1)) @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0))))) @ ((cnum_divides @ V0) @ ((cEXP @ V1) @ V2))))))))))
(TDIVIDES_DIVIDES_DIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((cnum_divides @ V0) @ V2))) @ ((c= @ ((cnum_divides @ V1) @ ((cDIV @ V2) @ V0))) @ ((cnum_divides @ ((c* @ V0) @ V1)) @ V2))))))))))
(TIN_DIMINDEX_SWAP_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))))))) @ ((c<= @ ((cswap @ ((c__comma__ @ V0) @ V1)) @ V2)) @ (cdimindex @ cUNIV))))))))))
(TIN_DIMINDEX_SWAP_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))))))) @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((cswap @ ((c__comma__ @ V0) @ V1)) @ V2))))))))))
(TMAT_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))))) @ ((c= @ ((c$ @ ((c$ @ (cmat @ V2)) @ V0)) @ V1)) @ (((cCOND @ ((c= @ V0) @ V1)) @ (creal_of_num @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))
(TNUMSEG_COMBINE_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c<= @ V0) @ V2))) @ ((c= @ ((cUNION @ ((c.. @ V1) @ V0)) @ ((c.. @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2))) @ ((c.. @ V1) @ V2))))))))))
(TNUMSEG_COMBINE_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V0)) @ ((c<= @ V0) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c= @ ((cUNION @ ((c.. @ V1) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c.. @ V0) @ V2))) @ ((c.. @ V1) @ V2))))))))))
(TLESS_EQ_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V0)) @ ((c<= @ V0) @ V2))) @ ((c<= @ V1) @ V2)))))))))
(TLESS_EQ_LESS_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V0)) @ ((c< @ V0) @ V2))) @ ((c< @ V1) @ V2)))))))))
(TORDER_WORKS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c< @ V2) @ ((corder @ V1) @ V0)))) @ (c~ @ (((c== @ ((cEXP @ V0) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V1)))))))))))
(TORDER_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c/__caret__ @ (((c== @ ((cEXP @ V1) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V0))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V3)) @ ((c< @ V3) @ V2))) @ (c~ @ (((c== @ ((cEXP @ V1) @ V3)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V0))))))))) @ ((c= @ ((corder @ V0) @ V1)) @ V2)))))))))
(TORDER_MINIMAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V1)) @ ((c< @ V1) @ ((corder @ V2) @ V0)))) @ (c~ @ (((c== @ ((cEXP @ V0) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V2)))))))))))
(TZAG_INVOLUTION_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V1)) @ ((c< @ (cNUMERAL @ c_0)) @ V2)))) @ ((c= @ (czag @ (czag @ ((c__comma__ @ V0) @ ((c__comma__ @ V1) @ V2))))) @ ((c__comma__ @ V0) @ ((c__comma__ @ V1) @ V2)))))))))))
(TLESS_LESS_EQ_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ V1) @ V0)) @ ((c<= @ V0) @ V2))) @ ((c< @ V1) @ V2)))))))))
(TLESS_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ V1) @ V0)) @ ((c< @ V0) @ V2))) @ ((c< @ V1) @ V2)))))))))
(TCONG_IMP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ V1) @ V0)) @ ((c/__caret__ @ ((c< @ V2) @ V0)) @ (((c== @ V1) @ V2) @ (cnum_mod @ V0))))) @ ((c= @ V1) @ V2)))))))))
(TBITSET_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ V0) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2))) @ ((cIN @ V1) @ (cbitset @ V0)))) @ ((c< @ V1) @ V2)))))))))
(TEXP_MONO_LT_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ V0) @ V1)) @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0))))) @ ((c< @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2))))))))))
(TDIV_MONO_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c<= @ ((c+ @ V0) @ V2)) @ V1))) @ ((c< @ ((cDIV @ V0) @ V2)) @ ((cDIV @ V1) @ V2))))))))))
(TDIV_MONO2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c<= @ V2) @ V0))) @ ((c<= @ ((cDIV @ V1) @ V0)) @ ((cDIV @ V1) @ V2))))))))))
(TDIV_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c<= @ V0) @ V1))) @ ((c<= @ ((cDIV @ V0) @ V2)) @ ((cDIV @ V1) @ V2))))))))))
(TLE_LDIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c<= @ V0) @ ((c* @ V1) @ V2)))) @ ((c<= @ ((cDIV @ V0) @ V1)) @ V2)))))))))
(TLT_LMULT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c< @ V0) @ V2))) @ ((c< @ ((c* @ V1) @ V0)) @ ((c* @ V1) @ V2))))))))))
(TLUCAS_COPRIME_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ (((c== @ ((cEXP @ V1) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V2)))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V2))))))))))
(TDIVIDES_EXP2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((cnum_divides @ ((cEXP @ V1) @ V0)) @ V2))) @ ((cnum_divides @ V1) @ V2)))))))))
(TMULT_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2)))) @ ((c= @ V1) @ V2)))))))))
(TCONG_SOLVE_UNIQUE_NONTRIVIAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cprime @ V2)) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V2) @ V1))) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c< @ V0) @ V2))))) @ (c?! @ (^[V3]: ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V3)) @ ((c/__caret__ @ ((c< @ V3) @ V2)) @ (((c== @ ((c* @ V0) @ V3)) @ V1) @ (cnum_mod @ V2))))))))))))))
(TPRIME_DIVEXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ ((cnum_divides @ V1) @ ((cEXP @ V2) @ V0)))) @ ((cnum_divides @ V1) @ V2)))))))))
(TPRIME_DIVPROD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ ((cnum_divides @ V1) @ ((c* @ V0) @ V2)))) @ ((c__caret__/ @ ((cnum_divides @ V1) @ V0)) @ ((cnum_divides @ V1) @ V2))))))))))
(TCOPRIME_PRIMEPOW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0))))) @ ((c= @ (cnum_coprime @ ((c__comma__ @ V2) @ ((cEXP @ V1) @ V0)))) @ (c~ @ ((cnum_divides @ V1) @ V2)))))))))))
(TPRIME_COPRIME_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ (cnum_coprime @ ((c__comma__ @ V0) @ V2)))) @ ((c__caret__/ @ (cnum_coprime @ ((c__comma__ @ V1) @ V0))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V2)))))))))))
(TPRIME_DIVEXP_N,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cprime @ V0)) @ ((cnum_divides @ V0) @ ((cEXP @ V1) @ V2)))) @ ((cnum_divides @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2))))))))))
(TPRIME_FACTOR_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cprime @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ V2) @ ((c* @ V0) @ V1))))) @ ((c< @ V1) @ V2)))))))))
(TCONG_SOLVE_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V0) @ V2))) @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0))))) @ (c?! @ (^[V3]: ((c/__caret__ @ ((c< @ V3) @ V2)) @ (((c== @ ((c* @ V0) @ V3)) @ V1) @ (cnum_mod @ V2)))))))))))))
(TCOPRIME_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (cnum_coprime @ ((c__comma__ @ V0) @ V2)))) @ (cnum_coprime @ ((c__comma__ @ V0) @ ((c* @ V1) @ V2)))))))))))
(TDIV_MOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ ((c* @ V2) @ V1)) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((cDIV @ V0) @ V2)) @ V1)) @ ((cDIV @ ((cMOD @ V0) @ ((c* @ V2) @ V1))) @ V2))))))))))
(TMOD_MOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ ((c* @ V2) @ V0)) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((cMOD @ V1) @ ((c* @ V2) @ V0))) @ V2)) @ ((cMOD @ V1) @ V2))))))))))
(TDIV_DIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ ((c* @ V1) @ V2)) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cDIV @ ((cDIV @ V0) @ V1)) @ V2)) @ ((cDIV @ V0) @ ((c* @ V1) @ V2)))))))))))
(TMOD_MULT2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ ((c* @ V0) @ V2)) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2))) @ ((c* @ V0) @ ((cMOD @ V1) @ V2)))))))))))
(TDIV_MULT2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ ((c* @ V0) @ V2)) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cDIV @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2))) @ ((cDIV @ V1) @ V2))))))))))
(TMOD_EXP_MOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((cEXP @ ((cMOD @ V0) @ V2)) @ V1)) @ V2)) @ ((cMOD @ ((cEXP @ V0) @ V1)) @ V2))))))))))
(TMOD_ADD_MOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((c+ @ ((cMOD @ V0) @ V2)) @ ((cMOD @ V1) @ V2))) @ V2)) @ ((cMOD @ ((c+ @ V0) @ V1)) @ V2))))))))))
(TMOD_MULT_MOD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((c* @ ((cMOD @ V0) @ V2)) @ ((cMOD @ V1) @ V2))) @ V2)) @ ((cMOD @ ((c* @ V0) @ V1)) @ V2))))))))))
(TMOD_MULT_LMOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((c* @ ((cMOD @ V0) @ V2)) @ V1)) @ V2)) @ ((cMOD @ ((c* @ V0) @ V1)) @ V2))))))))))
(TMOD_MULT_RMOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((c* @ V0) @ ((cMOD @ V1) @ V2))) @ V2)) @ ((cMOD @ ((c* @ V0) @ V1)) @ V2))))))))))
(TDIV_MULT_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cDIV @ ((c+ @ ((c* @ V0) @ V2)) @ V1)) @ V2)) @ ((c+ @ V0) @ ((cDIV @ V1) @ V2)))))))))))
(TCONG_LMOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ (((c== @ ((cMOD @ V0) @ V2)) @ V1) @ (cnum_mod @ V2))) @ (((c== @ V0) @ V1) @ (cnum_mod @ V2)))))))))))
(TCONG_RMOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ (((c== @ V0) @ ((cMOD @ V1) @ V2)) @ (cnum_mod @ V2))) @ (((c== @ V0) @ V1) @ (cnum_mod @ V2)))))))))))
(TDIV_ADD_MOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ ((c= @ ((cMOD @ ((c+ @ V0) @ V1)) @ V2)) @ ((c+ @ ((cMOD @ V0) @ V2)) @ ((cMOD @ V1) @ V2)))) @ ((c= @ ((cDIV @ ((c+ @ V0) @ V1)) @ V2)) @ ((c+ @ ((cDIV @ V0) @ V2)) @ ((cDIV @ V1) @ V2))))))))))))
(TMULT_DIV_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c<= @ ((c* @ V0) @ ((cDIV @ V1) @ V2))) @ ((cDIV @ ((c* @ V0) @ V1)) @ V2))))))))))
(TLE_LDIV_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ ((c<= @ ((cDIV @ V0) @ V1)) @ V2)) @ ((c< @ V0) @ ((c* @ V1) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))
(TDIVIDES_EXP2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cnum_divides @ ((cEXP @ V1) @ V0)) @ ((cEXP @ V2) @ V0))) @ ((cnum_divides @ V1) @ V2))))))))))
(TDIVIDES_RMUL2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cnum_divides @ ((c* @ V1) @ V0)) @ ((c* @ V2) @ V0))) @ ((cnum_divides @ V1) @ V2))))))))))
(TDIVIDES_LMUL2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cnum_divides @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2))) @ ((cnum_divides @ V1) @ V2))))))))))
(TLE_RDIV_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((c<= @ V1) @ ((cDIV @ V2) @ V0))) @ ((c<= @ ((c* @ V0) @ V1)) @ V2))))))))))
(TPRIME_XYZ_NONZERO_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cprime @ ((c+ @ ((cEXP @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ V0) @ V1))))) @ ((c< @ (cNUMERAL @ c_0)) @ V2)))))))))
(TPRIME_XYZ_NONZERO_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cprime @ ((c+ @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ V2) @ V1))))) @ ((c< @ (cNUMERAL @ c_0)) @ V2)))))))))
(TPRIME_XYZ_NONZERO_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cprime @ ((c+ @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ V1) @ V2))))) @ ((c< @ (cNUMERAL @ c_0)) @ V2)))))))))
(TDIVIDES_PRIMEPOW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cprime @ V2)) @ ((c= @ ((cnum_divides @ V1) @ ((cEXP @ V2) @ V0))) @ (c? @ (^[V3]: ((c/__caret__ @ ((c<= @ V3) @ V0)) @ ((c= @ V1) @ ((cEXP @ V2) @ V3))))))))))))))
(TPRIME_DIVPROD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cprime @ V1)) @ ((c= @ ((cnum_divides @ V1) @ ((c* @ V0) @ V2))) @ ((c__caret__/ @ ((cnum_divides @ V1) @ V0)) @ ((cnum_divides @ V1) @ V2)))))))))))
(TQUADRATIC_RESIDUE_PAIR_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cprime @ V0)) @ ((c= @ (((c== @ ((cEXP @ ((c+ @ V1) @ V2)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cnum_mod @ V0))) @ ((c__caret__/ @ ((cnum_divides @ V0) @ V2)) @ ((cnum_divides @ V0) @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ V2))))))))))))
(TPRIME_DIVEXP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cprime @ V0)) @ ((c= @ ((cnum_divides @ V0) @ ((cEXP @ V1) @ V2))) @ ((c/__caret__ @ ((cnum_divides @ V0) @ V1)) @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))))
(TEQ_PRIMEPOW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cprime @ V0)) @ ((c= @ ((c= @ ((cEXP @ V0) @ V1)) @ ((cEXP @ V0) @ V2))) @ ((c= @ V1) @ V2))))))))))
(TCOPRIME_RMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V1) @ ((c* @ V2) @ V0)))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V2))))))))))
(TCOPRIME_LMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V1) @ ((c* @ V0) @ V2)))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V2))))))))))
(TCOPRIME_PRIME,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V2))) @ (c~ @ ((c/__caret__ @ (cprime @ V1)) @ ((c/__caret__ @ ((cnum_divides @ V1) @ V0)) @ ((cnum_divides @ V1) @ V2))))))))))))
(TCONG_SOLVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V2))) @ (c? @ (^[V3]: (((c== @ ((c* @ V0) @ V3)) @ V1) @ (cnum_mod @ V2))))))))))))
(TCOPRIME_EXP_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (cnum_coprime @ ((c__comma__ @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2)))))))))))
(TCOPRIME_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (cnum_coprime @ ((c__comma__ @ V0) @ ((cEXP @ V1) @ V2)))))))))))
(Tzag,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (czag @ ((c__comma__ @ V0) @ ((c__comma__ @ V2) @ V1)))) @ (((cCOND @ ((c< @ ((c+ @ V0) @ V1)) @ V2)) @ ((c__comma__ @ ((c+ @ V0) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))) @ ((c__comma__ @ V1) @ ((c- @ V2) @ ((c+ @ V0) @ V1))))) @ (((cCOND @ ((c< @ V0) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2))) @ ((c__comma__ @ ((c- @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ V0)) @ ((c__comma__ @ V2) @ ((c- @ ((c+ @ V0) @ V1)) @ V2)))) @ ((c__comma__ @ ((c- @ V0) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2))) @ ((c__comma__ @ ((c- @ ((c+ @ V0) @ V1)) @ V2)) @ V2))))))))))))
(Ttag,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (ctag @ ((c__comma__ @ V0) @ ((c__comma__ @ V2) @ V1)))) @ ((c__comma__ @ V0) @ ((c__comma__ @ V1) @ V2))))))))))
(TARITHMETIC_PROGRESSION_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V1)) @ (^[V3]: ((c+ @ V0) @ ((c* @ V2) @ V3))))) @ ((cDIV @ ((c* @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ ((c* @ V1) @ V2)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TNSUM_CONST_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnsum @ ((c.. @ V1) @ V0)) @ (^[V3]: V2))) @ ((c* @ ((c- @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)) @ V2)))))))))
(TNPRODUCT_CONST_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnproduct @ ((c.. @ V2) @ V1)) @ (^[V3]: V0))) @ ((cEXP @ V0) @ ((c- @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2))))))))))
(TMOD_MULT_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMOD @ ((c+ @ ((c* @ V0) @ V2)) @ V1)) @ V2)) @ ((cMOD @ V1) @ V2)))))))))
(TEXP_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cEXP @ ((cEXP @ V0) @ V1)) @ V2)) @ ((cEXP @ V0) @ ((c* @ V1) @ V2))))))))))
(TBINOMIAL_THEOREM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cEXP @ ((c+ @ V0) @ V1)) @ V2)) @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V3]: ((c* @ (cbinom @ ((c__comma__ @ V2) @ V3))) @ ((c* @ ((cEXP @ V0) @ V3)) @ ((cEXP @ V1) @ ((c- @ V2) @ V3))))))))))))))
(TMULT_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cEXP @ ((c* @ V0) @ V1)) @ V2)) @ ((c* @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2))))))))))
(TEXP_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cEXP @ V1) @ ((c+ @ V0) @ V2))) @ ((c* @ ((cEXP @ V1) @ V0)) @ ((cEXP @ V1) @ V2))))))))))
(TEXP_MULT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cEXP @ V0) @ ((c* @ V1) @ V2))) @ ((cEXP @ ((cEXP @ V0) @ V1)) @ V2)))))))))
(TSUB_ADD_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c- @ ((c+ @ V1) @ V0)) @ ((c+ @ V2) @ V0))) @ ((c- @ V1) @ V2)))))))))
(TSUB_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c- @ ((c+ @ V0) @ V1)) @ ((c+ @ V0) @ V2))) @ ((c- @ V1) @ V2)))))))))
(TADD_AC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c+ @ ((c+ @ V0) @ V1)) @ V2)) @ ((c+ @ V0) @ ((c+ @ V1) @ V2))))))))))
(TADD_AC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c+ @ V1) @ ((c+ @ V0) @ V2))) @ ((c+ @ V0) @ ((c+ @ V1) @ V2))))))))))
(TADD_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c+ @ V0) @ ((c+ @ V1) @ V2))) @ ((c+ @ ((c+ @ V0) @ V1)) @ V2)))))))))
(TRIGHT_SUB_DISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c* @ ((c- @ V0) @ V1)) @ V2)) @ ((c- @ ((c* @ V0) @ V2)) @ ((c* @ V1) @ V2))))))))))
(TRIGHT_ADD_DISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c* @ ((c+ @ V0) @ V1)) @ V2)) @ ((c+ @ ((c* @ V0) @ V2)) @ ((c* @ V1) @ V2))))))))))
(TMULT_AC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c* @ ((c* @ V0) @ V1)) @ V2)) @ ((c* @ V0) @ ((c* @ V1) @ V2))))))))))
(TDIST_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c* @ (cdist @ ((c__comma__ @ V0) @ V1))) @ V2)) @ (cdist @ ((c__comma__ @ ((c* @ V0) @ V2)) @ ((c* @ V1) @ V2)))))))))))
(TLEFT_SUB_DISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c* @ V1) @ ((c- @ V0) @ V2))) @ ((c- @ ((c* @ V1) @ V0)) @ ((c* @ V1) @ V2))))))))))
(TLEFT_ADD_DISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c* @ V1) @ ((c+ @ V0) @ V2))) @ ((c+ @ ((c* @ V1) @ V0)) @ ((c* @ V1) @ V2))))))))))
(TMULT_AC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c* @ V1) @ ((c* @ V0) @ V2))) @ ((c* @ V0) @ ((c* @ V1) @ V2))))))))))
(TDIST_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c* @ V1) @ (cdist @ ((c__comma__ @ V0) @ V2)))) @ (cdist @ ((c__comma__ @ ((c* @ V1) @ V0)) @ ((c* @ V1) @ V2)))))))))))
(TMULT_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c* @ V0) @ ((c* @ V1) @ V2))) @ ((c* @ ((c* @ V0) @ V1)) @ V2)))))))))
(TGCD_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_gcd @ ((c__comma__ @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2)))) @ ((cEXP @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ V2)))))))))
(TGCD_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_gcd @ ((c__comma__ @ ((c* @ V1) @ V0)) @ ((c* @ V2) @ V0)))) @ ((c* @ V0) @ (cnum_gcd @ ((c__comma__ @ V1) @ V2)))))))))))
(TGCD_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_gcd @ ((c__comma__ @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2)))) @ ((c* @ V0) @ (cnum_gcd @ ((c__comma__ @ V1) @ V2)))))))))))
(TGCD_LCM_DISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_gcd @ ((c__comma__ @ V1) @ (clcm @ ((c__comma__ @ V0) @ V2))))) @ (clcm @ ((c__comma__ @ (cnum_gcd @ ((c__comma__ @ V1) @ V0))) @ (cnum_gcd @ ((c__comma__ @ V1) @ V2))))))))))))
(TGCD_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ (cnum_gcd @ ((c__comma__ @ V1) @ V2))))) @ (cnum_gcd @ ((c__comma__ @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ V2))))))))))
(TLCM_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (clcm @ ((c__comma__ @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2)))) @ ((cEXP @ (clcm @ ((c__comma__ @ V0) @ V1))) @ V2)))))))))
(TLCM_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (clcm @ ((c__comma__ @ ((c* @ V1) @ V0)) @ ((c* @ V2) @ V0)))) @ ((c* @ V0) @ (clcm @ ((c__comma__ @ V1) @ V2)))))))))))
(TLCM_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (clcm @ ((c__comma__ @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2)))) @ ((c* @ V0) @ (clcm @ ((c__comma__ @ V1) @ V2)))))))))))
(TLCM_GCD_DISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (clcm @ ((c__comma__ @ V1) @ (cnum_gcd @ ((c__comma__ @ V0) @ V2))))) @ (cnum_gcd @ ((c__comma__ @ (clcm @ ((c__comma__ @ V1) @ V0))) @ (clcm @ ((c__comma__ @ V1) @ V2))))))))))))
(TLCM_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (clcm @ ((c__comma__ @ V0) @ (clcm @ ((c__comma__ @ V1) @ V2))))) @ (clcm @ ((c__comma__ @ (clcm @ ((c__comma__ @ V0) @ V1))) @ V2))))))))))
(TDIST_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cdist @ ((c__comma__ @ ((c+ @ V1) @ V0)) @ ((c+ @ V2) @ V0)))) @ (cdist @ ((c__comma__ @ V1) @ V2))))))))))
(TDIST_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cdist @ ((c__comma__ @ ((c+ @ V0) @ V1)) @ ((c+ @ V0) @ V2)))) @ (cdist @ ((c__comma__ @ V1) @ V2))))))))))
(TFROM_INTER_NUMSEG_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cINTER @ (cfrom @ V0)) @ ((c.. @ V1) @ V2))) @ (((cCOND @ ((c< @ V1) @ V0)) @ ((c.. @ V0) @ V2)) @ ((c.. @ V1) @ V2))))))))))
(TNUMSEG_OFFSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c.. @ ((c+ @ V1) @ V0)) @ ((c+ @ V2) @ V0))) @ ((cIMAGE @ (^[V3]: ((c+ @ V3) @ V0))) @ ((c.. @ V1) @ V2))))))))))
(Tnat_mod,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cnum_mod @ V2) @ V0) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ ((c+ @ V0) @ ((c* @ V2) @ V3))) @ ((c+ @ V1) @ ((c* @ V2) @ V4)))))))))))))))
(Tnum_mod,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cnum_mod @ V0) @ V1) @ V2)) @ (((cint_mod @ (cint_of_num @ V0)) @ (cint_of_num @ V1)) @ (cint_of_num @ V2))))))))))
(TORDER_DIVIDES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ ((cEXP @ V1) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V0))) @ ((cnum_divides @ ((corder @ V0) @ V1)) @ V2)))))))))
(TCONG_ADD_RCANCEL_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ ((c+ @ V1) @ V0)) @ V0) @ (cnum_mod @ V2))) @ (((c== @ V1) @ (cNUMERAL @ c_0)) @ (cnum_mod @ V2))))))))))
(TCONG_ADD_LCANCEL_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ ((c+ @ V0) @ V1)) @ V0) @ (cnum_mod @ V2))) @ (((c== @ V1) @ (cNUMERAL @ c_0)) @ (cnum_mod @ V2))))))))))
(TCONG_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ V2) @ V0) @ (cnum_mod @ V1))) @ ((c__caret__/ @ (c? @ (^[V3]: ((c= @ V2) @ ((c+ @ ((c* @ V3) @ V1)) @ V0))))) @ (c? @ (^[V3]: ((c= @ V0) @ ((c+ @ ((c* @ V3) @ V1)) @ V2)))))))))))))
(TCONG_SUB_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ V0) @ V1) @ (cnum_mod @ V2))) @ (((cCOND @ ((c<= @ V0) @ V1)) @ (((c== @ ((c- @ V1) @ V0)) @ (cNUMERAL @ c_0)) @ (cnum_mod @ V2))) @ (((c== @ ((c- @ V0) @ V1)) @ (cNUMERAL @ c_0)) @ (cnum_mod @ V2)))))))))))
(Tnum_congruent,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ V0) @ V1) @ (cnum_mod @ V2))) @ (((c== @ (cint_of_num @ V0)) @ (cint_of_num @ V1)) @ (cint_mod @ (cint_of_num @ V2)))))))))))
(TLCM_DIVIDES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnum_divides @ (clcm @ ((c__comma__ @ V0) @ V1))) @ V2)) @ ((c/__caret__ @ ((cnum_divides @ V0) @ V2)) @ ((cnum_divides @ V1) @ V2))))))))))
(TDIVIDES_GCD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnum_divides @ V1) @ (cnum_gcd @ ((c__comma__ @ V0) @ V2)))) @ ((c/__caret__ @ ((cnum_divides @ V1) @ V0)) @ ((cnum_divides @ V1) @ V2))))))))))
(TEGCD_INVARIANT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnum_divides @ V1) @ (cegcd @ ((c__comma__ @ V0) @ V2)))) @ ((c/__caret__ @ ((cnum_divides @ V1) @ V0)) @ ((cnum_divides @ V1) @ V2))))))))))
(TDIVIDES_LCM_GCD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnum_divides @ V0) @ (clcm @ ((c__comma__ @ V1) @ V2)))) @ ((cnum_divides @ ((c* @ V0) @ (cnum_gcd @ ((c__comma__ @ V1) @ V2)))) @ ((c* @ V1) @ V2))))))))))
(TIN_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ V1) @ ((c.. @ V0) @ V2))) @ ((c/__caret__ @ ((c<= @ V0) @ V1)) @ ((c<= @ V1) @ V2))))))))))
(TSUB_LEFT_GREATER_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c>= @ V0) @ ((c- @ V2) @ V1))) @ ((c>= @ ((c+ @ V0) @ V1)) @ V2)))))))))
(TEXP_MONO_EQ_SUC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cEXP @ V1) @ (cSUC @ V0))) @ ((cEXP @ V2) @ (cSUC @ V0)))) @ ((c= @ V1) @ V2)))))))))
(TEXP_MONO_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TEQ_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cEXP @ V0) @ V1)) @ ((cEXP @ V0) @ V2))) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ V1) @ V2)))))))))))
(TEQ_ADD_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((c+ @ V1) @ V0)) @ ((c+ @ V2) @ V0))) @ ((c= @ V1) @ V2)))))))))
(TEQ_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((c+ @ V0) @ V1)) @ ((c+ @ V0) @ V2))) @ ((c= @ V1) @ V2)))))))))
(TMULT_MONO_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((c* @ (cSUC @ V0)) @ V1)) @ ((c* @ (cSUC @ V0)) @ V2))) @ ((c= @ V1) @ V2)))))))))
(TEQ_MULT_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((c* @ V0) @ V2)) @ ((c* @ V1) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TEQ_MULT_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V1) @ V2))))))))))
(TEXP_MONO_LE_SUC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c<= @ ((cEXP @ V1) @ (cSUC @ V0))) @ ((cEXP @ V2) @ (cSUC @ V0)))) @ ((c<= @ V1) @ V2)))))))))
(TEXP_MONO_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c<= @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2))) @ ((c__caret__/ @ ((c<= @ V0) @ V1)) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TLE_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c<= @ ((cEXP @ V0) @ V1)) @ ((cEXP @ V0) @ V2))) @ (((cCOND @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c==> @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c<= @ V1) @ V2)))))))))))
(TLE_ADD_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c<= @ ((c+ @ V1) @ V0)) @ ((c+ @ V2) @ V0))) @ ((c<= @ V1) @ V2)))))))))
(TLE_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c<= @ ((c+ @ V0) @ V1)) @ ((c+ @ V0) @ V2))) @ ((c<= @ V1) @ V2)))))))))
(TLE_MULT_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c<= @ ((c* @ V0) @ V2)) @ ((c* @ V1) @ V2))) @ ((c__caret__/ @ ((c<= @ V0) @ V1)) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TLE_MULT_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c<= @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c<= @ V1) @ V2))))))))))
(TDIST_LE_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c<= @ (cdist @ ((c__comma__ @ V1) @ V0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V1) @ ((c+ @ V0) @ V2))) @ ((c<= @ V0) @ ((c+ @ V1) @ V2)))))))))))
(TSUB_LEFT_LESS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c<= @ V2) @ ((c- @ V1) @ V0))) @ ((c__caret__/ @ ((c<= @ ((c+ @ V2) @ V0)) @ V1)) @ ((c<= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TEXP_MONO_LT_SUC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c< @ ((cEXP @ V1) @ (cSUC @ V0))) @ ((cEXP @ V2) @ (cSUC @ V0)))) @ ((c< @ V1) @ V2)))))))))
(TEXP_MONO_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c< @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2))) @ ((c/__caret__ @ ((c< @ V0) @ V1)) @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0))))))))))))
(TLT_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c< @ ((cEXP @ V0) @ V1)) @ ((cEXP @ V0) @ V2))) @ ((c__caret__/ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ ((c< @ V1) @ V2))) @ ((c/__caret__ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))))
(TLESS_MONO_ADD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c< @ ((c+ @ V1) @ V0)) @ ((c+ @ V2) @ V0))) @ ((c< @ V1) @ V2)))))))))
(TLT_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c< @ ((c+ @ V0) @ V1)) @ ((c+ @ V0) @ V2))) @ ((c< @ V1) @ V2)))))))))
(TLESS_MULT_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c< @ ((c* @ (cSUC @ V0)) @ V1)) @ ((c* @ (cSUC @ V0)) @ V2))) @ ((c< @ V1) @ V2)))))))))
(TLT_MULT_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c< @ ((c* @ V0) @ V2)) @ ((c* @ V1) @ V2))) @ ((c/__caret__ @ ((c< @ V0) @ V1)) @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0))))))))))))
(TLT_MULT_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c< @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c< @ V1) @ V2))))))))))
(TLT_MAX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c< @ V1) @ ((cMAX @ V0) @ V2))) @ ((c__caret__/ @ ((c< @ V1) @ V0)) @ ((c< @ V1) @ V2))))))))))
(TLCM_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ ((cnum_divides @ V1) @ V0)) @ ((c/__caret__ @ ((cnum_divides @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V1) @ V3)) @ ((cnum_divides @ V2) @ V3))) @ ((cnum_divides @ V0) @ V3))))))) @ ((c= @ V0) @ (clcm @ ((c__comma__ @ V1) @ V2)))))))))))
(TGCD_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ ((c/__caret__ @ ((cnum_divides @ V0) @ V1)) @ ((cnum_divides @ V0) @ V2))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V3) @ V1)) @ ((cnum_divides @ V3) @ V2))) @ ((cnum_divides @ V3) @ V0)))))) @ ((c= @ V0) @ (cnum_gcd @ ((c__comma__ @ V1) @ V2)))))))))))
(TCOPRIME_EXP2_SUC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_coprime @ ((c__comma__ @ ((cEXP @ V1) @ (cSUC @ V0))) @ ((cEXP @ V2) @ (cSUC @ V0))))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V2))))))))))
(TCOPRIME_EXP2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_coprime @ ((c__comma__ @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2)))) @ ((c__caret__/ @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TCOPRIME_LEXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_coprime @ ((c__comma__ @ ((cEXP @ V0) @ V2)) @ V1))) @ ((c__caret__/ @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TCOPRIME_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_coprime @ ((c__comma__ @ ((c* @ V0) @ V1)) @ V2))) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V0) @ V2))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V2)))))))))))
(TCOPRIME_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_coprime @ ((c__comma__ @ V1) @ ((c* @ V0) @ V2)))) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V1) @ V0))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V2)))))))))))
(TCOPRIME_REXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cnum_coprime @ ((c__comma__ @ V0) @ ((cEXP @ V1) @ V2)))) @ ((c__caret__/ @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TGCD_BEZOUT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: (c? @ (^[V4]: ((c__caret__/ @ ((c= @ ((c- @ ((c* @ V0) @ V3)) @ ((c* @ V1) @ V4))) @ V2)) @ ((c= @ ((c- @ ((c* @ V1) @ V3)) @ ((c* @ V0) @ V4))) @ V2))))))) @ ((cnum_divides @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ V2)))))))))
(TBOUNDS_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c<= @ ((c* @ V1) @ V3)) @ ((c+ @ ((c* @ V2) @ V3)) @ V0))))) @ ((c<= @ V1) @ V2)))))))))
(TBEZOUT_GCD_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c__caret__/ @ ((c= @ ((c- @ ((c* @ ((cEXP @ V0) @ V2)) @ V3)) @ ((c* @ ((cEXP @ V1) @ V2)) @ V4))) @ ((cEXP @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ V2))) @ ((c= @ ((c- @ ((c* @ ((cEXP @ V1) @ V2)) @ V3)) @ ((c* @ ((cEXP @ V0) @ V2)) @ V4))) @ ((cEXP @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ V2))))))))))))))
(TCONG_ADD_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((c== @ ((c+ @ V1) @ V0)) @ ((c+ @ V2) @ V0)) @ (cnum_mod @ V3))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3))))))))))))
(TCONG_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((c== @ ((c+ @ V0) @ V1)) @ ((c+ @ V0) @ V2)) @ (cnum_mod @ V3))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3))))))))))))
(TCONG_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((c== @ V0) @ V1) @ (cnum_mod @ V3))) @ (((c== @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V2)) @ (cnum_mod @ V3))))))))))))
(TNUMPAIR_INJ_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ ((cNUMPAIR @ V2) @ V0)) @ ((cNUMPAIR @ V3) @ V1))) @ ((c= @ V2) @ V3)))))))))))
(TMOD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ V1) @ ((c+ @ V2) @ ((c* @ V0) @ V3)))) @ ((c= @ ((cMOD @ V1) @ V3)) @ ((cMOD @ V2) @ V3))))))))))))
(TNPAIR_INJ_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c< @ ((c+ @ V0) @ V1)) @ ((c+ @ V2) @ V3))) @ ((c< @ ((cNPAIR @ V0) @ V1)) @ ((cNPAIR @ V2) @ V3))))))))))))
(TCONG_DIVIDES_MODULUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((c== @ V1) @ V2) @ (cnum_mod @ V0))) @ ((cnum_divides @ V3) @ V0))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3))))))))))))
(TCOPRIME_EXP_DIVPROD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ ((cEXP @ V1) @ V2)) @ ((c* @ V0) @ V3))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V0)))) @ ((cnum_divides @ ((cEXP @ V1) @ V2)) @ V3)))))))))))
(TCOPRIME_DIVISORS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V2) @ V0)) @ ((c/__caret__ @ ((cnum_divides @ V3) @ V1)) @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))))) @ (cnum_coprime @ ((c__comma__ @ V2) @ V3))))))))))))
(TDIVIDES_MUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cnum_divides @ V0) @ V2)) @ ((cnum_divides @ V1) @ V3))) @ ((cnum_divides @ ((c* @ V0) @ V1)) @ ((c* @ V2) @ V3))))))))))))
(TMULT_EQ_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ ((c* @ V1) @ V2)) @ ((c* @ V3) @ V0))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V3)))) @ (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((c* @ V1) @ V4))) @ ((c= @ V2) @ ((c* @ V3) @ V4)))))))))))))))
(TDIVIDES_DIV_NOT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ V3) @ ((c+ @ ((c* @ V0) @ V2)) @ V1))) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V1)) @ ((c< @ V1) @ V2)))) @ (c~ @ ((cnum_divides @ V2) @ V3))))))))))))
(TDIV_UNIQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ V1) @ ((c+ @ ((c* @ V3) @ V2)) @ V0))) @ ((c< @ V0) @ V2))) @ ((c= @ ((cDIV @ V1) @ V2)) @ V3)))))))))))
(TMOD_UNIQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ V1) @ ((c+ @ ((c* @ V0) @ V2)) @ V3))) @ ((c< @ V3) @ V2))) @ ((c= @ ((cMOD @ V1) @ V2)) @ V3)))))))))))
(TPOCKLINGTON,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ ((c/__caret__ @ ((c= @ ((c- @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c* @ V1) @ V0))) @ ((c/__caret__ @ ((c<= @ V3) @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (((c== @ ((cEXP @ V2) @ ((c- @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V3))) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cprime @ V4)) @ ((cnum_divides @ V4) @ V1))) @ (cnum_coprime @ ((c__comma__ @ ((c- @ ((cEXP @ V2) @ ((cDIV @ ((c- @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V4))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3)))))))))) @ (cprime @ V3)))))))))))
(TPOCKLINGTON_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ ((c/__caret__ @ ((c= @ ((c- @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c* @ V1) @ V0))) @ ((c/__caret__ @ ((c<= @ V3) @ ((cEXP @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (((c== @ ((cEXP @ V2) @ ((c- @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V3))) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cprime @ V4)) @ ((cnum_divides @ V4) @ V1))) @ (c? @ (^[V5]: ((c/__caret__ @ (((c== @ ((cEXP @ V2) @ ((cDIV @ ((c- @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V4))) @ V5) @ (cnum_mod @ V3))) @ (cnum_coprime @ ((c__comma__ @ ((c- @ V5) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3))))))))))))) @ (cprime @ V3)))))))))))
(TLE_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ V0) @ V2)) @ ((c<= @ V1) @ V3))) @ ((c<= @ ((c+ @ V0) @ V1)) @ ((c+ @ V2) @ V3))))))))))))
(TLESS_EQ_MULT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ V0) @ V2)) @ ((c<= @ V1) @ V3))) @ ((c<= @ ((c* @ V0) @ V1)) @ ((c* @ V2) @ V3))))))))))))
(TLET_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ V0) @ V2)) @ ((c< @ V1) @ V3))) @ ((c< @ ((c+ @ V0) @ V1)) @ ((c+ @ V2) @ V3))))))))))))
(TDIV_EQ_EXCLUSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ ((c* @ V1) @ V2)) @ ((c* @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3))) @ ((c< @ ((c* @ V0) @ V3)) @ ((c* @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)))) @ ((c= @ ((cDIV @ V0) @ V1)) @ ((cDIV @ V2) @ V3))))))))))))
(TZSET_BOUND_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V1)) @ ((c= @ ((c+ @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ V2) @ V1)))) @ V3)))) @ ((c<= @ V2) @ V3)))))))))))
(TZSET_BOUND_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V1)) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c= @ ((c+ @ ((cEXP @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ V1) @ V2)))) @ V3)))) @ ((c<= @ V2) @ V3)))))))))))
(TZSET_BOUND_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V1)) @ ((c= @ ((c+ @ ((cEXP @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c* @ V0) @ V1)))) @ V3)))) @ ((c<= @ V2) @ V3)))))))))))
(TLTE_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ V0) @ V2)) @ ((c<= @ V1) @ V3))) @ ((c< @ ((c+ @ V0) @ V1)) @ ((c+ @ V2) @ V3))))))))))))
(TLT_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ V0) @ V2)) @ ((c< @ V1) @ V3))) @ ((c< @ ((c+ @ V0) @ V1)) @ ((c+ @ V2) @ V3))))))))))))
(TLESS_MULT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ V0) @ V2)) @ ((c< @ V1) @ V3))) @ ((c< @ ((c* @ V0) @ V1)) @ ((c* @ V2) @ V3))))))))))))
(TGCD_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ V0) @ ((c* @ V2) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))) @ ((c= @ V1) @ ((c* @ V3) @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))))))) @ (cnum_coprime @ ((c__comma__ @ V2) @ V3))))))))))))
(TDIV_LE_EXCLUSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cNUMERAL @ c_0)))) @ ((c< @ ((c* @ V3) @ V0)) @ ((c* @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)))) @ ((c<= @ ((cDIV @ V0) @ V1)) @ ((cDIV @ V2) @ V3))))))))))))
(TMOD_MULT_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cNUMERAL @ c_0)))) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0))))) @ ((c= @ (((c== @ ((cMOD @ V1) @ ((c* @ V3) @ V0))) @ V2) @ (cnum_mod @ V3))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3)))))))))))))
(TEXP_MULT_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((c* @ ((cEXP @ V0) @ V3)) @ V2)) @ ((cEXP @ V1) @ V3)))) @ (c? @ (^[V4]: ((c= @ V2) @ ((cEXP @ V4) @ V3))))))))))))))
(TPRIME_POWER_MULT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cprime @ V3)) @ ((c= @ ((c* @ V1) @ V2)) @ ((cEXP @ V3) @ V0)))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V1) @ ((cEXP @ V3) @ V4))) @ ((c= @ V2) @ ((cEXP @ V3) @ V5)))))))))))))))))
(TPRIME_POWER_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cprime @ V3)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cEXP @ V2) @ V0)) @ ((cEXP @ V3) @ V1))))) @ (c? @ (^[V4]: ((c= @ V2) @ ((cEXP @ V3) @ V4))))))))))))))
(TPRIME_DIVPROD_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V0) @ V3))) @ ((cnum_divides @ ((cEXP @ V1) @ V2)) @ ((c* @ V0) @ V3))))) @ ((c__caret__/ @ ((cnum_divides @ ((cEXP @ V1) @ V2)) @ V0)) @ ((cnum_divides @ ((cEXP @ V1) @ V2)) @ V3))))))))))))
(TDIVIDES_PRIME_EXP_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cprime @ V0)) @ (cprime @ V1))) @ ((c= @ ((cnum_divides @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V3))) @ ((c__caret__/ @ ((c= @ V2) @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c<= @ V2) @ V3))))))))))))))
(TEQ_PRIME_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cprime @ V0)) @ (cprime @ V1))) @ ((c= @ ((c= @ ((cEXP @ V0) @ V2)) @ ((cEXP @ V1) @ V3))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V2) @ (cNUMERAL @ c_0))) @ ((c= @ V3) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ V3))))))))))))))
(TCONG_CHINESE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V2) @ V3))) @ ((c/__caret__ @ (((c== @ V0) @ V1) @ (cnum_mod @ V2))) @ (((c== @ V0) @ V1) @ (cnum_mod @ V3))))) @ (((c== @ V0) @ V1) @ (cnum_mod @ ((c* @ V2) @ V3)))))))))))))
(TCHINESE_REMAINDER_COPRIME_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V1) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V0) @ V1))) @ (cnum_coprime @ ((c__comma__ @ V2) @ V3))))))) @ (c?! @ (^[V4]: ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V4) @ ((c* @ V1) @ V3)))) @ ((c/__caret__ @ ((c< @ V4) @ ((c* @ V1) @ V3))) @ ((c/__caret__ @ (((c== @ V4) @ V0) @ (cnum_mod @ V1))) @ (((c== @ V4) @ V2) @ (cnum_mod @ V3)))))))))))))))))
(TCHINESE_REMAINDER_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V1) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ (c~ @ ((c= @ V3) @ (cNUMERAL @ c_0)))))) @ (c?! @ (^[V4]: ((c/__caret__ @ ((c< @ V4) @ ((c* @ V1) @ V3))) @ ((c/__caret__ @ (((c== @ V4) @ V0) @ (cnum_mod @ V1))) @ (((c== @ V4) @ V2) @ (cnum_mod @ V3))))))))))))))))
(TCHINESE_REMAINDER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V1) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ (c~ @ ((c= @ V3) @ (cNUMERAL @ c_0)))))) @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((c= @ V4) @ ((c+ @ V0) @ ((c* @ V5) @ V1)))) @ ((c= @ V4) @ ((c+ @ V2) @ ((c* @ V6) @ V3))))))))))))))))))))
(TCOPRIME_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V1) @ V2))) @ ((c= @ ((c* @ V1) @ V2)) @ ((cEXP @ V0) @ V3)))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V1) @ ((cEXP @ V4) @ V3))) @ ((c= @ V2) @ ((cEXP @ V5) @ V3)))))))))))))))))
(TCONG_MULT_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V0) @ V3))) @ (((c== @ ((c* @ V1) @ V0)) @ ((c* @ V2) @ V0)) @ (cnum_mod @ V3)))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3))))))))))))
(TCONG_MULT_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V0) @ V3))) @ (((c== @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2)) @ (cnum_mod @ V3)))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3))))))))))))
(TINDEX_ODDPART_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cODD @ V2)) @ (cODD @ V3))) @ ((c= @ ((c= @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ V2)) @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ V3)))))))))))))
(TMOD_MOD_EXP_MIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cMOD @ ((cMOD @ V0) @ ((cEXP @ V1) @ V2))) @ ((cEXP @ V1) @ V3))) @ ((cMOD @ V0) @ ((cEXP @ V1) @ ((cMIN @ V2) @ V3))))))))))))))
(TPRIMEPOW_DIVIDES_LCM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cprime @ V1)) @ ((c= @ ((cnum_divides @ ((cEXP @ V1) @ V2)) @ (clcm @ ((c__comma__ @ V0) @ V3)))) @ ((c__caret__/ @ ((cnum_divides @ ((cEXP @ V1) @ V2)) @ V0)) @ ((cnum_divides @ ((cEXP @ V1) @ V2)) @ V3)))))))))))))
(TORDER_DIVIDES_EXPDIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V2) @ V3))) @ ((c= @ (((c== @ ((cEXP @ V3) @ V0)) @ ((cEXP @ V3) @ V1)) @ (cnum_mod @ V2))) @ (((c== @ V0) @ V1) @ (cnum_mod @ ((corder @ V2) @ V3))))))))))))))
(TCONG_MULT_RCANCEL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V3))) @ ((c= @ (((c== @ ((c* @ V1) @ V0)) @ ((c* @ V2) @ V0)) @ (cnum_mod @ V3))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3)))))))))))))
(TCONG_MULT_LCANCEL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V3))) @ ((c= @ (((c== @ ((c* @ V0) @ V1)) @ ((c* @ V0) @ V2)) @ (cnum_mod @ V3))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3)))))))))))))
(TCONG_CHINESE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V0) @ V3))) @ ((c= @ (((c== @ V1) @ V2) @ (cnum_mod @ ((c* @ V0) @ V3)))) @ ((c/__caret__ @ (((c== @ V1) @ V2) @ (cnum_mod @ V0))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3))))))))))))))
(TGCD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c= @ ((c/__caret__ @ ((cnum_divides @ V4) @ V0)) @ ((cnum_divides @ V4) @ V1))) @ ((c/__caret__ @ ((cnum_divides @ V4) @ V2)) @ ((cnum_divides @ V4) @ V3)))))) @ ((c= @ (cnum_gcd @ ((c__comma__ @ V0) @ V1))) @ (cnum_gcd @ ((c__comma__ @ V2) @ V3)))))))))))))
(TLCM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c= @ ((c/__caret__ @ ((cnum_divides @ V0) @ V4)) @ ((cnum_divides @ V1) @ V4))) @ ((c/__caret__ @ ((cnum_divides @ V2) @ V4)) @ ((cnum_divides @ V3) @ V4)))))) @ ((c= @ (clcm @ ((c__comma__ @ V0) @ V1))) @ (clcm @ ((c__comma__ @ V2) @ V3)))))))))))))
(TCONG_ADD_RCANCEL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c== @ ((c+ @ V1) @ V0)) @ ((c+ @ V2) @ V0)) @ (cnum_mod @ V3))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3))))))))))))
(TCONG_ADD_LCANCEL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c== @ ((c+ @ V0) @ V1)) @ ((c+ @ V0) @ V2)) @ (cnum_mod @ V3))) @ (((c== @ V1) @ V2) @ (cnum_mod @ V3))))))))))))
(TSUBSET_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cSUBSET @ ((c.. @ V1) @ V2)) @ ((c.. @ V0) @ V3))) @ ((c__caret__/ @ ((c< @ V2) @ V1)) @ ((c/__caret__ @ ((c<= @ V0) @ V1)) @ ((c<= @ V2) @ V3)))))))))))))
(TDISJOINT_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cDISJOINT @ ((c.. @ V1) @ V0)) @ ((c.. @ V3) @ V2))) @ ((c__caret__/ @ ((c< @ V0) @ V3)) @ ((c__caret__/ @ ((c< @ V2) @ V1)) @ ((c__caret__/ @ ((c< @ V0) @ V1)) @ ((c< @ V2) @ V3))))))))))))))
(TNUMPAIR_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cNUMPAIR @ V0) @ V2)) @ ((cNUMPAIR @ V1) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ V3))))))))))))
(TNPAIR_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cNPAIR @ V0) @ V2)) @ ((cNPAIR @ V1) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ V3))))))))))))
(TDIST_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c<= @ (cdist @ ((c__comma__ @ ((c+ @ V0) @ V2)) @ ((c+ @ V1) @ V3)))) @ ((c+ @ (cdist @ ((c__comma__ @ V0) @ V1))) @ (cdist @ ((c__comma__ @ V2) @ V3)))))))))))))
(TDIST_ADD2_REV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c<= @ (cdist @ ((c__comma__ @ V0) @ V1))) @ ((c+ @ (cdist @ ((c__comma__ @ ((c+ @ V0) @ V2)) @ ((c+ @ V1) @ V3)))) @ (cdist @ ((c__comma__ @ V2) @ V3)))))))))))))
(TGCD_BEZOUT_SUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ ((c+ @ ((c* @ V2) @ V0)) @ ((c* @ V3) @ V1))) @ V4)) @ ((cnum_divides @ (cnum_gcd @ ((c__comma__ @ V2) @ V3))) @ V4)))))))))))))
(TCONG_MULT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c== @ V0) @ V2) @ (cnum_mod @ V4))) @ (((c== @ V1) @ V3) @ (cnum_mod @ V4)))) @ (((c== @ ((c* @ V0) @ V1)) @ ((c* @ V2) @ V3)) @ (cnum_mod @ V4))))))))))))))
(TPOCKLINGTON_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ ((c/__caret__ @ ((c= @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c* @ V4) @ V0))) @ ((c/__caret__ @ (((c== @ ((cEXP @ V1) @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V2))) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cprime @ V5)) @ ((cnum_divides @ V5) @ V4))) @ (cnum_coprime @ ((c__comma__ @ ((c- @ ((cEXP @ V1) @ ((cDIV @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V5))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2))))))))) @ ((c==> @ ((c/__caret__ @ (cprime @ V3)) @ ((cnum_divides @ V3) @ V2))) @ (((c== @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V4)))))))))))))))
(TSQUAREMOD_INJ_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cprime @ V3)) @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ ((c+ @ V1) @ V4))) @ V3)) @ ((c= @ ((c+ @ ((c* @ ((c+ @ V1) @ V4)) @ ((c+ @ V1) @ V4))) @ ((c* @ V0) @ V3))) @ ((c+ @ ((c* @ V1) @ V1)) @ ((c* @ V2) @ V3)))))) @ ((c= @ V4) @ (cNUMERAL @ c_0))))))))))))))
(TDIST_TRIANGLES_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cdist @ ((c__comma__ @ V0) @ V2))) @ V4)) @ ((c<= @ (cdist @ ((c__comma__ @ V1) @ V3))) @ V5))) @ ((c<= @ (cdist @ ((c__comma__ @ V0) @ V1))) @ ((c+ @ (cdist @ ((c__comma__ @ V2) @ V3))) @ ((c+ @ V4) @ V5)))))))))))))))))
(TDIVMOD_UNIQ_LEMMA_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c/__caret__ @ ((c= @ V1) @ ((c+ @ ((c* @ V4) @ V3)) @ V0))) @ ((c< @ V0) @ V3))) @ ((c/__caret__ @ ((c= @ V1) @ ((c+ @ ((c* @ V5) @ V3)) @ V2))) @ ((c< @ V2) @ V3)))) @ ((c= @ V4) @ V5)))))))))))))))
(TDIVMOD_UNIQ_LEMMA_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c/__caret__ @ ((c= @ V1) @ ((c+ @ ((c* @ V0) @ V3)) @ V4))) @ ((c< @ V4) @ V3))) @ ((c/__caret__ @ ((c= @ V1) @ ((c+ @ ((c* @ V2) @ V3)) @ V5))) @ ((c< @ V5) @ V3)))) @ ((c= @ V4) @ V5)))))))))))))))
(TAUBREY_LEMMA_4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V4) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (c~ @ ((c= @ V4) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((creal_add @ ((creal_pow @ ((creal_div @ (creal_of_num @ V0)) @ (creal_of_num @ V4))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ ((creal_div @ (creal_of_num @ V1)) @ (creal_of_num @ V4))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ ((creal_div @ (creal_of_num @ V2)) @ (creal_of_num @ V4))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ ((creal_div @ (creal_of_num @ V3)) @ (creal_of_num @ V4))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ V5))))) @ (c? @ (^[V6]: (c? @ (^[V7]: (c? @ (^[V8]: (c? @ (^[V9]: (c? @ (^[V10]: ((c/__caret__ @ (c~ @ ((c= @ V6) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c< @ V6) @ V4)) @ ((c= @ ((creal_add @ ((creal_pow @ ((creal_div @ (creal_of_num @ V7)) @ (creal_of_num @ V6))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ ((creal_div @ (creal_of_num @ V8)) @ (creal_of_num @ V6))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ ((creal_div @ (creal_of_num @ V9)) @ (creal_of_num @ V6))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ ((creal_div @ (creal_of_num @ V10)) @ (creal_of_num @ V6))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ V5))))))))))))))))))))))))))))
(TREAL_MUL_SUM_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c= @ ((creal_mul @ ((csum @ ((c.. @ V0) @ V1)) @ V4)) @ ((csum @ ((c.. @ V2) @ V3)) @ V5))) @ ((csum @ ((c.. @ V0) @ V1)) @ (^[V6]: ((csum @ ((c.. @ V2) @ V3)) @ (^[V7]: ((creal_mul @ (V4 @ V6)) @ (V5 @ V7))))))))))))))))))))
(TSUM_SWAP_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((csum @ ((c.. @ V2) @ V3)) @ (^[V5]: ((csum @ ((c.. @ V0) @ V1)) @ (V4 @ V5))))) @ ((csum @ ((c.. @ V0) @ V1)) @ (^[V5]: ((csum @ ((c.. @ V2) @ V3)) @ (^[V6]: ((V4 @ V6) @ V5)))))))))))))))))
(TSUM_SWAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((cpsum @ ((c__comma__ @ V2) @ V3)) @ (^[V5]: ((cpsum @ ((c__comma__ @ V0) @ V1)) @ (^[V6]: ((V4 @ V5) @ V6)))))) @ ((cpsum @ ((c__comma__ @ V0) @ V1)) @ (^[V5]: ((cpsum @ ((c__comma__ @ V2) @ V3)) @ (^[V6]: ((V4 @ V6) @ V5)))))))))))))))))
(TNSUM_SWAP_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((cnsum @ ((c.. @ V2) @ V3)) @ (^[V5]: ((cnsum @ ((c.. @ V0) @ V1)) @ (V4 @ V5))))) @ ((cnsum @ ((c.. @ V0) @ V1)) @ (^[V5]: ((cnsum @ ((c.. @ V2) @ V3)) @ (^[V6]: ((V4 @ V6) @ V5)))))))))))))))))
(TVSUM_SWAP_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((cvsum @ ((c.. @ V2) @ V3)) @ (^[V5]: ((cvsum @ ((c.. @ V0) @ V1)) @ (V4 @ V5))))) @ ((cvsum @ ((c.. @ V0) @ V1)) @ (^[V5]: ((cvsum @ ((c.. @ V2) @ V3)) @ (^[V6]: ((V4 @ V6) @ V5)))))))))))))))))
(TSUM_ADD_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((csum @ ((c.. @ V0) @ ((c+ @ V1) @ V2))) @ V3)) @ ((creal_add @ ((csum @ ((c.. @ V0) @ V1)) @ V3)) @ ((csum @ ((c.. @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c+ @ V1) @ V2))) @ V3)))))))))))))
(TPRODUCT_ADD_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cproduct @ ((c.. @ V0) @ ((c+ @ V1) @ V2))) @ V3)) @ ((creal_mul @ ((cproduct @ ((c.. @ V0) @ V1)) @ V3)) @ ((cproduct @ ((c.. @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c+ @ V1) @ V2))) @ V3)))))))))))))
(TVARIATION_SPLIT_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ ((c.. @ V0) @ V2))) @ (c~ @ ((c= @ (V3 @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((c= @ ((cvariation @ ((c.. @ V0) @ V2)) @ V3)) @ ((c+ @ ((cvariation @ ((c.. @ V0) @ V1)) @ V3)) @ ((cvariation @ ((c.. @ V1) @ V2)) @ V3)))))))))))))
(TSUM_MORETERMS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ V2) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ ((c+ @ V1) @ V2)) @ V4)) @ ((c< @ V4) @ ((c+ @ V1) @ V0)))) @ ((c= @ (V3 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((cpsum @ ((c__comma__ @ V1) @ V0)) @ V3)) @ ((cpsum @ ((c__comma__ @ V1) @ V2)) @ V3))))))))))))
(TSUM_COMBINE_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c<= @ V0) @ V2))) @ ((c= @ ((creal_add @ ((csum @ ((c.. @ V1) @ V0)) @ V3)) @ ((csum @ ((c.. @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2)) @ V3))) @ ((csum @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TSUM_COMBINE_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c/__caret__ @ ((c<= @ V1) @ V0)) @ ((c<= @ V0) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((c= @ ((creal_add @ ((csum @ ((c.. @ V1) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V3)) @ ((csum @ ((c.. @ V0) @ V2)) @ V3))) @ ((csum @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TVARIATION_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ V0) @ V1)) @ ((c< @ V1) @ V2))) @ ((c= @ ((cvariation @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY)))) @ V3)) @ (((cCOND @ ((c= @ (V3 @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((cvariation @ ((cINSERT @ V0) @ ((cINSERT @ V2) @ cEMPTY))) @ V3)) @ ((c+ @ ((cvariation @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))) @ V3)) @ ((cvariation @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))) @ V3))))))))))))))
(TSUM_ZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((c>= @ V4) @ V0)) @ ((c= @ (V3 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ ((c==> @ ((c>= @ V1) @ V0)) @ ((c= @ ((cpsum @ ((c__comma__ @ V1) @ V2)) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))))
(TSUM_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((creal_add @ ((cpsum @ ((c__comma__ @ V0) @ V1)) @ V3)) @ ((cpsum @ ((c__comma__ @ ((c+ @ V0) @ V1)) @ V2)) @ V3))) @ ((cpsum @ ((c__comma__ @ V0) @ ((c+ @ V1) @ V2))) @ V3)))))))))))
(TSERIES_DIRICHLET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cbounded @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((cIN @ V6) @ cUNIV)) @ ((cvsum @ ((c.. @ V0) @ V6)) @ V4)))))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c<= @ V1) @ V5)) @ ((creal_le @ (V3 @ ((c+ @ V5) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V3 @ V5)))))) @ (((c--> @ ((co @ clift) @ V3)) @ (cvec @ (cNUMERAL @ c_0))) @ csequentially)))) @ ((csummable @ (cfrom @ V2)) @ (^[V5]: ((c% @ (V3 @ V5)) @ (V4 @ V5))))))))))))))))
(TNSUM_ADD_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cnsum @ ((c.. @ V0) @ ((c+ @ V1) @ V2))) @ V3)) @ ((c+ @ ((cnsum @ ((c.. @ V0) @ V1)) @ V3)) @ ((cnsum @ ((c.. @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c+ @ V1) @ V2))) @ V3)))))))))))))
(TNPRODUCT_ADD_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cnproduct @ ((c.. @ V0) @ ((c+ @ V1) @ V2))) @ V3)) @ ((c* @ ((cnproduct @ ((c.. @ V0) @ V1)) @ V3)) @ ((cnproduct @ ((c.. @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c+ @ V1) @ V2))) @ V3)))))))))))))
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(TRELPOW_LEMMA_2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ ((c/__caret__ @ ((c< @ V4) @ V1)) @ ((c/__caret__ @ ((c< @ V5) @ V1)) @ ((c/__caret__ @ (c? @ (^[V6]: ((c= @ V0) @ ((c+ @ V4) @ ((c* @ V1) @ V6)))))) @ ((c/__caret__ @ (c? @ (^[V6]: ((c/__caret__ @ ((c< @ V6) @ ((cEXP @ V1) @ V2))) @ ((c= @ V0) @ ((c+ @ V6) @ ((c* @ ((cEXP @ V1) @ V2)) @ V5))))))) @ (c! @ (^[V6]: ((c==> @ ((c< @ V6) @ ((cEXP @ V1) @ V2))) @ ((c==> @ ((cprimepow @ V1) @ V6)) @ (c? @ (^[V7]: (c? @ (^[V8]: (c? @ (^[V9]: (c? @ (^[V10]: ((c/__caret__ @ ((c= @ V0) @ ((c+ @ V7) @ ((c* @ V6) @ ((c+ @ V8) @ ((c* @ V1) @ ((c+ @ V9) @ ((c* @ V1) @ V10)))))))) @ ((c/__caret__ @ ((c< @ V7) @ V6)) @ ((c/__caret__ @ ((c< @ V8) @ V1)) @ ((c/__caret__ @ ((c< @ V9) @ V1)) @ ((V3 @ V8) @ V9))))))))))))))))))))))) @ ((((cRELPOW @ V2) @ V3) @ V4) @ V5)))))))))))))))
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(TVSUM_COMBINE_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c/__caret__ @ ((c<= @ V1) @ V0)) @ ((c<= @ V0) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((c= @ ((cvector_add @ ((cvsum @ ((c.. @ V1) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V3)) @ ((cvsum @ ((c.. @ V0) @ V2)) @ V3))) @ ((cvsum @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TVSUM_ADD_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V0) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ ((c.. @ V0) @ ((c+ @ V1) @ V2))) @ V3)) @ ((cvector_add @ ((cvsum @ ((c.. @ V0) @ V1)) @ V3)) @ ((cvsum @ ((c.. @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c+ @ V1) @ V2))) @ V3)))))))))))))
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(TVSUM_PARTIAL_SUC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cvsum @ ((c.. @ V0) @ V1)) @ (^[V4]: ((c% @ (V2 @ V4)) @ ((cvector_sub @ (V3 @ ((c+ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V3 @ V4)))))) @ (((cCOND @ ((c<= @ V0) @ V1)) @ ((cvector_sub @ ((cvector_sub @ ((c% @ (V2 @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V3 @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c% @ (V2 @ V0)) @ (V3 @ V0)))) @ ((cvsum @ ((c.. @ V0) @ V1)) @ (^[V4]: ((c% @ ((creal_sub @ (V2 @ ((c+ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V2 @ V4))) @ (V3 @ ((c+ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ (cvec @ (cNUMERAL @ c_0)))))))))))))
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(TNPRODUCT_OFFSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cnproduct @ ((c.. @ ((c+ @ V0) @ V3)) @ ((c+ @ V1) @ V3))) @ V2)) @ ((cnproduct @ ((c.. @ V0) @ V1)) @ (^[V4]: (V2 @ ((c+ @ V4) @ V3))))))))))))))
(TNSUM_BOUND_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ ((cnsum @ ((c.. @ V0) @ V1)) @ V2)) @ V4)) @ ((c==> @ ((c/__caret__ @ ((c<= @ V0) @ V3)) @ ((c<= @ V3) @ V1))) @ ((c<= @ (V2 @ V3)) @ V4))))))))))))))
(TKLE_RANGE_COMBINE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((ckle @ V3) @ V4) @ V2)) @ ((c/__caret__ @ (((ckle @ V3) @ V2) @ V5)) @ ((c/__caret__ @ ((c__caret__/ @ (((ckle @ V3) @ V4) @ V5)) @ (((ckle @ V3) @ V5) @ V4))) @ ((c/__caret__ @ ((c<= @ V0) @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3))) @ ((c< @ (V4 @ V7)) @ (V2 @ V7)))) @ V7)))))))) @ ((c<= @ V1) @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3))) @ ((c< @ (V2 @ V7)) @ (V5 @ V7)))) @ V7)))))))))))) @ (((ckle @ V3) @ V4) @ V5)))))))))))))))
(TNSUM_PERMUTE_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cpermutes @ V3) @ ((c.. @ V0) @ V1))) @ ((c= @ ((cnsum @ ((c.. @ V0) @ V1)) @ V2)) @ ((cnsum @ ((c.. @ V0) @ V1)) @ ((co @ V2) @ V3)))))))))))))
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(TRTC_SIGMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cRTC @ V2) @ V0) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((cprimepow @ V4) @ V5)) @ ((c/__caret__ @ ((c< @ V0) @ V4)) @ ((c/__caret__ @ ((c< @ V1) @ V4)) @ ((c/__caret__ @ (c? @ (^[V6]: ((c= @ V3) @ ((c+ @ V0) @ ((c* @ V4) @ V6)))))) @ ((c/__caret__ @ (c? @ (^[V6]: ((c/__caret__ @ ((c< @ V6) @ V5)) @ ((c= @ V3) @ ((c+ @ V6) @ ((c* @ V5) @ V1))))))) @ (c! @ (^[V6]: ((c==> @ ((c< @ V6) @ V5)) @ ((c==> @ ((cprimepow @ V4) @ V6)) @ (c? @ (^[V7]: (c? @ (^[V8]: (c? @ (^[V9]: (c? @ (^[V10]: ((c/__caret__ @ ((c= @ V3) @ ((c+ @ V7) @ ((c* @ V6) @ ((c+ @ V8) @ ((c* @ V4) @ ((c+ @ V9) @ ((c* @ V4) @ V10)))))))) @ ((c/__caret__ @ ((c< @ V7) @ V6)) @ ((c/__caret__ @ ((c< @ V8) @ V4)) @ ((c/__caret__ @ ((c< @ V9) @ V4)) @ ((V2 @ V8) @ V9))))))))))))))))))))))))))))))))))))
(TDIVMOD_ELIM_THM',(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((V2 @ ((cDIV @ V0) @ V1)) @ ((cMOD @ V0) @ V1))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ ((c= @ V3) @ (cNUMERAL @ c_0))) @ ((c= @ V4) @ V0)))) @ ((c/__caret__ @ ((c= @ V0) @ ((c+ @ ((c* @ V3) @ V1)) @ V4))) @ ((c< @ V4) @ V1)))) @ ((V2 @ V3) @ V4))))))))))))))
(TDIVMOD_ELIM_THM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((V2 @ ((cDIV @ V0) @ V1)) @ ((cMOD @ V0) @ V1))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ ((c= @ V3) @ (cNUMERAL @ c_0))) @ ((c= @ V4) @ V0)))) @ ((c/__caret__ @ ((c= @ V0) @ ((c+ @ ((c* @ V3) @ V1)) @ V4))) @ ((c< @ V4) @ V1)))) @ ((V2 @ V3) @ V4))))))))))))))
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(TSUMMABLE_FROM_ELSEWHERE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((csummable @ (cfrom @ V0)) @ V2)) @ ((csummable @ (cfrom @ V1)) @ V2)))))))))
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(TVSUM_SUC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvsum @ ((c.. @ (cSUC @ V0)) @ (cSUC @ V1))) @ V2)) @ ((cvsum @ ((c.. @ V0) @ V1)) @ ((co @ V2) @ cSUC))))))))))
(TVSUM_TRIV_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c< @ V1) @ V0)) @ ((c= @ ((cvsum @ ((c.. @ V0) @ V1)) @ V2)) @ (cvec @ (cNUMERAL @ c_0)))))))))))
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(TVSUM_CLAUSES_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V0) @ V1)) @ ((c= @ ((cvsum @ ((c.. @ V0) @ V1)) @ V2)) @ ((cvector_add @ (V2 @ V0)) @ ((cvsum @ ((c.. @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)) @ V2)))))))))))
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(TSUB_ELIM_THM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (V2 @ ((c- @ V0) @ V1))) @ (c! @ (^[V3]: ((c==> @ ((c__caret__/ @ ((c= @ V0) @ ((c+ @ V1) @ V3))) @ ((c/__caret__ @ ((c< @ V0) @ V1)) @ ((c= @ V3) @ (cNUMERAL @ c_0))))) @ (V2 @ V3))))))))))))
(TDIST_ELIM_THM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (V2 @ (cdist @ ((c__comma__ @ V1) @ V0)))) @ (c! @ (^[V3]: ((c/__caret__ @ ((c==> @ ((c= @ V1) @ ((c+ @ V0) @ V3))) @ (V2 @ V3))) @ ((c==> @ ((c= @ V0) @ ((c+ @ V1) @ V3))) @ (V2 @ V3)))))))))))))
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(TSUM_PERMUTATIONS_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((csum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cpermutes @ V4) @ ((c.. @ V0) @ V1))) @ V4)))))) @ V2)) @ ((csum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cpermutes @ V4) @ ((c.. @ V0) @ V1))) @ V4)))))) @ (^[V3]: (V2 @ (cinverse @ V3))))))))))))
(TSUM_PERMUTATIONS_COMPOSE_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cpermutes @ V3) @ ((c.. @ V0) @ V1))) @ ((c= @ ((csum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cpermutes @ V5) @ ((c.. @ V0) @ V1))) @ V5)))))) @ V2)) @ ((csum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cpermutes @ V5) @ ((c.. @ V0) @ V1))) @ V5)))))) @ (^[V4]: (V2 @ ((co @ V4) @ V3)))))))))))))))
(TSUM_PERMUTATIONS_COMPOSE_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cpermutes @ V3) @ ((c.. @ V0) @ V1))) @ ((c= @ ((csum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cpermutes @ V5) @ ((c.. @ V0) @ V1))) @ V5)))))) @ V2)) @ ((csum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cpermutes @ V5) @ ((c.. @ V0) @ V1))) @ V5)))))) @ (^[V4]: (V2 @ ((co @ V3) @ V4)))))))))))))))
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(TDET_IDENTICAL_ROWS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c= @ ((crow @ V0) @ V2)) @ ((crow @ V1) @ V2)))))))) @ ((c= @ (cdet @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))
(TDET_IDENTICAL_COLUMNS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c= @ ((ccolumn @ V0) @ V2)) @ ((ccolumn @ V1) @ V2)))))))) @ ((c= @ (cdet @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))
(TMATRIX_COMPONENT_LE_ONORM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((creal_le @ (creal_abs @ ((c$ @ ((c$ @ V2) @ V0)) @ V1))) @ (conorm @ (^[V3]: ((cmatrix_vector_mul @ V2) @ V3)))))))))))
(TCONSTR_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c= @ ((c= @ (((cCONSTR @ V0) @ V2) @ V4)) @ (((cCONSTR @ V1) @ V3) @ V5))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c/__caret__ @ ((c= @ V2) @ V3)) @ ((c= @ V4) @ V5)))))))))))))))))
(THAS_DERIVATIVE_LIFT_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (((chas_derivative @ (^[V2]: (clift @ ((c$ @ V2) @ V0)))) @ (^[V2]: (clift @ ((c$ @ V2) @ V0)))) @ V1))))))
(TDIFFERENTIABLE_LIFT_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((cdifferentiable @ (^[V2]: (clift @ ((c$ @ V2) @ V0)))) @ V1))))))
(TNADD_ARCH_MULT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((cnadd_eq @ V1) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V2]: ((cnadd_le @ (cnadd_of_num @ V0)) @ ((cnadd_mul @ (cnadd_of_num @ V2)) @ V1))))))))))
(TNADD_MUL_LINV_LEMMA7a,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((cnadd_eq @ V1) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c<= @ V4) @ V0)) @ ((c<= @ (cdist @ ((c__comma__ @ ((c* @ V4) @ ((cnadd_rinv @ V1) @ V5))) @ ((c* @ V5) @ ((cnadd_rinv @ V1) @ V4))))) @ ((c+ @ ((c* @ V2) @ V5)) @ V3)))))))))))))))))
(TLENGTH_POLY_DIFF_AUX,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cLENGTH @ ((cpoly_diff_aux @ V0) @ V1))) @ (cLENGTH @ V1)))))))
(TPERMUTATION_MEM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cPERMUTATION @ V1)) @ ((c= @ ((cMEM @ V0) @ V1)) @ ((c< @ V0) @ (cLENGTH @ V1)))))))))
(TPRIMEFACT_VARIANT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cprimefact @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ (((cITLIST @ c*) @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ ((cALL @ cprime) @ V1))))))))
(Tprimefact,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cprimefact @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ (((cITLIST @ c*) @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cMEM @ V2) @ V1)) @ (cprime @ V2)))))))))))
(TLUCAS_PRIMEFACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ ((c/__caret__ @ (((c== @ ((cEXP @ V0) @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V2))) @ ((c/__caret__ @ ((c= @ (((cITLIST @ c*) @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cALL @ (^[V3]: ((c/__caret__ @ (cprime @ V3)) @ (c~ @ (((c== @ ((cEXP @ V0) @ ((cDIV @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cnum_mod @ V2)))))) @ V1))))) @ (cprime @ V2)))))))))
(TEL_TL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cEL @ V0) @ (cTL @ V1))) @ ((cEL @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)))))))
(TEL_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cEL @ V0) @ ((cAPPEND @ V1) @ V2))) @ (((cCOND @ ((c< @ V0) @ (cLENGTH @ V1))) @ ((cEL @ V0) @ V1)) @ ((cEL @ ((c- @ V0) @ (cLENGTH @ V1))) @ V2))))))))))
(TMEM_EL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c< @ V0) @ (cLENGTH @ V1))) @ ((cMEM @ ((cEL @ V0) @ V1)) @ V1)))))))
(TEL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cEL @ (cSUC @ V0)) @ V1)) @ ((cEL @ V0) @ (cTL @ V1))))))))
(TINT_POW_MONO_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)) @ ((c< @ V0) @ V2))) @ ((cint_lt @ ((cint_pow @ V1) @ V0)) @ ((cint_pow @ V1) @ V2))))))))))
(TINT_POW_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)) @ ((c<= @ V0) @ V2))) @ ((cint_le @ ((cint_pow @ V1) @ V0)) @ ((cint_pow @ V1) @ V2))))))))))
(TINT_POW_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_pow @ V1) @ ((c+ @ V0) @ V2))) @ ((cint_mul @ ((cint_pow @ V1) @ V0)) @ ((cint_pow @ V1) @ V2))))))))))
(TINT_POW_LT2_REV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((cint_lt @ ((cint_pow @ V1) @ V0)) @ ((cint_pow @ V2) @ V0)))) @ ((cint_lt @ V1) @ V2)))))))))
(TINT_DIVIDES_POW2_REV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ ((cint_pow @ V1) @ V0)) @ ((cint_pow @ V2) @ V0))) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0))))) @ ((cint_divides @ V1) @ V2)))))))))
(TINT_DIVIDES_POW2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((cint_divides @ ((cint_pow @ V1) @ V0)) @ V2))) @ ((cint_divides @ V1) @ V2)))))))))
(TINT_POW_EQ_ABS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cint_pow @ V1) @ V0)) @ ((cint_pow @ V2) @ V0)))) @ ((c= @ (cint_abs @ V1)) @ (cint_abs @ V2))))))))))
(TINT_POW_LE2_REV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((cint_le @ ((cint_pow @ V1) @ V0)) @ ((cint_pow @ V2) @ V0))))) @ ((cint_le @ V1) @ V2)))))))))
(TINT_POW_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c= @ ((cint_pow @ V1) @ V0)) @ ((cint_pow @ V2) @ V0)))))) @ ((c= @ V1) @ V2)))))))))
(TINT_PRIME_DIVPOW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cint_prime @ V1)) @ ((cint_divides @ V1) @ ((cint_pow @ V2) @ V0)))) @ ((cint_divides @ V1) @ V2)))))))))
(TINT_COPRIME_PRIMEPOW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cint_prime @ V1)) @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0))))) @ ((c= @ (cint_coprime @ ((c__comma__ @ V2) @ ((cint_pow @ V1) @ V0)))) @ (c~ @ ((cint_divides @ V1) @ V2)))))))))))
(TINT_DIVIDES_POW2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (cNUMERAL @ c_0)))) @ ((c= @ ((cint_divides @ ((cint_pow @ V1) @ V0)) @ ((cint_pow @ V2) @ V0))) @ ((cint_divides @ V1) @ V2))))))))))
(TREAL_POLYFUN_ROOTBOUND_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ ((c.. @ (cNUMERAL @ c_0)) @ V0))) @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V4]: ((creal_mul @ (V1 @ V4)) @ ((creal_pow @ V3) @ V4))))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V3))))))))))))
(TSUM_SPLIT_2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))) @ V1)) @ ((creal_add @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ V1)) @ ((csum @ ((c.. @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))) @ V1))))))))
(TOLD_SUM_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpsum @ ((c__comma__ @ V0) @ (cNUMERAL @ c_0))) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TPRODUCT_SPLIT_2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))) @ V1)) @ ((creal_mul @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ V1)) @ ((cproduct @ ((c.. @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0))) @ V1))))))))
(TPRODUCT_NEG_NUMSEG_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ (^[V2]: (creal_neg @ (V1 @ V2))))) @ ((creal_mul @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)) @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ V1))))))))
(TVARIATION_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvariation @ ((cINSERT @ V0) @ cEMPTY)) @ V1)) @ (cNUMERAL @ c_0)))))))
(TREAL_POLYFUN_FINITE_ROOTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V4]: ((creal_mul @ (V1 @ V4)) @ ((creal_pow @ V3) @ V4))))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V3))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ ((c.. @ (cNUMERAL @ c_0)) @ V0))) @ (c~ @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))
(TREAL_POLYFUN_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c= @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V3]: ((creal_mul @ (V1 @ V3)) @ ((creal_pow @ V2) @ V3))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ ((c.. @ (cNUMERAL @ c_0)) @ V0))) @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))
(TSUM_NSUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_sub @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0)) @ V1)) @ ((creal_mul @ (creal_of_num @ V0)) @ V2))) @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0)) @ (^[V3]: ((creal_sub @ (V1 @ V3)) @ V2)))))))))))
(TSUM_HORNER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ (cSUC @ V0))) @ (^[V3]: ((creal_mul @ (V1 @ V3)) @ ((creal_pow @ V2) @ V3))))) @ ((creal_add @ (V1 @ (cNUMERAL @ c_0))) @ ((creal_mul @ V2) @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0)) @ (^[V3]: ((creal_mul @ (V1 @ (cSUC @ V3))) @ ((creal_pow @ V2) @ V3))))))))))))))
(TREAL_SUB_POLYFUN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c= @ ((creal_sub @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V4]: ((creal_mul @ (V1 @ V4)) @ ((creal_pow @ V3) @ V4))))) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V4]: ((creal_mul @ (V1 @ V4)) @ ((creal_pow @ V2) @ V4)))))) @ ((creal_mul @ ((creal_sub @ V3) @ V2)) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (^[V4]: ((creal_mul @ ((csum @ ((c.. @ ((c+ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ (^[V5]: ((creal_mul @ (V1 @ V5)) @ ((creal_pow @ V2) @ ((c- @ ((c- @ V5) @ V4)) @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((creal_pow @ V3) @ V4))))))))))))))))
(TREAL_SUB_POLYFUN_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c= @ ((creal_sub @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V4]: ((creal_mul @ (V1 @ V4)) @ ((creal_pow @ V3) @ V4))))) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V4]: ((creal_mul @ (V1 @ V4)) @ ((creal_pow @ V2) @ V4)))))) @ ((creal_mul @ ((creal_sub @ V3) @ V2)) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (^[V4]: ((creal_mul @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ ((c- @ V0) @ V4)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (^[V5]: ((creal_mul @ (V1 @ ((c+ @ V4) @ ((c+ @ V5) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((creal_pow @ V2) @ V5))))) @ ((creal_pow @ V3) @ V4))))))))))))))))
(TSUM_DIFFS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V2) @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((csum @ ((c.. @ V2) @ V0)) @ (^[V3]: ((creal_sub @ (V1 @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V1 @ V3))))) @ ((creal_sub @ (V1 @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V1 @ V2)))))))))))
(TSUM_OFFSET_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V2) @ V0)) @ ((c= @ ((csum @ ((c.. @ V2) @ V0)) @ V1)) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ V0) @ V2))) @ (^[V3]: (V1 @ ((c+ @ V3) @ V2)))))))))))))
(TSUM_CLAUSES_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c<= @ V0) @ V2))) @ ((c= @ ((csum @ ((c.. @ V0) @ V2)) @ V1)) @ ((creal_add @ ((csum @ ((c.. @ V0) @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V1)) @ (V1 @ V2)))))))))))
(TPRODUCT_CLAUSES_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c<= @ V0) @ V2))) @ ((c= @ ((cproduct @ ((c.. @ V0) @ V2)) @ V1)) @ ((creal_mul @ ((cproduct @ ((c.. @ V0) @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V1)) @ (V1 @ V2)))))))))))
(TALTERNATING_SUM_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c/__caret__ @ ((creal_le @ (V1 @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3))))))) @ (c! @ (^[V3]: ((creal_le @ (creal_abs @ (V1 @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (creal_abs @ (V1 @ V3))))))) @ ((creal_le @ (creal_abs @ ((cpsum @ ((c__comma__ @ V2) @ V0)) @ V1))) @ (creal_abs @ (V1 @ V2)))))))))))
(TALTERNATING_SUM_BOUNDS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c/__caret__ @ ((creal_le @ (V1 @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3))))))) @ (c! @ (^[V3]: ((creal_le @ (creal_abs @ (V1 @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (creal_abs @ (V1 @ V3))))))) @ ((c==> @ (cEVEN @ V2)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cpsum @ ((c__comma__ @ V2) @ V0)) @ V1))) @ ((creal_le @ ((cpsum @ ((c__comma__ @ V2) @ V0)) @ V1)) @ (V1 @ V2))))))))))))
(TSUM_DIFFS_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((csum @ ((c.. @ V2) @ V0)) @ (^[V3]: ((creal_sub @ (V1 @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V1 @ V3))))) @ (((cCOND @ ((c<= @ V2) @ V0)) @ ((creal_sub @ (V1 @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V1 @ V2))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))
(TSUM_CANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpsum @ ((c__comma__ @ V2) @ V0)) @ (^[V3]: ((creal_sub @ (V1 @ (cSUC @ V3))) @ (V1 @ V3))))) @ ((creal_sub @ (V1 @ ((c+ @ V2) @ V0))) @ (V1 @ V2))))))))))
(TVARIATION_2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvariation @ ((cINSERT @ V0) @ ((cINSERT @ V2) @ cEMPTY))) @ V1)) @ (((cCOND @ ((creal_lt @ ((creal_mul @ (V1 @ V0)) @ (V1 @ V2))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ c_0))))))))))
(TSUM_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V0) @ V4)) @ ((c< @ V4) @ ((c+ @ V0) @ V2)))) @ ((creal_le @ (V1 @ V4)) @ V3))))) @ ((creal_le @ ((cpsum @ ((c__comma__ @ V0) @ V2)) @ V1)) @ ((creal_mul @ (creal_of_num @ V2)) @ V3))))))))))))
(TREAL_SUB_SUM0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_sub @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0)) @ V1)) @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0)) @ V2))) @ ((cpsum @ ((c__comma__ @ (cNUMERAL @ c_0)) @ V0)) @ (^[V3]: ((creal_sub @ (V1 @ V3)) @ (V2 @ V3))))))))))))
(TKLE_REFL,(c! @ (^[V0]: (c! @ (^[V1]: (((ckle @ V0) @ V1) @ V1))))))
(TSUM_CONG_3,(c! @ (^[V0]: (c! @ (^[V1]: (((c== @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V2]: ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V2)) @ (V1 @ V2))))) @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V2]: (V1 @ V2)))) @ (cnum_mod @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))))))
(TREFLECT_INJ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ V0)) @ ((c< @ (V1 @ V2)) @ V0))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ V0)) @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3)))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ V0)) @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c= @ ((c- @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (V1 @ V2))) @ ((c- @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (V1 @ V3)))))) @ ((c= @ V2) @ V3))))))))))))
(TDIVISIBILITY_BY_3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnum_divides @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))) @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V2]: ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V2)) @ (V1 @ V2)))))) @ ((cnum_divides @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))) @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V2]: (V1 @ V2))))))))))
(TNSUM_OFFSET_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V2) @ V0)) @ ((c= @ ((cnsum @ ((c.. @ V2) @ V0)) @ V1)) @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ V0) @ V2))) @ (^[V3]: (V1 @ ((c+ @ V3) @ V2)))))))))))))
(TPERMUTES_IN_NUMSEG_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpermutes @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0))) @ ((cIN @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)))) @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ (V1 @ V2))))))))))
(TNSUM_CLAUSES_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c<= @ V0) @ V2))) @ ((c= @ ((cnsum @ ((c.. @ V0) @ V2)) @ V1)) @ ((c+ @ ((cnsum @ ((c.. @ V0) @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V1)) @ (V1 @ V2)))))))))))
(TNPRODUCT_CLAUSES_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c<= @ V0) @ V2))) @ ((c= @ ((cnproduct @ ((c.. @ V0) @ V2)) @ V1)) @ ((c* @ ((cnproduct @ ((c.. @ V0) @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V1)) @ (V1 @ V2)))))))))))
(TPSEQ_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((((cPSEQ @ V0) @ V1) @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (V1 @ V2)))))))))
(TPSEQ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((((cPSEQ @ V0) @ V1) @ V2) @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0)))))))))
(TPSEQ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((cPSEQ @ V0) @ V1) @ V2) @ (cSUC @ V3))) @ ((c+ @ (V1 @ V2)) @ ((c* @ V0) @ ((((cPSEQ @ V0) @ V1) @ (cSUC @ V2)) @ V3)))))))))))))
(TPSEQ_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((((cPSEQ @ V0) @ V1) @ V2) @ ((c+ @ V3) @ V4))) @ ((c+ @ ((((cPSEQ @ V0) @ V1) @ V2) @ V3)) @ ((c* @ ((cEXP @ V0) @ V3)) @ ((((cPSEQ @ V0) @ V1) @ ((c+ @ V2) @ V3)) @ V4)))))))))))))))
(TKLE_RANGE_COMBINE_R_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((ckle @ V2) @ V3) @ V1)) @ ((c/__caret__ @ (((ckle @ V2) @ V1) @ V4)) @ ((c/__caret__ @ ((c__caret__/ @ (((ckle @ V2) @ V3) @ V4)) @ (((ckle @ V2) @ V4) @ V3))) @ ((c<= @ V0) @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2))) @ ((c< @ (V3 @ V6)) @ (V1 @ V6)))) @ V6))))))))))) @ (((ckle @ V2) @ V3) @ V4)))))))))))))
(TKLE_RANGE_COMBINE_L_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((ckle @ V2) @ V3) @ V1)) @ ((c/__caret__ @ (((ckle @ V2) @ V1) @ V4)) @ ((c/__caret__ @ ((c__caret__/ @ (((ckle @ V2) @ V3) @ V4)) @ (((ckle @ V2) @ V4) @ V3))) @ ((c<= @ V0) @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2))) @ ((c< @ (V1 @ V6)) @ (V4 @ V6)))) @ V6))))))))))) @ (((ckle @ V2) @ V3) @ V4)))))))))))))
(TKLE_SUC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((ckle @ V0) @ V1) @ V2)) @ (((ckle @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1) @ V2)))))))))
(TKLE_STRICT_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((ckle @ V0) @ V1) @ V2)) @ (c~ @ ((c= @ V1) @ V2)))) @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cCARD @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0))) @ ((c< @ (V1 @ V4)) @ (V2 @ V4)))) @ V4)))))))))))))))
(TKLE_STRICT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((ckle @ V0) @ V1) @ V2)) @ (c~ @ ((c= @ V1) @ V2)))) @ (c? @ (^[V3]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ V0)) @ ((c< @ (V1 @ V3)) @ (V2 @ V3))))))))))))))
(TKLE_STRICT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((ckle @ V0) @ V1) @ V2)) @ (c~ @ ((c= @ V1) @ V2)))) @ (c! @ (^[V3]: ((c<= @ (V1 @ V3)) @ (V2 @ V3))))))))))))
(TPIGEONHOLE_LEMMA_P12,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cODD @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c< @ (V1 @ V3)) @ V0))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V4)) @ V0)) @ ((c= @ (V1 @ V3)) @ (V1 @ V4))))) @ ((c= @ V3) @ V4))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c< @ (V2 @ V3)) @ V0))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V4)) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))))))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V4)) @ V0)) @ ((c= @ (V1 @ V3)) @ (V2 @ V4))))))))))))))))
(Tkle,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((ckle @ V0) @ V2) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0))) @ (c! @ (^[V4]: ((c= @ (V1 @ V4)) @ ((c+ @ (V2 @ V4)) @ (((cCOND @ ((cIN @ V4) @ V3)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ c_0)))))))))))))))))
(TKLE_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ (((ckle @ V0) @ V1) @ V2)) @ (((ckle @ V0) @ V2) @ V1))) @ ((c= @ V1) @ V2)))))))))
(TKLE_TRANS_1_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((ckle @ V0) @ V2) @ V1)) @ ((c<= @ (V1 @ V3)) @ ((c+ @ (V2 @ V3)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))
(TKLE_IMP_POINTWISE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((ckle @ V0) @ V1) @ V2)) @ ((c<= @ (V1 @ V3)) @ (V2 @ V3))))))))))))
(TVSUM_VSUM_DIVISORS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ (^[V2]: ((cvsum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cnum_divides @ V4) @ V2)) @ V4)))))) @ (V1 @ V2))))) @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ (^[V2]: ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((cDIV @ V0) @ V2))) @ (^[V3]: ((V1 @ ((c* @ V3) @ V2)) @ V2)))))))))))
(Tis_quadratic_residue,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cis_quadratic_residue @ V0) @ V1)) @ (c? @ (^[V2]: (((c== @ ((cEXP @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0) @ V1)))))))))
(TSUMMABLE_IMP_SUMS_BOUNDED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csummable @ (cfrom @ V0)) @ V1)) @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ ((cvsum @ ((c.. @ V0) @ V3)) @ V1)))))))))))))
(TBOUNDED_PARTIAL_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ ((cvsum @ ((c.. @ V0) @ V3)) @ V1)))))))) @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ cUNIV)) @ ((cIN @ V4) @ cUNIV))) @ ((cvsum @ ((c.. @ V3) @ V4)) @ V1)))))))))))))))
(TVSUM_PAIR_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V1)) @ ((cvsum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V2]: ((cvector_add @ (V1 @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2))) @ (V1 @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TVSUM_CLAUSES_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V2)) @ ((c<= @ V0) @ V2))) @ ((c= @ ((cvsum @ ((c.. @ V0) @ V2)) @ V1)) @ ((cvector_add @ ((cvsum @ ((c.. @ V0) @ ((c- @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V1)) @ (V1 @ V2)))))))))))
(TSERIES_FROM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((csums @ V1) @ V2) @ (cfrom @ V0))) @ (((c--> @ (^[V3]: ((cvsum @ ((c.. @ V0) @ V3)) @ V1))) @ V2) @ csequentially)))))))))
(TSEQ_OFFSET_REV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c--> @ (^[V3]: (V1 @ ((c+ @ V3) @ V0)))) @ V2) @ csequentially)) @ (((c--> @ V1) @ V2) @ csequentially)))))))))
(TLIM_CASES_SEQUENTIALLY_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c--> @ (^[V4]: (((cCOND @ ((c<= @ V4) @ V0)) @ (V1 @ V4)) @ (V2 @ V4)))) @ V3) @ csequentially)) @ (((c--> @ V2) @ V3) @ csequentially)))))))))))
(TLIM_CASES_SEQUENTIALLY_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c--> @ (^[V4]: (((cCOND @ ((c<= @ V0) @ V4)) @ (V2 @ V4)) @ (V1 @ V4)))) @ V3) @ csequentially)) @ (((c--> @ V2) @ V3) @ csequentially)))))))))))
(TLIM_CASES_SEQUENTIALLY_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c--> @ (^[V4]: (((cCOND @ ((c< @ V4) @ V0)) @ (V1 @ V4)) @ (V2 @ V4)))) @ V3) @ csequentially)) @ (((c--> @ V2) @ V3) @ csequentially)))))))))))
(TLIM_CASES_SEQUENTIALLY_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c--> @ (^[V4]: (((cCOND @ ((c< @ V0) @ V4)) @ (V2 @ V4)) @ (V1 @ V4)))) @ V3) @ csequentially)) @ (((c--> @ V2) @ V3) @ csequentially)))))))))))
(TVSUM_OFFSET_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V2) @ V0)) @ ((c= @ ((cvsum @ ((c.. @ V2) @ V0)) @ V1)) @ ((cvsum @ ((c.. @ (cNUMERAL @ c_0)) @ ((c- @ V0) @ V2))) @ (^[V3]: (V1 @ ((c+ @ V3) @ V2)))))))))))))
(TVSUM_DIFFS_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvsum @ ((c.. @ V2) @ V0)) @ (^[V3]: ((cvector_sub @ (V1 @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V1 @ V3))))) @ (((cCOND @ ((c<= @ V2) @ V0)) @ ((cvector_sub @ (V1 @ ((c+ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V1 @ V2))) @ (cvec @ (cNUMERAL @ c_0)))))))))))
(TVSUM_DIFFS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvsum @ ((c.. @ V0) @ V2)) @ (^[V3]: ((cvector_sub @ (V1 @ V3)) @ (V1 @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ (((cCOND @ ((c<= @ V0) @ V2)) @ ((cvector_sub @ (V1 @ V0)) @ (V1 @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (cvec @ (cNUMERAL @ c_0)))))))))))
(TMATRIC_POLY_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c= @ ((cmatrix_mul @ ((cmsum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V5]: ((c%% @ ((creal_pow @ V4) @ V5)) @ (V1 @ V5))))) @ ((cmatrix_sub @ V2) @ ((c%% @ V4) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ V3)))) @ ((c= @ V3) @ (cmat @ (cNUMERAL @ c_0)))))))))))))
(TMATRIC_POLYFUN_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c= @ ((cmsum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V3]: ((c%% @ ((creal_pow @ V2) @ V3)) @ (V1 @ V3))))) @ (cmat @ (cNUMERAL @ c_0)))))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ ((c.. @ (cNUMERAL @ c_0)) @ V0))) @ ((c= @ (V1 @ V2)) @ (cmat @ (cNUMERAL @ c_0))))))))))))
(TCODESET_SETCODE_BIJECTIONS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0))) @ ((c/__caret__ @ ((cIN @ (csetcode @ V1)) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)))) @ ((c= @ (ccodeset @ (csetcode @ V1))) @ V1))))))))
(TBOUNDED_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c<= @ V2) @ V0))))) @ (cFINITE @ V1)))))))
(TMBASIS_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c< @ V0) @ V2))))) @ ((c= @ (cmbasis @ ((cINSERT @ V0) @ V1))) @ ((couter @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY))) @ (cmbasis @ V1)))))))))
(TFORALL_SETCODE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0))) @ (V1 @ (csetcode @ V2)))))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V0)))) @ (V1 @ V2))))))))))
(TPRE_ELIM_THM',(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (V1 @ (cPRE @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((c__caret__/ @ ((c= @ V0) @ (cSUC @ V2))) @ ((c/__caret__ @ ((c= @ V2) @ (cNUMERAL @ c_0))) @ ((c= @ V0) @ (cNUMERAL @ c_0))))) @ (V1 @ V2))))))))))
(TPRE_ELIM_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (V1 @ (cPRE @ V0))) @ (c! @ (^[V2]: ((c==> @ ((c__caret__/ @ ((c= @ V0) @ (cSUC @ V2))) @ ((c/__caret__ @ ((c= @ V2) @ (cNUMERAL @ c_0))) @ ((c= @ V0) @ (cNUMERAL @ c_0))))) @ (V1 @ V2))))))))))
(TALLN_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cALLN @ V1) @ ((cNPAIR @ V0) @ V2))) @ ((c/__caret__ @ (V1 @ V0)) @ ((cALLN @ V1) @ V2))))))))))
(TNPRODUCT_CANCEL_PRIME_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ ((c* @ ((cEXP @ V2) @ V0)) @ ((cnproduct @ ((cDELETE @ V1) @ V2)) @ (^[V5]: ((cEXP @ V5) @ (V3 @ V5)))))) @ ((c* @ V2) @ V4))) @ ((c==> @ ((c/__caret__ @ (cprime @ V2)) @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ (cprime @ V5))))))) @ ((c= @ ((c* @ ((cEXP @ V2) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cnproduct @ ((cDELETE @ V1) @ V2)) @ (^[V5]: ((cEXP @ V5) @ (V3 @ V5)))))) @ V4))))))))))))))
(TPARTIAL_SUMS_DROP_LE_INFSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ (V2 @ V3))))))) @ ((csummable @ V1) @ V2))) @ ((creal_le @ (cdrop @ ((cvsum @ ((cINTER @ V1) @ ((c.. @ (cNUMERAL @ c_0)) @ V0))) @ V2))) @ (cdrop @ ((cinfsum @ V1) @ V2)))))))))))
(TPARTIAL_SUMS_COMPONENT_LE_INFSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ (V2 @ V4)) @ V3)))))) @ ((csummable @ V1) @ V2))))) @ ((creal_le @ ((c$ @ ((cvsum @ ((cINTER @ V1) @ ((c.. @ (cNUMERAL @ c_0)) @ V0))) @ V2)) @ V3)) @ ((c$ @ ((cinfsum @ V1) @ V2)) @ V3))))))))))))
(TBINARY_UNIQUE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V4]: (((cCOND @ (V1 @ V4)) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V4)) @ (cNUMERAL @ c_0))))) @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V0)) @ (^[V4]: (((cCOND @ (V2 @ V4)) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V4)) @ (cNUMERAL @ c_0)))))) @ ((c==> @ ((c<= @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ (V2 @ V3)))))))))))))
(TSUM_OVER_PERMUTATIONS_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V2) @ V0)) @ ((c= @ ((csum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cpermutes @ V4) @ ((c.. @ V2) @ V0))) @ V4)))))) @ V1)) @ ((csum @ ((c.. @ V2) @ V0)) @ (^[V3]: ((csum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cpermutes @ V5) @ ((c.. @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))) @ V5)))))) @ (^[V4]: (V1 @ ((co @ (cswap @ ((c__comma__ @ V2) @ V3))) @ V4)))))))))))))))
(TKUHN_SIMPLEX_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ (((cksimplex @ V0) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3)) @ ((cSUBSET @ ((cIMAGE @ V1) @ V3)) @ ((c.. @ (cNUMERAL @ c_0)) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ (cODD @ (cCARD @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ (((cksimplex @ V0) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V5)) @ ((c/__caret__ @ ((cIN @ V6) @ V5)) @ ((c= @ V4) @ ((cDELETE @ V5) @ V6))))))))) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ V4)) @ ((c.. @ (cNUMERAL @ c_0)) @ V2))) @ ((c__caret__/ @ (c? @ (^[V5]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V4)) @ ((c= @ (V6 @ V5)) @ (cNUMERAL @ c_0)))))))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V4)) @ ((c= @ (V6 @ V5)) @ V0)))))))))))) @ V4))))))))) @ (cODD @ (cCARD @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ (((cksimplex @ V0) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V6)) @ V6))))))) @ ((c= @ ((cIMAGE @ V1) @ V4)) @ ((c.. @ (cNUMERAL @ c_0)) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ V4)))))))))))))))
(TKUHN_INDUCTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c<= @ (V3 @ V5)) @ V0)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (V3 @ V4)) @ (cNUMERAL @ c_0)))))) @ ((c= @ ((V1 @ V3) @ V4)) @ (cNUMERAL @ c_0)))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c<= @ (V3 @ V5)) @ V0)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (V3 @ V4)) @ V0))))) @ ((c= @ ((V1 @ V3) @ V4)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))) @ ((c==> @ (cODD @ (cCARD @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ (((cksimplex @ V0) @ V2) @ V4)) @ ((c= @ ((cIMAGE @ ((creduced @ V1) @ V2)) @ V4)) @ ((c.. @ (cNUMERAL @ c_0)) @ V2)))) @ V4)))))))) @ (cODD @ (cCARD @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ (((cksimplex @ V0) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V4)) @ ((c= @ ((cIMAGE @ ((creduced @ V1) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V4)) @ ((c.. @ (cNUMERAL @ c_0)) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ V4))))))))))))))))
(TKUHN_COMBINATORIAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ c_0)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c<= @ (V3 @ V5)) @ V0)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ V2)) @ ((c= @ (V3 @ V4)) @ (cNUMERAL @ c_0)))))) @ ((c= @ ((V1 @ V3) @ V4)) @ (cNUMERAL @ c_0)))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c<= @ (V3 @ V5)) @ V0)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ V2)) @ ((c= @ (V3 @ V4)) @ V0))))) @ ((c= @ ((V1 @ V3) @ V4)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))) @ (cODD @ (cCARD @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ (((cksimplex @ V0) @ V2) @ V4)) @ ((c= @ ((cIMAGE @ ((creduced @ V1) @ V2)) @ V4)) @ ((c.. @ (cNUMERAL @ c_0)) @ V2)))) @ V4)))))))))))))))
(Treduced,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((creduced @ V1) @ V0) @ V2)) @ (c__at__ @ (^[V3]: ((c/__caret__ @ ((c<= @ V3) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c< @ V4) @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c= @ ((V1 @ V2) @ V4)) @ (cNUMERAL @ c_0)))))) @ ((c__caret__/ @ ((c= @ V3) @ V0)) @ (c~ @ ((c= @ ((V1 @ V2) @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ c_0))))))))))))))))
(TREDUCED_LABELLING_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c< @ V3) @ ((c+ @ (((creduced @ V1) @ V0) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c= @ ((V1 @ V2) @ V3)) @ (cNUMERAL @ c_0))))))))))))
(TKSIMPLEX_EXTREMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cksimplex @ V0) @ V2) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ (((ckle @ V2) @ V3) @ V5)) @ (((ckle @ V2) @ V5) @ V4)))))) @ (c! @ (^[V5]: ((c= @ (V4 @ V5)) @ (((cCOND @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ V2))) @ ((c+ @ (V3 @ V5)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (V3 @ V5))))))))))))))))))))
(TKSIMPLEX_EXTREMA_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((cksimplex @ V0) @ V2) @ V1)) @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0))))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V4))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ (((ckle @ V2) @ V3) @ V5)) @ (((ckle @ V2) @ V5) @ V4)))))) @ (c! @ (^[V5]: ((c= @ (V4 @ V5)) @ (((cCOND @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ V2))) @ ((c+ @ (V3 @ V5)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (V3 @ V5)))))))))))))))))))))
(Tksimplex,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cksimplex @ V0) @ V2) @ V1)) @ ((c/__caret__ @ ((cHAS_SIZE @ V1) @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c<= @ (V3 @ V4)) @ V0))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ (c~ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ V2))))) @ ((c= @ (V3 @ V4)) @ V0))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((cIN @ V4) @ V1))) @ ((c__caret__/ @ (((ckle @ V2) @ V3) @ V4)) @ (((ckle @ V2) @ V4) @ V3))))))))))))))))))
(TKSIMPLEX_SUCCESSOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cksimplex @ V0) @ V2) @ V1)) @ ((cIN @ V3) @ V1))) @ ((c__caret__/ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ (((ckle @ V2) @ V4) @ V3))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (c? @ (^[V5]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ V2)) @ (c! @ (^[V6]: ((c= @ (V4 @ V6)) @ (((cCOND @ ((c= @ V6) @ V5)) @ ((c+ @ (V3 @ V6)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (V3 @ V6)))))))))))))))))))))))
(TKSIMPLEX_PREDECESSOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cksimplex @ V0) @ V2) @ V1)) @ ((cIN @ V3) @ V1))) @ ((c__caret__/ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ (((ckle @ V2) @ V3) @ V4))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (c? @ (^[V5]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ V2)) @ (c! @ (^[V6]: ((c= @ (V3 @ V6)) @ (((cCOND @ ((c= @ V6) @ V5)) @ ((c+ @ (V4 @ V6)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (V4 @ V6)))))))))))))))))))))))
(THELLY_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V1) @ V0)) @ ((c/__caret__ @ ((c>= @ V0) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (cconvex @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((c= @ (cCARD @ V2)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (c~ @ ((c= @ (cINTERS @ V2)) @ cEMPTY))))))))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY))))))))
(TORTHOGONAL_TRANSFORMATION_GENERATED_BY_REFLECTIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (corthogonal_transformation @ V1)) @ ((c<= @ (cdimindex @ cUNIV)) @ ((c+ @ (cdim @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ (V1 @ V3)) @ V3)) @ V3))))))) @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((c<= @ (cLENGTH @ V2)) @ V0)) @ ((c/__caret__ @ ((cALL @ (^[V3]: (c~ @ ((c= @ V3) @ (cvec @ (cNUMERAL @ c_0)))))) @ V2)) @ ((c= @ V1) @ (((cITLIST @ (^[V3]: (^[V4]: ((co @ (creflect_along @ V3)) @ V4)))) @ V2) @ cI))))))))))))
(TLOWDIM_EXPAND_BASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cdim @ V1)) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cHAS_SIZE @ V2) @ V0)) @ ((c/__caret__ @ (cindependent @ V2)) @ ((cSUBSET @ (cspan @ V1)) @ (cspan @ V2))))))))))))
(TLOWDIM_EXPAND_DIMENSION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cdim @ V1)) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ (cdim @ V2)) @ V0)) @ ((cSUBSET @ (cspan @ V1)) @ (cspan @ V2)))))))))))
(TCONTINUOUS_ON_LIFT_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((ccontinuous_on @ (^[V2]: (clift @ ((c$ @ V2) @ V0)))) @ V1)))))))
(TRELPOW_RTC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((((cRELPOW @ V0) @ V1) @ V2) @ V3)) @ (((cRTC @ V1) @ V2) @ V3)))))))))))
(TNSUM_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnsum @ V1) @ (^[V3]: ((c* @ V0) @ (V2 @ V3))))) @ ((c* @ V0) @ ((cnsum @ V1) @ V2))))))))))
(TSWAPSEQ_INVERSE_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cswapseq @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cswapseq @ V0) @ V2)) @ ((c/__caret__ @ ((c= @ ((co @ V1) @ V2)) @ cI)) @ ((c= @ ((co @ V2) @ V1)) @ cI)))))))))))
(TINVOLUTION_EVEN_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((c= @ (cCARD @ V2)) @ V0)) @ ((c/__caret__ @ ((cinvolution @ V1) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (c~ @ ((c= @ (V1 @ V3)) @ V3))))))))) @ (cEVEN @ (cCARD @ V2))))))))))
(TSWAPSEQ_ENDSWAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cswapseq @ V0) @ V1)) @ (c~ @ ((c= @ V2) @ V3)))) @ ((cswapseq @ (cSUC @ V0)) @ ((co @ V1) @ (cswap @ ((c__comma__ @ V2) @ V3))))))))))))))
(TITER_FIXPOINT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V1 @ V2)) @ V2)) @ ((c= @ (((cITER @ V0) @ V1) @ V2)) @ V2)))))))))
(TITERATE_OVER_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cmonoidal @ V1)) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V0) @ V2))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (((c== @ V4) @ V5) @ (cnum_mod @ V2))) @ ((c= @ (V3 @ V4)) @ (V3 @ V5)))))))))) @ ((c= @ (((citerate @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V5) @ V2))) @ ((c< @ V5) @ V2))) @ V5)))))) @ (^[V4]: (V3 @ ((c* @ V0) @ V4))))) @ (((citerate @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V5) @ V2))) @ ((c< @ V5) @ V2))) @ V5)))))) @ V3))))))))))))
(TCOPRIME_NPRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (cnum_coprime @ ((c__comma__ @ V0) @ (V2 @ V3)))))))) @ (cnum_coprime @ ((c__comma__ @ V0) @ (((citerate @ c*) @ V1) @ V2)))))))))))
(TNPRODUCT_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ (((citerate @ c*) @ V1) @ (^[V3]: ((c* @ V0) @ (V2 @ V3))))) @ ((c* @ ((cEXP @ V0) @ (cCARD @ V1))) @ (((citerate @ c*) @ V1) @ V2)))))))))))
(THAS_SIZE_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cHAS_SIZE @ V1) @ (cSUC @ V0))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cHAS_SIZE @ V3) @ V0)) @ ((c/__caret__ @ (c~ @ ((cIN @ V2) @ V3))) @ ((c= @ V1) @ ((cINSERT @ V2) @ V3))))))))))))))
(TNPRODUCT_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cnproduct @ V1) @ (^[V2]: V0))) @ ((cEXP @ V0) @ (cCARD @ V1)))))))))
(TEVENPERM_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cswapseq @ V0) @ V1)) @ ((c= @ (cEVEN @ V0)) @ V2))) @ ((c= @ (cevenperm @ V1)) @ V2)))))))))
(TSWAPSEQ_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cswapseq @ V0) @ V1)) @ ((cswapseq @ V0) @ (cinverse @ V1))))))))
(Tswapseq_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cswapseq @ V0) @ V1)) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V1) @ cI))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ (cSUC @ V5))) @ ((c/__caret__ @ ((c= @ V1) @ ((co @ (cswap @ ((c__comma__ @ V2) @ V3))) @ V4))) @ ((c/__caret__ @ ((cswapseq @ V5) @ V4)) @ (c~ @ ((c= @ V2) @ V3))))))))))))))))))))
(TCUBIC_ROOT_RADICAL_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (crational @ V2)) @ ((c/__caret__ @ (crational @ V3)) @ (crational @ V4)))) @ ((c==> @ ((c/__caret__ @ (cwellformed @ V1)) @ ((c/__caret__ @ ((c= @ (cCARD @ (cradicals @ V1))) @ V0)) @ ((c= @ ((creal_add @ ((creal_pow @ (cvalue @ V1)) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ V2) @ ((creal_pow @ (cvalue @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V3) @ (cvalue @ V1))) @ V4)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ (c? @ (^[V5]: ((c/__caret__ @ (crational @ V5)) @ ((c= @ ((creal_add @ ((creal_pow @ V5) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ V2) @ ((creal_pow @ V5) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V3) @ V5)) @ V4)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))))))
(Tgrade,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cgrade @ V0) @ V1)) @ (clambdas @ (^[V2]: (((cCOND @ ((cHAS_SIZE @ V2) @ V0)) @ ((c$$ @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))
(TOUTER_ACI_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((couter @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY))) @ ((couter @ (cmbasis @ ((cINSERT @ V0) @ cEMPTY))) @ V1))) @ (cvec @ (cNUMERAL @ c_0))))))))
(TMULTIVECTOR_GRADE,(c! @ (^[V0]: (c! @ (^[V1]: ((cmultivector @ V0) @ ((cgrade @ V0) @ V1)))))))
(TCOMPONENT_LE_NORM,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (creal_abs @ ((c$ @ V1) @ V0))) @ (cvector_norm @ V1)))))))
(TCOMPONENT_LE_INFNORM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_abs @ ((c$ @ V1) @ V0))) @ (cinfnorm @ V1))))))))
(TCONTINUOUS_AT_LIFT_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((ccontinuous @ (^[V2]: (clift @ ((c$ @ V2) @ V0)))) @ (cat @ V1))))))))
(TROTATION_RIGHTWARD_LINE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (corthogonal_transformation @ V3)) @ ((c/__caret__ @ ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c= @ (cdet @ (cmatrix @ V3))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((c= @ (V3 @ ((c% @ V2) @ (cbasis @ V0)))) @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2))))))))))))))
(TDET_ROW_SPAN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((cIN @ V1) @ (cspan @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V4) @ V0))))) @ ((crow @ V4) @ V2))))))))))) @ ((c= @ (cdet @ (clambda @ (^[V3]: (((cCOND @ ((c= @ V3) @ V0)) @ ((cvector_add @ ((crow @ V0) @ V2)) @ V1)) @ ((crow @ V3) @ V2)))))) @ (cdet @ V2))))))))))
(TDET_ZERO_ROW,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c= @ ((crow @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((c= @ (cdet @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TDET_ZERO_COLUMN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c/__caret__ @ ((c<= @ V0) @ (cdimindex @ cUNIV))) @ ((c= @ ((ccolumn @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((c= @ (cdet @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TMPOW_SUC,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmpow @ V1) @ (cSUC @ V0))) @ ((cmatrix_mul @ ((cmpow @ V1) @ V0)) @ V1)))))))
(TMPOW_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmpow @ V1) @ ((c+ @ V0) @ V2))) @ ((cmatrix_mul @ ((cmpow @ V1) @ V0)) @ ((cmpow @ V1) @ V2))))))))))
(TNORM_COLUMN_LE_ONORM,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cvector_norm @ ((ccolumn @ V0) @ V1))) @ (conorm @ (^[V2]: ((cmatrix_vector_mul @ V1) @ V2)))))))))
(TROW_TRANSP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((c= @ ((crow @ V0) @ (ctransp @ V1))) @ ((ccolumn @ V0) @ V1))))))))
(TCOLUMN_TRANSP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((c= @ ((ccolumn @ V0) @ (ctransp @ V1))) @ ((crow @ V0) @ V1))))))))
(TMATRIX_VECTOR_MUL_BASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0)) @ ((c<= @ V0) @ (cdimindex @ cUNIV)))) @ ((c= @ ((cmatrix_vector_mul @ V1) @ (cbasis @ V0))) @ ((ccolumn @ V0) @ V1))))))))
(TNUMSUM_DEST_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cNUMLEFT @ ((cNUMSUM @ V1) @ V0))) @ V1))))))
(TCONG_COND_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))) @ V0)) @ (((c== @ (((cCOND @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (((cCOND @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cnum_mod @ V0)))) @ ((c= @ V1) @ V2)))))))))
(TRELPOW_M,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((((cRELPOW @ ((c+ @ V0) @ V2)) @ V3) @ V1) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ ((((cRELPOW @ V0) @ V3) @ V1) @ V5)) @ ((((cRELPOW @ V2) @ V3) @ V5) @ V4))))))))))))))))
(TCONSTR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cCONSTR @ V0) @ V1) @ V2)) @ (c_mk_rec @ (((cZCONSTR @ V0) @ V1) @ (^[V3]: (c_dest_rec @ (V2 @ V3)))))))))))))
(TCONSTR_BOT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c~ @ ((c= @ (((cCONSTR @ V0) @ V1) @ V2)) @ cBOTTOM)))))))))
(TZRECSPACE_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (cZRECSPACE @ (V2 @ V3))))) @ (cZRECSPACE @ (((cZCONSTR @ V0) @ V1) @ V2))))))))))
(TZCONSTR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cZCONSTR @ V0) @ V1) @ V2)) @ ((cINJP @ (cINJN @ (cSUC @ V0))) @ ((cINJP @ (cINJA @ V1)) @ (cINJF @ V2)))))))))))
(TZCONSTR_ZBOT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c~ @ ((c= @ (((cZCONSTR @ V0) @ V1) @ V2)) @ cZBOT)))))))))
(TRELPOW_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((cRELPOW @ (cSUC @ V0)) @ V2) @ V1) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((((cRELPOW @ V0) @ V2) @ V1) @ V4)) @ ((V2 @ V4) @ V3))))))))))))))
(TMULTISET_INDUCT_LEMMA1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cSUBSET @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ (c~ @ ((c= @ ((cmultiplicity @ V5) @ V7)) @ (cNUMERAL @ c_0)))) @ V7)))))) @ V2)) @ (V3 @ V5))))) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (V3 @ V6)) @ (V3 @ ((cmunion @ V6) @ (cmsing @ V5)))))))))) @ ((c==> @ ((c/__caret__ @ ((c= @ ((cmultiplicity @ V4) @ V1)) @ V0)) @ ((cSUBSET @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ (c~ @ ((c= @ ((cmultiplicity @ V4) @ V6)) @ (cNUMERAL @ c_0)))) @ V6)))))) @ ((cINSERT @ V1) @ V2)))) @ (V3 @ V4))))))))))))))
(TFIXING_SWAPSEQ_DECREASE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cswapseq @ V0) @ V3)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ ((c= @ (((co @ (cswap @ ((c__comma__ @ V1) @ V2))) @ V3) @ V1)) @ V1)))) @ ((cswapseq @ ((c- @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((co @ (cswap @ ((c__comma__ @ V1) @ V2))) @ V3))))))))))))
(TREPLICATE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cREPLICATE @ (cSUC @ V0)) @ V1)) @ ((cCONS @ V1) @ ((cREPLICATE @ V0) @ V1))))))))
(THAS_VECTOR_DERIVATIVE_ID,(c! @ (^[V0]: (((chas_vector_derivative @ (^[V1]: V1)) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))
(TDIFFERENTIABLE_ID,(c! @ (^[V0]: ((cdifferentiable @ (^[V1]: V1)) @ V0))))
(THAS_DERIVATIVE_ID,(c! @ (^[V0]: (((chas_derivative @ (^[V1]: V1)) @ (^[V1]: V1)) @ V0))))
(Tnet_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (cmk_net @ (cnetord @ V0))) @ V0))))
(Ttrivial_limit,(c! @ (^[V0]: ((c= @ (ctrivial_limit @ V0)) @ ((c__caret__/ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ V1) @ V2)))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ (c! @ (^[V3]: ((c/__caret__ @ (c~ @ (((cnetord @ V0) @ V3) @ V1))) @ (c~ @ (((cnetord @ V0) @ V3) @ V2)))))))))))))))
(TLIM_CONST_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c--> @ (^[V3]: V1)) @ V2) @ V0)) @ ((c__caret__/ @ (ctrivial_limit @ V0)) @ ((c= @ V1) @ V2))))))))))
(Tnetlimit,(c! @ (^[V0]: ((c= @ (cnetlimit @ V0)) @ (c__at__ @ (^[V1]: (c! @ (^[V2]: (c~ @ (((cnetord @ V0) @ V2) @ V1))))))))))
(TTENDSTO_LIM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V0))) @ (((c--> @ V1) @ V2) @ V0))) @ ((c= @ ((clim @ V0) @ V1)) @ V2)))))))))
(TLIM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c--> @ V1) @ V2) @ V0)) @ ((c__caret__/ @ (ctrivial_limit @ V0)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ (c? @ (^[V5]: (((cnetord @ V0) @ V5) @ V4)))) @ (c! @ (^[V5]: ((c==> @ (((cnetord @ V0) @ V5) @ V4)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V1 @ V5)) @ V2))) @ V3)))))))))))))))))))
(TEVENTUALLY_TRUE,(c! @ (^[V0]: ((c= @ ((ceventually @ (^[V1]: cT)) @ V0)) @ cT))))
(TEVENTUALLY_FALSE,(c! @ (^[V0]: ((c= @ ((ceventually @ (^[V1]: cF)) @ V0)) @ (ctrivial_limit @ V0)))))
(TEVENTUALLY_HAPPENS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ceventually @ V1) @ V0)) @ ((c__caret__/ @ (ctrivial_limit @ V0)) @ (c? @ (^[V2]: (V1 @ V2))))))))))
(Teventually,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ceventually @ V1) @ V0)) @ ((c__caret__/ @ (ctrivial_limit @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (c? @ (^[V3]: (((cnetord @ V0) @ V3) @ V2)))) @ (c! @ (^[V3]: ((c==> @ (((cnetord @ V0) @ V3) @ V2)) @ (V1 @ V3))))))))))))))
(TNONTRIVIAL_LIMIT_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (ctrivial_limit @ V0)) @ (ctrivial_limit @ ((cwithin @ V0) @ V1))))))))
(TWITHIN_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cwithin @ ((cwithin @ V0) @ V1)) @ V2)) @ ((cwithin @ V0) @ ((cINTER @ V1) @ V2))))))))))
(TWITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((cnetord @ ((cwithin @ V0) @ V3)) @ V2) @ V1)) @ ((c/__caret__ @ (((cnetord @ V0) @ V2) @ V1)) @ ((cIN @ V2) @ V3))))))))))))
(Twithin,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cwithin @ V0) @ V1)) @ (cmk_net @ (^[V2]: (^[V3]: ((c/__caret__ @ (((cnetord @ V0) @ V2) @ V3)) @ ((cIN @ V2) @ V1)))))))))))
(TNET_DILEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c? @ (^[V3]: ((c/__caret__ @ (c? @ (^[V4]: (((cnetord @ V0) @ V4) @ V3)))) @ (c! @ (^[V4]: ((c==> @ (((cnetord @ V0) @ V4) @ V3)) @ (V1 @ V4)))))))) @ (c? @ (^[V3]: ((c/__caret__ @ (c? @ (^[V4]: (((cnetord @ V0) @ V4) @ V3)))) @ (c! @ (^[V4]: ((c==> @ (((cnetord @ V0) @ V4) @ V3)) @ (V2 @ V4))))))))) @ (c? @ (^[V3]: ((c/__caret__ @ (c? @ (^[V4]: (((cnetord @ V0) @ V4) @ V3)))) @ (c! @ (^[V4]: ((c==> @ (((cnetord @ V0) @ V4) @ V3)) @ ((c/__caret__ @ (V1 @ V4)) @ (V2 @ V4))))))))))))))))
(TNADD_LE_0,(c! @ (^[V0]: ((cnadd_le @ (cnadd_of_num @ (cNUMERAL @ c_0))) @ V0))))
(TNADD_LE_REFL,(c! @ (^[V0]: ((cnadd_le @ V0) @ V0))))
(TNADD_MUL_LID,(c! @ (^[V0]: ((cnadd_eq @ ((cnadd_mul @ (cnadd_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ V0))))
(TNADD_ADD_LID,(c! @ (^[V0]: ((cnadd_eq @ ((cnadd_add @ (cnadd_of_num @ (cNUMERAL @ c_0))) @ V0)) @ V0))))
(TNADD_EQ_REFL,(c! @ (^[V0]: ((cnadd_eq @ V0) @ V0))))
(TNADD_MUL_LINV,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ ((cnadd_eq @ ((cnadd_mul @ (cnadd_inv @ V0)) @ V0)) @ (cnadd_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TNADD_LBOUND,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V2) @ V3)) @ ((c<= @ V3) @ ((c* @ V1) @ ((cdest_nadd @ V0) @ V3))))))))))))))
(TNADD_MUL_LINV_LEMMA0,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: ((c<= @ ((cnadd_rinv @ V0) @ V3)) @ ((c+ @ ((c* @ V1) @ V3)) @ V2))))))))))))
(TNADD_MUL_LINV_LEMMA5,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V2) @ V3)) @ ((c<= @ V2) @ V4))) @ ((c<= @ ((c* @ ((c* @ ((cdest_nadd @ V0) @ V3)) @ ((cdest_nadd @ V0) @ V4))) @ (cdist @ ((c__comma__ @ ((c* @ V3) @ ((cnadd_rinv @ V0) @ V4))) @ ((c* @ V4) @ ((cnadd_rinv @ V0) @ V3)))))) @ ((c* @ V1) @ ((c* @ ((c* @ V3) @ V4)) @ ((c+ @ V3) @ V4)))))))))))))))))
(TNADD_MUL_LINV_LEMMA6,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V2) @ V3)) @ ((c<= @ V2) @ V4))) @ ((c<= @ ((c* @ ((c* @ V3) @ V4)) @ (cdist @ ((c__comma__ @ ((c* @ V3) @ ((cnadd_rinv @ V0) @ V4))) @ ((c* @ V4) @ ((cnadd_rinv @ V0) @ V3)))))) @ ((c* @ V1) @ ((c* @ ((c* @ V3) @ V4)) @ ((c+ @ V3) @ V4)))))))))))))))))
(TNADD_MUL_LINV_LEMMA7,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V2) @ V3)) @ ((c<= @ V2) @ V4))) @ ((c<= @ (cdist @ ((c__comma__ @ ((c* @ V3) @ ((cnadd_rinv @ V0) @ V4))) @ ((c* @ V4) @ ((cnadd_rinv @ V0) @ V3))))) @ ((c* @ V1) @ ((c+ @ V3) @ V4))))))))))))))))
(TNADD_MUL_LINV_LEMMA2,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ ((c<= @ (cdist @ ((c__comma__ @ ((c* @ ((cdest_nadd @ V0) @ V2)) @ ((cnadd_rinv @ V0) @ V2))) @ ((c* @ V2) @ V2)))) @ ((cdest_nadd @ V0) @ V2)))))))))))
(TNADD_NONZERO,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ (c~ @ ((c= @ ((cdest_nadd @ V0) @ V2)) @ (cNUMERAL @ c_0))))))))))))
(TNADD_MUL_LINV_LEMMA3,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V1) @ V3)) @ ((c<= @ (cdist @ ((c__comma__ @ ((c* @ V2) @ ((c* @ ((cdest_nadd @ V0) @ V2)) @ ((c* @ ((cdest_nadd @ V0) @ V3)) @ ((cnadd_rinv @ V0) @ V3))))) @ ((c* @ V2) @ ((c* @ ((cdest_nadd @ V0) @ V2)) @ ((c* @ V3) @ V3)))))) @ ((c* @ V2) @ ((c* @ ((cdest_nadd @ V0) @ V2)) @ ((cdest_nadd @ V0) @ V3)))))))))))))))
(TNADD_MUL_LINV_LEMMA4,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V2)) @ ((c<= @ V1) @ V3))) @ ((c<= @ ((c* @ ((c* @ ((cdest_nadd @ V0) @ V2)) @ ((cdest_nadd @ V0) @ V3))) @ (cdist @ ((c__comma__ @ ((c* @ V2) @ ((cnadd_rinv @ V0) @ V3))) @ ((c* @ V3) @ ((cnadd_rinv @ V0) @ V2)))))) @ ((c+ @ ((c* @ ((c* @ V2) @ V3)) @ (cdist @ ((c__comma__ @ ((c* @ V2) @ ((cdest_nadd @ V0) @ V3))) @ ((c* @ V3) @ ((cdest_nadd @ V0) @ V2)))))) @ ((c* @ ((c* @ ((cdest_nadd @ V0) @ V2)) @ ((cdest_nadd @ V0) @ V3))) @ ((c+ @ V2) @ V3)))))))))))))))
(TNADD_MUL_LINV_LEMMA8,(c! @ (^[V0]: ((c==> @ (c~ @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c<= @ (cdist @ ((c__comma__ @ ((c* @ V2) @ ((cnadd_rinv @ V0) @ V3))) @ ((c* @ V3) @ ((cnadd_rinv @ V0) @ V2))))) @ ((c* @ V1) @ ((c+ @ V2) @ V3)))))))))))))
(Tnadd_inv,(c! @ (^[V0]: ((c= @ (cnadd_inv @ V0)) @ (((cCOND @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0)))) @ (cnadd_of_num @ (cNUMERAL @ c_0))) @ (cmk_nadd @ (cnadd_rinv @ V0)))))))
(Tnadd_abs,(c! @ (^[V0]: ((c= @ (cmk_nadd @ (cdest_nadd @ V0))) @ V0))))
(Threal_inv_th,(c! @ (^[V0]: ((c= @ (cmk_hreal @ (cnadd_eq @ (cnadd_inv @ V0)))) @ (chreal_inv @ (cmk_hreal @ (cnadd_eq @ V0)))))))
(Tnadd_rinv,(c! @ (^[V0]: ((c= @ (cnadd_rinv @ V0)) @ (^[V1]: ((cDIV @ ((c* @ V1) @ V1)) @ ((cdest_nadd @ V0) @ V1)))))))
(TNADD_INV,(c! @ (^[V0]: ((c= @ (cdest_nadd @ (cnadd_inv @ V0))) @ (((cCOND @ ((cnadd_eq @ V0) @ (cnadd_of_num @ (cNUMERAL @ c_0)))) @ (^[V1]: (cNUMERAL @ c_0))) @ (cnadd_rinv @ V0))))))
(TNADD_ARCH,(c! @ (^[V0]: (c? @ (^[V1]: ((cnadd_le @ V0) @ (cnadd_of_num @ V1)))))))
(TNADD_UBOUND,(c! @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V2) @ V3)) @ ((c<= @ ((cdest_nadd @ V0) @ V3)) @ ((c* @ V1) @ V3))))))))))))
(TNADD_BOUND,(c! @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: ((c<= @ ((cdest_nadd @ V0) @ V3)) @ ((c+ @ ((c* @ V1) @ V3)) @ V2)))))))))))
(TNADD_SUC,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: ((c<= @ (cdist @ ((c__comma__ @ ((cdest_nadd @ V0) @ (cSUC @ V2))) @ ((cdest_nadd @ V0) @ V2)))) @ V1))))))))
(TNADD_DIST_LEMMA,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c<= @ (cdist @ ((c__comma__ @ ((cdest_nadd @ V0) @ ((c+ @ V2) @ V3))) @ ((cdest_nadd @ V0) @ V2)))) @ ((c* @ V1) @ V3)))))))))))
(TNADD_ADDITIVE,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c<= @ (cdist @ ((c__comma__ @ ((cdest_nadd @ V0) @ ((c+ @ V2) @ V3))) @ ((c+ @ ((cdest_nadd @ V0) @ V2)) @ ((cdest_nadd @ V0) @ V3))))) @ V1))))))))))
(TNADD_MULTIPLICATIVE,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c<= @ (cdist @ ((c__comma__ @ ((cdest_nadd @ V0) @ ((c* @ V2) @ V3))) @ ((c* @ V2) @ ((cdest_nadd @ V0) @ V3))))) @ ((c+ @ ((c* @ V1) @ V2)) @ V1)))))))))))
(TNADD_DIST,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c<= @ (cdist @ ((c__comma__ @ ((cdest_nadd @ V0) @ V2)) @ ((cdest_nadd @ V0) @ V3)))) @ ((c* @ V1) @ (cdist @ ((c__comma__ @ V2) @ V3)))))))))))))
(TNADD_CAUCHY,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c<= @ (cdist @ ((c__comma__ @ ((c* @ V2) @ ((cdest_nadd @ V0) @ V3))) @ ((c* @ V3) @ ((cdest_nadd @ V0) @ V2))))) @ ((c* @ V1) @ ((c+ @ V2) @ V3))))))))))))
(TNADD_MUL_LINV_LEMMA1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ ((cdest_nadd @ V0) @ V1)) @ (cNUMERAL @ c_0)))) @ ((c<= @ (cdist @ ((c__comma__ @ ((c* @ ((cdest_nadd @ V0) @ V1)) @ ((cnadd_rinv @ V0) @ V1))) @ ((c* @ V1) @ V1)))) @ ((cdest_nadd @ V0) @ V1))))))))
(TNADD_LE_TOTAL_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((cnadd_le @ V2) @ V0))) @ (c? @ (^[V3]: ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cNUMERAL @ c_0)))) @ ((c< @ ((c+ @ ((cdest_nadd @ V0) @ V3)) @ V1)) @ ((cdest_nadd @ V2) @ V3)))))))))))))
(TNADD_LE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((cnadd_le @ V0) @ ((cnadd_add @ V0) @ V1)))))))
(TNADD_MUL_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((cnadd_eq @ ((cnadd_mul @ V1) @ V0)) @ ((cnadd_mul @ V0) @ V1)))))))
(TNADD_ADD_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((cnadd_eq @ ((cnadd_add @ V1) @ V0)) @ ((cnadd_add @ V0) @ V1)))))))
(TNADD_LE_TOTAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((cnadd_le @ V1) @ V0)) @ ((cnadd_le @ V0) @ V1)))))))
(TNADD_LE_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cnadd_le @ V1) @ V0)) @ (c? @ (^[V2]: ((cnadd_eq @ V0) @ ((cnadd_add @ V1) @ V2))))))))))
(TNADD_EQ_IMP_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cnadd_eq @ V0) @ V1)) @ ((cnadd_le @ V0) @ V1)))))))
(TNADD_INV_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cnadd_eq @ V0) @ V1)) @ ((cnadd_eq @ (cnadd_inv @ V0)) @ (cnadd_inv @ V1))))))))
(TNADD_ARCH_ZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((cnadd_le @ ((cnadd_mul @ (cnadd_of_num @ V2)) @ V1)) @ V0)))) @ ((cnadd_eq @ V1) @ (cnadd_of_num @ (cNUMERAL @ c_0)))))))))
(Tnadd_mul,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnadd_mul @ V0) @ V1)) @ (cmk_nadd @ (^[V2]: ((cdest_nadd @ V0) @ ((cdest_nadd @ V1) @ V2))))))))))
(Tnadd_add,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnadd_add @ V0) @ V1)) @ (cmk_nadd @ (^[V2]: ((c+ @ ((cdest_nadd @ V0) @ V2)) @ ((cdest_nadd @ V1) @ V2))))))))))
(Threal_mul_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmk_hreal @ (cnadd_eq @ ((cnadd_mul @ V0) @ V1)))) @ ((chreal_mul @ (cmk_hreal @ (cnadd_eq @ V0))) @ (cmk_hreal @ (cnadd_eq @ V1)))))))))
(Threal_add_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmk_hreal @ (cnadd_eq @ ((cnadd_add @ V0) @ V1)))) @ ((chreal_add @ (cmk_hreal @ (cnadd_eq @ V0))) @ (cmk_hreal @ (cnadd_eq @ V1)))))))))
(TNADD_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdest_nadd @ ((cnadd_mul @ V0) @ V1))) @ (^[V2]: ((cdest_nadd @ V0) @ ((cdest_nadd @ V1) @ V2)))))))))
(TNADD_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdest_nadd @ ((cnadd_add @ V0) @ V1))) @ (^[V2]: ((c+ @ ((cdest_nadd @ V0) @ V2)) @ ((cdest_nadd @ V1) @ V2)))))))))
(Threal_le_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnadd_le @ V0) @ V1)) @ ((chreal_le @ (cmk_hreal @ (cnadd_eq @ V0))) @ (cmk_hreal @ (cnadd_eq @ V1)))))))))
(Tnadd_le,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnadd_le @ V0) @ V1)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c<= @ ((cdest_nadd @ V0) @ V3)) @ ((c+ @ ((cdest_nadd @ V1) @ V3)) @ V2))))))))))))
(TNADD_EQ_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnadd_eq @ V1) @ V0)) @ ((cnadd_eq @ V0) @ V1)))))))
(Tnadd_eq,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnadd_eq @ V0) @ V1)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c<= @ (cdist @ ((c__comma__ @ ((cdest_nadd @ V0) @ V3)) @ ((cdest_nadd @ V1) @ V3)))) @ V2)))))))))))
(TNADD_LE_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cnadd_le @ V0) @ V1)) @ ((cnadd_le @ V1) @ V0))) @ ((cnadd_eq @ V0) @ V1)))))))
(TNADD_ALTMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (c! @ (^[V4]: ((c<= @ (cdist @ ((c__comma__ @ ((c* @ V4) @ ((cdest_nadd @ V0) @ ((cdest_nadd @ V1) @ V4)))) @ ((c* @ ((cdest_nadd @ V0) @ V4)) @ ((cdest_nadd @ V1) @ V4))))) @ ((c+ @ ((c* @ V2) @ V4)) @ V3)))))))))))))
(TNADD_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((cnadd_eq @ ((cnadd_mul @ ((cnadd_add @ V0) @ V1)) @ V2)) @ ((cnadd_add @ ((cnadd_mul @ V0) @ V2)) @ ((cnadd_mul @ V1) @ V2))))))))))
(TNADD_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((cnadd_eq @ ((cnadd_mul @ V1) @ ((cnadd_add @ V0) @ V2))) @ ((cnadd_add @ ((cnadd_mul @ V1) @ V0)) @ ((cnadd_mul @ V1) @ V2))))))))))
(TNADD_MUL_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((cnadd_eq @ ((cnadd_mul @ V0) @ ((cnadd_mul @ V1) @ V2))) @ ((cnadd_mul @ ((cnadd_mul @ V0) @ V1)) @ V2)))))))))
(TNADD_ADD_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((cnadd_eq @ ((cnadd_add @ V0) @ ((cnadd_add @ V1) @ V2))) @ ((cnadd_add @ ((cnadd_add @ V0) @ V1)) @ V2)))))))))
(TNADD_LE_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnadd_le @ V0) @ V2)) @ ((cnadd_le @ ((cnadd_mul @ V1) @ V0)) @ ((cnadd_mul @ V1) @ V2))))))))))
(TNADD_LE_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnadd_le @ V0) @ V1)) @ ((cnadd_le @ ((cnadd_mul @ V0) @ V2)) @ ((cnadd_mul @ V1) @ V2))))))))))
(TNADD_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnadd_eq @ ((cnadd_add @ V0) @ V1)) @ ((cnadd_add @ V0) @ V2))) @ ((cnadd_eq @ V1) @ V2)))))))))
(TNADD_MUL_WELLDEF_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cnadd_eq @ V0) @ V2)) @ ((cnadd_eq @ ((cnadd_mul @ V1) @ V0)) @ ((cnadd_mul @ V1) @ V2))))))))))
(TNADD_LE_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnadd_le @ V1) @ V0)) @ ((cnadd_le @ V0) @ V2))) @ ((cnadd_le @ V1) @ V2)))))))))
(TNADD_EQ_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cnadd_eq @ V1) @ V0)) @ ((cnadd_eq @ V0) @ V2))) @ ((cnadd_eq @ V1) @ V2)))))))))
(TNADD_ARCH_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((cnadd_le @ ((cnadd_mul @ (cnadd_of_num @ V3)) @ V1)) @ ((cnadd_add @ ((cnadd_mul @ (cnadd_of_num @ V3)) @ V2)) @ V0))))) @ ((cnadd_le @ V1) @ V2)))))))))
(TNADD_LE_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnadd_le @ ((cnadd_add @ V1) @ V0)) @ ((cnadd_add @ V2) @ V0))) @ ((cnadd_le @ V1) @ V2)))))))))
(TNADD_LE_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnadd_le @ ((cnadd_add @ V0) @ V1)) @ ((cnadd_add @ V0) @ V2))) @ ((cnadd_le @ V1) @ V2)))))))))
(TNADD_MUL_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cnadd_eq @ V0) @ V2)) @ ((cnadd_eq @ V1) @ V3))) @ ((cnadd_eq @ ((cnadd_mul @ V0) @ V1)) @ ((cnadd_mul @ V2) @ V3))))))))))))
(TNADD_ADD_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cnadd_eq @ V0) @ V2)) @ ((cnadd_eq @ V1) @ V3))) @ ((cnadd_eq @ ((cnadd_add @ V0) @ V1)) @ ((cnadd_add @ V2) @ V3))))))))))))
(TNADD_LE_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cnadd_eq @ V0) @ V2)) @ ((cnadd_eq @ V1) @ V3))) @ ((c= @ ((cnadd_le @ V0) @ V1)) @ ((cnadd_le @ V2) @ V3))))))))))))
(TNADD_LE_WELLDEF_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cnadd_eq @ V0) @ V2)) @ ((c/__caret__ @ ((cnadd_eq @ V1) @ V3)) @ ((cnadd_le @ V0) @ V1)))) @ ((cnadd_le @ V2) @ V3)))))))))))
(Tmultivector_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (cmk_multivector @ (cdest_multivector @ V0))) @ V0))))
(Tmultiset_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (cmultiset @ (cmultiplicity @ V0))) @ V0))))
(TLEMMA_2_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((cmorder @ V2) @ V0) @ ((cmunion @ V1) @ (cmsing @ V3)))) @ ((c__caret__/ @ (c? @ (^[V4]: ((c/__caret__ @ (((cmorder @ V2) @ V4) @ V1)) @ ((c= @ V0) @ ((cmunion @ V4) @ (cmsing @ V3))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((cmunion @ V1) @ V4))) @ (c! @ (^[V5]: ((c==> @ ((cmmember @ V5) @ V4)) @ ((V2 @ V5) @ V3))))))))))))))))))
(TMDIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmultiplicity @ ((cmdiff @ V0) @ V1)) @ V2)) @ ((c- @ ((cmultiplicity @ V0) @ V2)) @ ((cmultiplicity @ V1) @ V2))))))))))
(TMMEMBER_MDIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cmmember @ V1) @ V0)) @ ((c= @ V0) @ ((cmunion @ ((cmdiff @ V0) @ (cmsing @ V1))) @ (cmsing @ V1)))))))))
(TMUNION_MEMPTY,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c= @ ((cmunion @ V0) @ (cmsing @ V1))) @ cmempty)))))))
(TLEMMA_2_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((V2 @ V4) @ V1)) @ ((cIN @ V3) @ (cWFP @ (cmorder @ V2))))) @ ((cIN @ ((cmunion @ V3) @ (cmsing @ V4))) @ (cWFP @ (cmorder @ V2))))))))) @ ((c/__caret__ @ ((cIN @ V0) @ (cWFP @ (cmorder @ V2)))) @ (c! @ (^[V3]: ((c==> @ (((cmorder @ V2) @ V3) @ V0)) @ ((cIN @ ((cmunion @ V3) @ (cmsing @ V1))) @ (cWFP @ (cmorder @ V2))))))))) @ ((cIN @ ((cmunion @ V0) @ (cmsing @ V1))) @ (cWFP @ (cmorder @ V2)))))))))))
(TLEMMA_2_4,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cWF @ V1)) @ ((cIN @ V0) @ (cWFP @ (cmorder @ V1)))))))))
(TLEMMA_2_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cWF @ V2)) @ ((c==> @ ((cIN @ V0) @ (cWFP @ (cmorder @ V2)))) @ ((cIN @ ((cmunion @ V0) @ (cmsing @ V1))) @ (cWFP @ (cmorder @ V2))))))))))))
(TLEMMA_2_2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((V2 @ V4) @ V1)) @ ((cIN @ V3) @ (cWFP @ (cmorder @ V2))))) @ ((cIN @ ((cmunion @ V3) @ (cmsing @ V4))) @ (cWFP @ (cmorder @ V2))))))))) @ ((c==> @ ((cIN @ V0) @ (cWFP @ (cmorder @ V2)))) @ ((cIN @ ((cmunion @ V0) @ (cmsing @ V1))) @ (cWFP @ (cmorder @ V2))))))))))))
(Tmorder,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cmorder @ V2) @ V1) @ V0)) @ (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ ((cmunion @ V3) @ (cmsing @ V4)))) @ ((c/__caret__ @ ((c= @ V1) @ ((cmunion @ V3) @ V5))) @ (c! @ (^[V6]: ((c==> @ ((cmmember @ V6) @ V5)) @ ((V2 @ V6) @ V4))))))))))))))))))))
(TMUNION_11,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cmunion @ V1) @ V0)) @ ((cmunion @ V2) @ V0))) @ ((c= @ V1) @ V2)))))))))
(TMUNION_AC_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmunion @ V1) @ V0)) @ ((cmunion @ V0) @ V1)))))))
(TMUNION_AC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmunion @ ((cmunion @ V0) @ V1)) @ V2)) @ ((cmunion @ V0) @ ((cmunion @ V1) @ V2))))))))))
(TMUNION_AC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmunion @ V1) @ ((cmunion @ V0) @ V2))) @ ((cmunion @ V0) @ ((cmunion @ V1) @ V2))))))))))
(TMUNION_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmunion @ V0) @ ((cmunion @ V1) @ V2))) @ ((cmunion @ ((cmunion @ V0) @ V1)) @ V2)))))))))
(TMUNION_EMPTY,(c! @ (^[V0]: ((c= @ ((cmunion @ V0) @ cmempty)) @ V0))))
(TMMEMBER_MUNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmmember @ V1) @ ((cmunion @ V0) @ V2))) @ ((c__caret__/ @ ((cmmember @ V1) @ V0)) @ ((cmmember @ V1) @ V2))))))))))
(TMUNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmultiplicity @ ((cmunion @ V0) @ V1)) @ V2)) @ ((c+ @ ((cmultiplicity @ V0) @ V2)) @ ((cmultiplicity @ V1) @ V2))))))))))
(TMEXTENSION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ ((cmultiplicity @ V0) @ V2)) @ ((cmultiplicity @ V1) @ V2))))))))))
(Tmdiff,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmdiff @ V0) @ V1)) @ (cmultiset @ (^[V2]: ((c- @ ((cmultiplicity @ V0) @ V2)) @ ((cmultiplicity @ V1) @ V2))))))))))
(Tmunion,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmunion @ V0) @ V1)) @ (cmultiset @ (^[V2]: ((c+ @ ((cmultiplicity @ V0) @ V2)) @ ((cmultiplicity @ V1) @ V2))))))))))
(Tmmember,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmmember @ V1) @ V0)) @ (c~ @ ((c= @ ((cmultiplicity @ V0) @ V1)) @ (cNUMERAL @ c_0)))))))))
(TTERM_UNION_conjunct0,(c! @ (^[V0]: ((c= @ ((cTERM_UNION @ cNIL) @ V0)) @ V0))))
(Tproves_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c|- @ V0) @ V1)) @ ((c__caret__/ @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ V0) @ cNIL)) @ ((c/__caret__ @ ((c= @ V1) @ ((c=== @ V2) @ V2))) @ (cwelltyped @ V2)))))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (c? @ (^[V7]: ((c/__caret__ @ ((c= @ V0) @ ((cTERM_UNION @ V2) @ V3))) @ ((c/__caret__ @ ((c= @ V1) @ ((c=== @ V4) @ V7))) @ ((c/__caret__ @ ((c|- @ V2) @ ((c=== @ V4) @ V5))) @ ((c/__caret__ @ ((c|- @ V3) @ ((c=== @ V6) @ V7))) @ ((cACONV @ V5) @ V6)))))))))))))))))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (c? @ (^[V7]: ((c/__caret__ @ ((c= @ V0) @ ((cTERM_UNION @ V2) @ V5))) @ ((c/__caret__ @ ((c= @ V1) @ ((c=== @ ((cComb @ V3) @ V6)) @ ((cComb @ V4) @ V7)))) @ ((c/__caret__ @ ((c|- @ V2) @ ((c=== @ V3) @ V4))) @ ((c/__caret__ @ ((c|- @ V5) @ ((c=== @ V6) @ V7))) @ (cwelltyped @ ((cComb @ V3) @ V6))))))))))))))))))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V1) @ ((c=== @ (((cAbs @ V2) @ V3) @ V4)) @ (((cAbs @ V2) @ V3) @ V5)))) @ ((c/__caret__ @ (c~ @ ((cEX @ (cVFREE_IN @ ((cVar @ V2) @ V3))) @ V0))) @ ((c|- @ V0) @ ((c=== @ V4) @ V5))))))))))))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ cNIL)) @ ((c/__caret__ @ ((c= @ V1) @ ((c=== @ ((cComb @ (((cAbs @ V2) @ V3) @ V4)) @ ((cVar @ V2) @ V3))) @ V4))) @ (cwelltyped @ V4)))))))))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V0) @ ((cCONS @ V1) @ cNIL))) @ ((chas_type @ V1) @ cBool))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ ((cTERM_UNION @ V2) @ V3))) @ ((c/__caret__ @ ((c|- @ V2) @ ((c=== @ V4) @ V1))) @ ((c/__caret__ @ ((c|- @ V3) @ V5)) @ ((cACONV @ V4) @ V5))))))))))))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ ((cTERM_UNION @ ((cFILTER @ ((co @ c~) @ (cACONV @ V5))) @ V2)) @ ((cFILTER @ ((co @ c~) @ (cACONV @ V4))) @ V3)))) @ ((c/__caret__ @ ((c= @ V1) @ ((c=== @ V4) @ V5))) @ ((c/__caret__ @ ((c|- @ V2) @ V4)) @ ((c|- @ V3) @ V5))))))))))))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((cMAP @ (cINST @ V2)) @ V3))) @ ((c/__caret__ @ ((c= @ V1) @ ((cINST @ V2) @ V4))) @ ((c|- @ V3) @ V4)))))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((cMAP @ (cVSUBST @ V2)) @ V3))) @ ((c/__caret__ @ ((c= @ V1) @ ((cVSUBST @ V2) @ V4))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((cMEM @ ((c__comma__ @ V6) @ V5)) @ V2)) @ (c? @ (^[V7]: (c? @ (^[V8]: ((c/__caret__ @ ((c= @ V5) @ ((cVar @ V7) @ V8))) @ ((chas_type @ V6) @ V8)))))))))))) @ ((c|- @ V3) @ V4)))))))))))))))))))))))))
(Tprove_RULES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c|- @ V0) @ ((c=== @ V1) @ V2))) @ ((c/__caret__ @ ((c|- @ V3) @ ((c=== @ V4) @ V5))) @ (cwelltyped @ ((cComb @ V1) @ V4))))) @ ((c|- @ ((cTERM_UNION @ V0) @ V3)) @ ((c=== @ ((cComb @ V1) @ V4)) @ ((cComb @ V2) @ V5)))))))))))))))))
(TTERM_UNION_NONEW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cMEM @ V1) @ ((cTERM_UNION @ V0) @ V2))) @ ((c__caret__/ @ ((cMEM @ V1) @ V0)) @ ((cMEM @ V1) @ V2))))))))))
(TALL_BOOL_TERM_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cALL @ (^[V2]: ((chas_type @ V2) @ cBool))) @ V0)) @ ((cALL @ (^[V2]: ((chas_type @ V2) @ cBool))) @ V1))) @ ((cALL @ (^[V2]: ((chas_type @ V2) @ cBool))) @ ((cTERM_UNION @ V0) @ V1))))))))
(TTERM_UNION_THM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c__caret__/ @ ((cMEM @ V2) @ V0)) @ ((cMEM @ V2) @ V1))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cMEM @ V3) @ ((cTERM_UNION @ V0) @ V1))) @ ((cACONV @ V2) @ V3))))))))))))
(Tprove_RULES_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c|- @ V0) @ V2)) @ ((c|- @ V1) @ V3))) @ ((c|- @ ((cTERM_UNION @ ((cFILTER @ ((co @ c~) @ (cACONV @ V3))) @ V0)) @ ((cFILTER @ ((co @ c~) @ (cACONV @ V2))) @ V1))) @ ((c=== @ V2) @ V3))))))))))))
(Tprove_RULES_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c|- @ V0) @ ((c=== @ V2) @ V3))) @ ((c/__caret__ @ ((c|- @ V1) @ V4)) @ ((cACONV @ V2) @ V4)))) @ ((c|- @ ((cTERM_UNION @ V0) @ V1)) @ V3)))))))))))))
(Tprove_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c|- @ V0) @ ((c=== @ V2) @ V3))) @ ((c/__caret__ @ ((c|- @ V1) @ ((c=== @ V4) @ V5))) @ ((cACONV @ V3) @ V4)))) @ ((c|- @ ((cTERM_UNION @ V0) @ V1)) @ ((c=== @ V2) @ V5))))))))))))))))
(Tprove_RULES_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((cEX @ (cVFREE_IN @ ((cVar @ V1) @ V2))) @ V0))) @ ((c|- @ V0) @ ((c=== @ V3) @ V4)))) @ ((c|- @ V0) @ ((c=== @ (((cAbs @ V1) @ V2) @ V3)) @ (((cAbs @ V1) @ V2) @ V4)))))))))))))))
(TLENGTH_POLY_DIFF,(c! @ (^[V0]: ((c= @ (cLENGTH @ (cpoly_diff @ V0))) @ (cPRE @ (cLENGTH @ V0))))))
(TPOLY_MUL_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((cpoly_mul @ cNIL) @ V0)) @ cNIL))))
(Tpoly_exp_conjunct0,(c! @ (^[V0]: ((c= @ ((cpoly_exp @ V0) @ (cNUMERAL @ c_0))) @ ((cCONS @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL)))))
(TPOLY_ADD_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((cpoly_add @ cNIL) @ V0)) @ V0))))
(TPOLY_ADD_CLAUSES_conjunct1,(c! @ (^[V0]: ((c= @ ((cpoly_add @ V0) @ cNIL)) @ V0))))
(Tpoly_diff,(c! @ (^[V0]: ((c= @ (cpoly_diff @ V0)) @ (((cCOND @ ((c= @ V0) @ cNIL)) @ cNIL) @ ((cpoly_diff_aux @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cTL @ V0)))))))
(TPOLY_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpoly @ (cpoly_neg @ V0)) @ V1)) @ (creal_neg @ ((cpoly @ V0) @ V1))))))))
(TALL_LT_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cALL @ (^[V3]: ((creal_lt @ V3) @ V2))) @ ((cCONS @ V1) @ V0))) @ ((creal_lt @ ((cMAXL @ V0) @ V1)) @ V2)))))))))
(TPOLY_EXP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpoly @ ((cpoly_exp @ V0) @ V2)) @ V1)) @ ((creal_pow @ ((cpoly @ V0) @ V1)) @ V2)))))))))
(Tpoly_exp_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpoly_exp @ V0) @ (cSUC @ V1))) @ ((cpoly_mul @ V0) @ ((cpoly_exp @ V0) @ V1))))))))
(TPOLY_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpoly @ ((cpoly_mul @ V0) @ V1)) @ V2)) @ ((creal_mul @ ((cpoly @ V0) @ V2)) @ ((cpoly @ V1) @ V2))))))))))
(TPOLY_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpoly @ ((cpoly_add @ V0) @ V1)) @ V2)) @ ((creal_add @ ((cpoly @ V0) @ V2)) @ ((cpoly @ V1) @ V2))))))))))
(TTYPE_SUBST_conjunct2,(c! @ (^[V0]: ((c= @ ((cTYPE_SUBST @ V0) @ cInd)) @ cInd))))
(TTYPE_SUBST_conjunct1,(c! @ (^[V0]: ((c= @ ((cTYPE_SUBST @ V0) @ cBool)) @ cBool))))
(TINST_DEF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINST @ V0) @ V1)) @ (cRESULT @ (((cINST_CORE @ cNIL) @ V0) @ V1))))))))
(Tprove_RULES_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c|- @ V1) @ V2)) @ ((c|- @ ((cMAP @ (cINST @ V0)) @ V1)) @ ((cINST @ V0) @ V2))))))))))
(TTYPE_SUBST_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cTYPE_SUBST @ V0) @ (cTyvar @ V1))) @ (((cREV_ASSOCD @ (cTyvar @ V1)) @ V0) @ (cTyvar @ V1))))))))
(TRACONV_RULES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((cRACONV @ V0) @ ((c__comma__ @ (cSelect @ V1)) @ (cSelect @ V1))))))))
(TRACONV_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cRACONV @ V0) @ ((c__comma__ @ (cEqual @ V1)) @ (cEqual @ V1))))))))
(TVSUBST_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cVSUBST @ V0) @ (cSelect @ V1))) @ (cSelect @ V1)))))))
(TVSUBST_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cVSUBST @ V0) @ (cEqual @ V1))) @ (cEqual @ V1)))))))
(TRACONV_conjunct12,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ (cSelect @ V1)) @ (cSelect @ V2)))) @ ((c= @ V1) @ V2)))))))))
(TRACONV_conjunct11,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ (cSelect @ V1)) @ (cEqual @ V2)))) @ cF))))))))
(TRACONV_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ (cEqual @ V1)) @ (cSelect @ V2)))) @ cF))))))))
(TRACONV_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ (cEqual @ V1)) @ (cEqual @ V2)))) @ ((c= @ V1) @ V2)))))))))
(TRACONV_conjunct13,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ (cSelect @ V1)) @ ((cComb @ V2) @ V3)))) @ cF))))))))))
(TRACONV_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ (cEqual @ V1)) @ ((cComb @ V2) @ V3)))) @ cF))))))))))
(TRACONV_conjunct10,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ (cSelect @ V1)) @ ((cVar @ V2) @ V3)))) @ cF))))))))))
(TRACONV_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ (cEqual @ V1)) @ ((cVar @ V2) @ V3)))) @ cF))))))))))
(TRACONV_conjunct14,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ (cSelect @ V1)) @ (((cAbs @ V2) @ V3) @ V4)))) @ cF))))))))))))
(TRACONV_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ (cEqual @ V1)) @ (((cAbs @ V2) @ V3) @ V4)))) @ cF))))))))))))
(TRACONV_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cALL @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ ((c= @ V3) @ V4))))))))) @ V0)) @ ((cRACONV @ V0) @ ((c__comma__ @ V1) @ V1))))))))
(TVSUBST_WELLTYPED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cwelltyped @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cMEM @ ((c__comma__ @ V3) @ V2)) @ V0)) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V2) @ ((cVar @ V4) @ V5))) @ ((chas_type @ V3) @ V5))))))))))))) @ (cwelltyped @ ((cVSUBST @ V0) @ V1))))))))
(TSIZEOF_VSUBST,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cMEM @ ((c__comma__ @ V2) @ V3)) @ V0)) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c= @ V2) @ ((cVar @ V4) @ V5)))))))))))) @ ((c= @ (csizeof @ ((cVSUBST @ V0) @ V1))) @ (csizeof @ V1))))))))
(TVSUBST_HAS_TYPE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_type @ V1) @ V2)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cMEM @ ((c__comma__ @ V4) @ V3)) @ V0)) @ (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((c= @ V3) @ ((cVar @ V5) @ V6))) @ ((chas_type @ V4) @ V6))))))))))))) @ ((chas_type @ ((cVSUBST @ V0) @ V1)) @ V2)))))))))
(TALPHAVARS_TYPE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cALPHAVARS @ V0) @ ((c__comma__ @ V1) @ V2))) @ ((c/__caret__ @ ((cALL @ (cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ ((c/__caret__ @ (cwelltyped @ V4)) @ ((c/__caret__ @ (cwelltyped @ V5)) @ ((c= @ (ctypeof @ V4)) @ (ctypeof @ V5)))))))))))) @ V0)) @ ((c/__caret__ @ (cwelltyped @ V1)) @ (cwelltyped @ V2))))) @ ((c= @ (ctypeof @ V1)) @ (ctypeof @ V2))))))))))
(TRACONV_conjunct17,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ ((cComb @ V1) @ V2)) @ (cSelect @ V3)))) @ cF))))))))))
(TRACONV_conjunct16,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cRACONV @ V0) @ ((c__comma__ @ ((cComb @ V1) @ V2)) @ (cEqual @ V3)))) @ cF))))))))))
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(TVARIANT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c~ @ ((cVFREE_IN @ ((cVar @ (((cVARIANT @ V2) @ V0) @ V1)) @ V1)) @ V2)))))))))
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(TVFREE_IN_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cVFREE_IN @ V2) @ (((cAbs @ V0) @ V1) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ ((cVar @ V0) @ V1)) @ V2))) @ ((cVFREE_IN @ V2) @ V3))))))))))))
(Tterm_DISTINCT_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c~ @ ((c= @ ((cVar @ V0) @ V1)) @ ((cComb @ V2) @ V3))))))))))))
(Tterm_INJ_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c= @ ((c= @ (((cAbs @ V0) @ V1) @ V2)) @ (((cAbs @ V3) @ V4) @ V5))) @ ((c/__caret__ @ ((c= @ V0) @ V3)) @ ((c/__caret__ @ ((c= @ V1) @ V4)) @ ((c= @ V2) @ V5)))))))))))))))))
(Tterm_INJ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cVar @ V0) @ V1)) @ ((cVar @ V2) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V2)) @ ((c= @ V1) @ V3))))))))))))
(Tterm_DISTINCT_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c~ @ ((c= @ ((cVar @ V0) @ V1)) @ (((cAbs @ V2) @ V3) @ V4))))))))))))))
(TRACONV_conjunct24,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c= @ ((cRACONV @ V4) @ ((c__comma__ @ (((cAbs @ V0) @ V1) @ V5)) @ (((cAbs @ V2) @ V3) @ V6)))) @ ((c/__caret__ @ ((c= @ V1) @ V3)) @ ((cRACONV @ ((cCONS @ ((c__comma__ @ ((cVar @ V0) @ V1)) @ ((cVar @ V2) @ V3))) @ V4)) @ ((c__comma__ @ V5) @ V6)))))))))))))))))))
(Ttype_INJ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cTyvar @ V0)) @ (cTyvar @ V1))) @ ((c= @ V0) @ V1)))))))
(THAS_MEASURE_SIMPLEX_0,(c! @ (^[V0]: ((c==> @ ((c= @ (cLENGTH @ V0)) @ (cdimindex @ cUNIV))) @ ((chas_measure @ ((chull @ cconvex) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ (cset_of_list @ V0)))) @ ((creal_div @ (creal_abs @ (cdet @ (cvector @ V0)))) @ (creal_of_num @ (cFACT @ (cdimindex @ cUNIV)))))))))
(TMEASURABLE_SIMPLEX,(c! @ (^[V0]: (cmeasurable @ ((chull @ cconvex) @ (cset_of_list @ V0))))))
(TEULERIAN_ODD_LEMMA_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((ceulerian @ V1) @ V0) @ V2)) @ ((c==> @ (cgraph @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (cvertices @ V1))) @ ((c= @ (cODD @ ((cdegree @ V1) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ (cFST @ V2)) @ (cSND @ V2)))) @ ((c__caret__/ @ ((c= @ V3) @ (cFST @ V2))) @ ((c= @ V3) @ (cSND @ V2)))))))))))))))))
(TEULERIAN_ODD_LEMMA_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((ceulerian @ V2) @ V0) @ V1)) @ ((c==> @ (cgraph @ V2)) @ (cFINITE @ (cedges @ V2)))))))))))
(Tlist_CASES,(c! @ (^[V0]: ((c__caret__/ @ ((c= @ V0) @ cNIL)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ ((cCONS @ V1) @ V2))))))))))
(TAPPEND_conjunct0,(c! @ (^[V0]: ((c= @ ((cAPPEND @ cNIL) @ V0)) @ V0))))
(TAPPEND_NIL,(c! @ (^[V0]: ((c= @ ((cAPPEND @ V0) @ cNIL)) @ V0))))
(TREVERSE_REVERSE,(c! @ (^[V0]: ((c= @ (cREVERSE @ (cREVERSE @ V0))) @ V0))))
(Tvector,(c! @ (^[V0]: ((c= @ (cvector @ V0)) @ (clambda @ (^[V1]: ((cEL @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)))))))
(TPERMUTED_NIL_EQ_NIL_conjunct0,(c! @ (^[V0]: ((c= @ ((cPERMUTED @ cNIL) @ V0)) @ ((c= @ V0) @ cNIL)))))
(TPERMUTED_NIL_EQ_NIL_conjunct1,(c! @ (^[V0]: ((c= @ ((cPERMUTED @ V0) @ cNIL)) @ ((c= @ V0) @ cNIL)))))
(TLENGTH_EQ_NIL,(c! @ (^[V0]: ((c= @ ((c= @ (cLENGTH @ V0)) @ (cNUMERAL @ c_0))) @ ((c= @ V0) @ cNIL)))))
(TLIST_UNIQ_CARD_LENGTH,(c! @ (^[V0]: ((c= @ (cLIST_UNIQ @ V0)) @ ((c= @ (cCARD @ (cset_of_list @ V0))) @ (cLENGTH @ V0))))))
(TLIST_UNIQ_COUNT,(c! @ (^[V0]: ((c= @ (cLIST_UNIQ @ V0)) @ (c! @ (^[V1]: ((c= @ ((cCOUNT @ V1) @ V0)) @ (((cCOND @ ((cMEM @ V1) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ c_0)))))))))
(TCARD_LENGTH,(c! @ (^[V0]: ((c<= @ (cCARD @ (cset_of_list @ V0))) @ (cLENGTH @ V0)))))
(TLENGTH_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cLENGTH @ ((cAPPEND @ V0) @ V1))) @ ((c+ @ (cLENGTH @ V0)) @ (cLENGTH @ V1))))))))
(TREVERSE_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cREVERSE @ ((cAPPEND @ V1) @ V0))) @ ((cAPPEND @ (cREVERSE @ V0)) @ (cREVERSE @ V1))))))))
(TPERMUTED_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cPERMUTED @ V1) @ V0)) @ ((cPERMUTED @ V0) @ V1)))))))
(TPERMUTED_COUNT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cPERMUTED @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ ((cCOUNT @ V2) @ V0)) @ ((cCOUNT @ V2) @ V1))))))))))
(THD_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cHD @ ((cAPPEND @ V1) @ V0))) @ (((cCOND @ ((c= @ V1) @ cNIL)) @ (cHD @ V0)) @ (cHD @ V1))))))))
(TAPPEND_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cAPPEND @ V0) @ ((cAPPEND @ V1) @ V2))) @ ((cAPPEND @ ((cAPPEND @ V0) @ V1)) @ V2)))))))))
(TPERMUTED_PAIRWISE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ V4) @ V3))))))) @ ((cPERMUTED @ V0) @ V2))) @ ((c= @ ((cPAIRWISE @ V1) @ V0)) @ ((cPAIRWISE @ V1) @ V2))))))))))
(TPERMUTED_IMP_PAIRWISE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((V1 @ V3) @ V4)) @ ((V1 @ V4) @ V3))))))) @ ((c/__caret__ @ ((cPERMUTED @ V0) @ V2)) @ ((cPAIRWISE @ V1) @ V0)))) @ ((cPAIRWISE @ V1) @ V2)))))))))
(TMAP_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMAP @ V1) @ ((cAPPEND @ V0) @ V2))) @ ((cAPPEND @ ((cMAP @ V1) @ V0)) @ ((cMAP @ V1) @ V2))))))))))
(TREVERSE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cREVERSE @ ((cCONS @ V1) @ V0))) @ ((cAPPEND @ (cREVERSE @ V0)) @ ((cCONS @ V1) @ cNIL))))))))
(TMEM_APPEND_DECOMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cMEM @ V1) @ V0)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ V0) @ ((cAPPEND @ V2) @ ((cCONS @ V1) @ V3)))))))))))))
(TMEM_APPEND_DECOMPOSE_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cMEM @ V1) @ V0)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c~ @ ((cMEM @ V1) @ V2))) @ ((c= @ V0) @ ((cAPPEND @ V2) @ ((cCONS @ V1) @ V3))))))))))))))
(THD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cHD @ ((cCONS @ V1) @ V0))) @ V1))))))
(TPERMUTED_MEM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cPERMUTED @ V0) @ V2)) @ ((c= @ ((cMEM @ V1) @ V0)) @ ((cMEM @ V1) @ V2))))))))))
(TPERMUTED_DELETE1_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cPERMUTED @ ((cCONS @ V1) @ V0)) @ V2)) @ ((c/__caret__ @ ((cMEM @ V1) @ V2)) @ ((cPERMUTED @ V0) @ ((cDELETE1 @ V1) @ V2)))))))))))
(TEULERIAN_ODD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cgraph @ V1)) @ (((ceulerian @ V1) @ V0) @ ((c__comma__ @ V2) @ V4)))) @ ((c==> @ ((cIN @ V3) @ (cvertices @ V1))) @ ((c= @ (cODD @ ((cdegree @ V1) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V4))) @ ((c__caret__/ @ ((c= @ V3) @ V2)) @ ((c= @ V3) @ V4)))))))))))))))))
(TEULERIAN_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((ceulerian @ V2) @ V0) @ V1)) @ (cFINITE @ (cedges @ V2))))))))))
(Teulerian_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((ceulerian @ V2) @ V0) @ V1)) @ ((c__caret__/ @ (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ cNIL)) @ ((c/__caret__ @ ((c= @ V1) @ ((c__comma__ @ V3) @ V3))) @ ((c/__caret__ @ ((cIN @ V3) @ (cvertices @ V2))) @ ((c= @ (cedges @ V2)) @ cEMPTY))))))) @ (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (c? @ (^[V7]: ((c/__caret__ @ ((c= @ V0) @ ((cCONS @ V6) @ V7))) @ ((c/__caret__ @ ((c= @ V1) @ ((c__comma__ @ V3) @ V5))) @ ((c/__caret__ @ ((cIN @ V6) @ (cedges @ V2))) @ ((c/__caret__ @ (((cconnects @ V2) @ V6) @ ((c__comma__ @ V3) @ V4))) @ (((ceulerian @ ((cdelete_edge @ V6) @ V2)) @ V7) @ ((c__comma__ @ V4) @ V5)))))))))))))))))))))))))
(TORDERED_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cORDERED @ V1) @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ cNIL)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ ((cCONS @ V2) @ V3))) @ ((c/__caret__ @ ((cORDERED @ V1) @ V3)) @ ((cALL @ (V1 @ V2)) @ V3))))))))))))))
(TLIST_UNIQ_PERMUTED_SET_OF_LIST,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cLIST_UNIQ @ V0)) @ (cLIST_UNIQ @ V1))) @ ((c= @ ((cPERMUTED @ V0) @ V1)) @ ((c= @ (cset_of_list @ V0)) @ (cset_of_list @ V1)))))))))
(TPERMUTED_APPEND_SWAP,(c! @ (^[V0]: (c! @ (^[V1]: ((cPERMUTED @ ((cAPPEND @ V1) @ V0)) @ ((cAPPEND @ V0) @ V1)))))))
(TPERMUTED_LIST_UNIQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cPERMUTED @ V0) @ V1)) @ ((c= @ (cLIST_UNIQ @ V0)) @ (cLIST_UNIQ @ V1))))))))
(TPERMUTED_ALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cPERMUTED @ V0) @ V2)) @ ((c= @ ((cALL @ V1) @ V0)) @ ((cALL @ V1) @ V2))))))))))
(TPERMUTED_LENGTH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cPERMUTED @ V0) @ V1)) @ ((c= @ (cLENGTH @ V0)) @ (cLENGTH @ V1))))))))
(TPERMUTED_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cPERMUTED @ V0) @ V2)) @ ((cPERMUTED @ ((cMAP @ V1) @ V0)) @ ((cMAP @ V1) @ V2))))))))))
(TPERMUTED_TAIL_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cPERMUTED @ V0) @ V2)) @ ((cPERMUTED @ ((cCONS @ V1) @ V0)) @ ((cCONS @ V1) @ V2))))))))))
(TPERMUTED_TRS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cPERMUTED @ V1) @ V0)) @ ((cPERMUTED @ V0) @ V2))) @ ((cPERMUTED @ V1) @ V2)))))))))
(TPERMUTED_RFL,(c! @ (^[V0]: ((cPERMUTED @ V0) @ V0))))
(TPERMUTED_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cPERMUTED @ V0) @ V1)) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V0) @ cNIL)) @ ((c= @ V1) @ cNIL))) @ ((c__caret__/ @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((cCONS @ V2) @ V3))) @ ((c/__caret__ @ ((c= @ V1) @ ((cCONS @ V2) @ V4))) @ ((cPERMUTED @ V3) @ V4)))))))))) @ ((c__caret__/ @ (c? @ (^[V2]: ((c/__caret__ @ ((cPERMUTED @ V0) @ V2)) @ ((cPERMUTED @ V2) @ V1))))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((cCONS @ V2) @ ((cCONS @ V3) @ V4)))) @ ((c= @ V1) @ ((cCONS @ V3) @ ((cCONS @ V2) @ V4)))))))))))))))))))
(TPERMUTED_RULES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cPERMUTED @ V0) @ V1)) @ ((cPERMUTED @ V1) @ V2))) @ ((cPERMUTED @ V0) @ V2)))))))))
(TLIST_UNIQ_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cLIST_UNIQ @ ((cAPPEND @ V0) @ V1))) @ ((c/__caret__ @ (cLIST_UNIQ @ V0)) @ ((c/__caret__ @ (cLIST_UNIQ @ V1)) @ (c! @ (^[V2]: (c~ @ ((c/__caret__ @ ((cMEM @ V2) @ V0)) @ ((cMEM @ V2) @ V1)))))))))))))
(TLIST_UNIQ_CASES,(c! @ (^[V0]: ((c= @ (cLIST_UNIQ @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ cNIL)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c= @ V0) @ ((cCONS @ V1) @ V2))) @ ((c/__caret__ @ (cLIST_UNIQ @ V2)) @ (c~ @ ((cMEM @ V1) @ V2)))))))))))))
(TCOUNT_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cCOUNT @ V1) @ ((cAPPEND @ V0) @ V2))) @ ((c+ @ ((cCOUNT @ V1) @ V0)) @ ((cCOUNT @ V1) @ V2))))))))))
(TDELETE1_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cDELETE1 @ V1) @ ((cAPPEND @ V0) @ V2))) @ (((cCOND @ ((cMEM @ V1) @ V0)) @ ((cAPPEND @ ((cDELETE1 @ V1) @ V0)) @ V2)) @ ((cAPPEND @ V0) @ ((cDELETE1 @ V1) @ V2)))))))))))
(TNULL_LENGTH,(c! @ (^[V0]: ((c= @ (cNULL @ V0)) @ ((c= @ (cLENGTH @ V0)) @ (cNUMERAL @ c_0))))))
(TNULL_EQ_NIL,(c! @ (^[V0]: ((c= @ (cNULL @ V0)) @ ((c= @ V0) @ cNIL)))))
(THAS_SIZE_SET_OF_LIST,(c! @ (^[V0]: ((c= @ ((cHAS_SIZE @ (cset_of_list @ V0)) @ (cLENGTH @ V0))) @ ((cPAIRWISE @ (^[V1]: (^[V2]: (c~ @ ((c= @ V1) @ V2))))) @ V0)))))
(TCARD_SET_OF_LIST_LE,(c! @ (^[V0]: ((c<= @ (cCARD @ (cset_of_list @ V0))) @ (cLENGTH @ V0)))))
(TSET_OF_LIST_EQ_EMPTY,(c! @ (^[V0]: ((c= @ ((c= @ (cset_of_list @ V0)) @ cEMPTY)) @ ((c= @ V0) @ cNIL)))))
(TSET_OF_LIST_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cset_of_list @ ((cAPPEND @ V0) @ V1))) @ ((cUNION @ (cset_of_list @ V0)) @ (cset_of_list @ V1))))))))
(TFINITE_SET_OF_LIST,(c! @ (^[V0]: (cFINITE @ (cset_of_list @ V0)))))
(TCONS_HD_TL,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ cNIL))) @ ((c= @ V0) @ ((cCONS @ (cHD @ V0)) @ (cTL @ V0)))))))
(TLAST_EL,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ cNIL))) @ ((c= @ (cLAST @ V0)) @ ((cEL @ ((c- @ (cLENGTH @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))))
(TLENGTH_TL,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ cNIL))) @ ((c= @ (cLENGTH @ (cTL @ V0))) @ ((c- @ (cLENGTH @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TLAST_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cLAST @ ((cAPPEND @ V0) @ V1))) @ (((cCOND @ ((c= @ V1) @ cNIL)) @ (cLAST @ V0)) @ (cLAST @ V1))))))))
(TAPPEND_BUTLAST_LAST,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ cNIL))) @ ((c= @ ((cAPPEND @ (cBUTLAST @ V0)) @ ((cCONS @ (cLAST @ V0)) @ cNIL))) @ V0)))))
(TMAP_ID,(c! @ (^[V0]: ((c= @ ((cMAP @ (^[V1]: V1)) @ V0)) @ V0))))
(TAPPEND_EQ_NIL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cAPPEND @ V0) @ V1)) @ cNIL)) @ ((c/__caret__ @ ((c= @ V0) @ cNIL)) @ ((c= @ V1) @ cNIL))))))))
(TALL_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cALL @ V1) @ ((cAPPEND @ V0) @ V2))) @ ((c/__caret__ @ ((cALL @ V1) @ V0)) @ ((cALL @ V1) @ V2))))))))))
(TMAP_SND_ZIP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (cLENGTH @ V0)) @ (cLENGTH @ V1))) @ ((c= @ ((cMAP @ cSND) @ ((cZIP @ V0) @ V1))) @ V1)))))))
(TMAP_FST_ZIP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (cLENGTH @ V1)) @ (cLENGTH @ V0))) @ ((c= @ ((cMAP @ cFST) @ ((cZIP @ V1) @ V0))) @ V1)))))))
(TFILTER_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cFILTER @ V1) @ ((cAPPEND @ V0) @ V2))) @ ((cAPPEND @ ((cFILTER @ V1) @ V0)) @ ((cFILTER @ V1) @ V2))))))))))
(TMEM_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMEM @ V1) @ ((cMAP @ V2) @ V0))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cMEM @ V3) @ V0)) @ ((c= @ V1) @ (V2 @ V3)))))))))))))
(TMEM_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMEM @ V1) @ ((cAPPEND @ V0) @ V2))) @ ((c__caret__/ @ ((cMEM @ V1) @ V0)) @ ((cMEM @ V1) @ V2))))))))))
(TITLIST_EXTRA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((cITLIST @ V1) @ ((cAPPEND @ V0) @ ((cCONS @ V2) @ cNIL))) @ V3)) @ (((cITLIST @ V1) @ V0) @ ((V1 @ V2) @ V3))))))))))))
(TITLIST_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((cITLIST @ V1) @ ((cAPPEND @ V0) @ V2)) @ V3)) @ (((cITLIST @ V1) @ V0) @ (((cITLIST @ V1) @ V2) @ V3))))))))))))
(TMAP_EQ_ALL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cALL2 @ (^[V3]: (^[V4]: ((c= @ (V1 @ V3)) @ (V1 @ V4))))) @ V0) @ V2)) @ ((c= @ ((cMAP @ V1) @ V0)) @ ((cMAP @ V1) @ V2))))))))))
(TALL_T,(c! @ (^[V0]: ((cALL @ (^[V1]: cT)) @ V0))))
(TLENGTH_EQ_CONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cLENGTH @ V0)) @ (cSUC @ V1))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ ((cCONS @ V2) @ V3))) @ ((c= @ (cLENGTH @ V3)) @ V1))))))))))))
(TZIP_DEF_conjunct0,(c! @ (^[V0]: ((c= @ ((cZIP @ cNIL) @ V0)) @ cNIL))))
(TEL_conjunct0,(c! @ (^[V0]: ((c= @ ((cEL @ (cNUMERAL @ c_0)) @ V0)) @ (cHD @ V0)))))
(Thomol_conjunct1,(c! @ (^[V0]: ((c= @ V0) @ (cprojl @ (chomol @ V0))))))
(Tpoint_tybij_conjunct1,(c! @ (^[V0]: ((c= @ cT) @ ((c= @ (cdest_point @ (cmk_point @ V0))) @ V0)))))
(Thomol_conjunct0,(c! @ (^[V0]: (c~ @ ((c= @ (chomol @ V0)) @ (cvec @ (cNUMERAL @ c_0)))))))
(TAXIOM_4,(c! @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V3))) @ ((c/__caret__ @ ((con @ V1) @ V0)) @ ((c/__caret__ @ ((con @ V2) @ V0)) @ ((con @ V3) @ V0)))))))))))))))
(TLINE_AXIOM_4,(c! @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V3))) @ ((c/__caret__ @ ((cperpl @ V1) @ V0)) @ ((c/__caret__ @ ((cperpl @ V2) @ V0)) @ ((cperpl @ V3) @ V0)))))))))))))))
(TPROJL_TOTAL,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V0) @ (cprojl @ V1))))))))
(TLINE_AXIOM_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cperpl @ V0) @ V2)) @ ((c/__caret__ @ ((cperpl @ V1) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cperpl @ V0) @ V3)) @ ((cperpl @ V1) @ V3))) @ ((c= @ V3) @ V2))))))))))))))
(Tperpl,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cperpl @ V0) @ V1)) @ (c__at__ @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ ((c_|_ @ V3) @ V4)) @ V2)) @ ((c/__caret__ @ ((cdest_line @ V0) @ V3)) @ ((cdest_line @ V1) @ V4)))))))))))))))
(TAXIOM_2,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((con @ V2) @ V0)) @ ((con @ V2) @ V1)))))))))
(TLINE_AXIOM_2,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cperpl @ V2) @ V0)) @ ((cperpl @ V2) @ V1)))))))))
(TEVEN_SQUARE_MOD4,(c! @ (^[V0]: (((c== @ ((cint_pow @ ((cint_mul @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_mod @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))))))
(TODD_SQUARE_MOD4,(c! @ (^[V0]: (((c== @ ((cint_pow @ ((cint_add @ ((cint_mul @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cint_mod @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))))))
(TCONG_SELF_ABS,(c! @ (^[V0]: (((c== @ (cint_abs @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_mod @ V0)))))
(TCONG_SELF,(c! @ (^[V0]: (((c== @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_mod @ V0)))))
(TINT_LE_SQUARE,(c! @ (^[V0]: ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_mul @ V0) @ V0)))))
(TINT_ABS_POS,(c! @ (^[V0]: ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_abs @ V0)))))
(TINT_ABS_LE,(c! @ (^[V0]: ((cint_le @ V0) @ (cint_abs @ V0)))))
(TINT_LE_REFL,(c! @ (^[V0]: ((cint_le @ V0) @ V0))))
(TINT_DIVIDES_1,(c! @ (^[V0]: ((cint_divides @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))
(TINT_DIVIDES_0,(c! @ (^[V0]: ((cint_divides @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))))))
(TINT_DIVIDES_REFL,(c! @ (^[V0]: ((cint_divides @ V0) @ V0))))
(TINT_LE_NEGTOTAL,(c! @ (^[V0]: ((c__caret__/ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_neg @ V0))))))
(TINT_SGN_CASES,(c! @ (^[V0]: ((c__caret__/ @ ((c= @ (cint_sgn @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ (cint_sgn @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cint_sgn @ V0)) @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TINT_ABS_CASES,(c! @ (^[V0]: ((c__caret__/ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_abs @ V0))))))
(TINT_LT_NEGTOTAL,(c! @ (^[V0]: ((c__caret__/ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_neg @ V0)))))))
(TINT_IMAGE,(c! @ (^[V0]: ((c__caret__/ @ (c? @ (^[V1]: ((c= @ V0) @ (cint_of_num @ V1))))) @ (c? @ (^[V1]: ((c= @ V0) @ (cint_neg @ (cint_of_num @ V1)))))))))
(TINT_POS_NZ,(c! @ (^[V0]: ((c==> @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (c~ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))))))))
(TINT_OF_NUM_OF_INT,(c! @ (^[V0]: ((c==> @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ (cint_of_num @ (cnum_of_int @ V0))) @ V0)))))
(TINT_DIVIDES_ONE_POS,(c! @ (^[V0]: ((c==> @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ ((cint_divides @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TCHOOSE_SIMPLEX,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)) @ ((cint_le @ V0) @ (cint_of_num @ (cdimindex @ cUNIV))))) @ (c? @ (^[V1]: ((csimplex @ V0) @ V1)))))))
(TCHOOSE_POLYTOPE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)) @ ((cint_le @ V0) @ (cint_of_num @ (cdimindex @ cUNIV))))) @ (c? @ (^[V1]: ((c/__caret__ @ (cpolytope @ V1)) @ ((c= @ (caff_dim @ V1)) @ V0))))))))
(TINT_PRIME_FACTOR,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cint_abs @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (c? @ (^[V1]: ((c/__caret__ @ (cint_prime @ V1)) @ ((cint_divides @ V1) @ V0))))))))
(TINT_PRIME_GE_2,(c! @ (^[V0]: ((c==> @ (cint_prime @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cint_abs @ V0))))))
(TINT_PRIME_IMP_NZ,(c! @ (^[V0]: ((c==> @ (cint_prime @ V0)) @ (c~ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))))))))
(Tint_sgn_th,(c! @ (^[V0]: ((c= @ (creal_of_int @ (cint_sgn @ V0))) @ (creal_sgn @ (creal_of_int @ V0))))))
(Tint_neg_th,(c! @ (^[V0]: ((c= @ (creal_of_int @ (cint_neg @ V0))) @ (creal_neg @ (creal_of_int @ V0))))))
(Tint_abs_th,(c! @ (^[V0]: ((c= @ (creal_of_int @ (cint_abs @ V0))) @ (creal_abs @ (creal_of_int @ V0))))))
(Tnum_of_int,(c! @ (^[V0]: ((c= @ (cnum_of_int @ V0)) @ (c__at__ @ (^[V1]: ((c= @ (cint_of_num @ V1)) @ V0)))))))
(TINT_SUB_LZERO,(c! @ (^[V0]: ((c= @ ((cint_sub @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (cint_neg @ V0)))))
(TINT_SUB_RZERO,(c! @ (^[V0]: ((c= @ ((cint_sub @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ V0))))
(TINT_SUB_REFL,(c! @ (^[V0]: ((c= @ ((cint_sub @ V0) @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0))))))
(TINT_POW2_ABS,(c! @ (^[V0]: ((c= @ ((cint_pow @ (cint_abs @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cint_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))
(TINT_POW_1,(c! @ (^[V0]: ((c= @ ((cint_pow @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))
(TINT_POW_2,(c! @ (^[V0]: ((c= @ ((cint_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cint_mul @ V0) @ V0)))))
(TINT_POW_conjunct0,(c! @ (^[V0]: ((c= @ ((cint_pow @ V0) @ (cNUMERAL @ c_0))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TINT_SGN_ABS,(c! @ (^[V0]: ((c= @ ((cint_mul @ (cint_sgn @ V0)) @ (cint_abs @ V0))) @ V0))))
(TINT_MUL_LID,(c! @ (^[V0]: ((c= @ ((cint_mul @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ V0))))
(TINT_MUL_LZERO,(c! @ (^[V0]: ((c= @ ((cint_mul @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0))))))
(TINT_MUL_RID,(c! @ (^[V0]: ((c= @ ((cint_mul @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0))))
(TINT_MUL_RZERO,(c! @ (^[V0]: ((c= @ ((cint_mul @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ (cint_of_num @ (cNUMERAL @ c_0))))))
(TINT_MIN_ACI_conjunct3,(c! @ (^[V0]: ((c= @ ((cint_min @ V0) @ V0)) @ V0))))
(TINT_MAX_ACI_conjunct3,(c! @ (^[V0]: ((c= @ ((cint_max @ V0) @ V0)) @ V0))))
(TINT_ADD_LID,(c! @ (^[V0]: ((c= @ ((cint_add @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ V0))))
(TINT_ADD_LINV,(c! @ (^[V0]: ((c= @ ((cint_add @ (cint_neg @ V0)) @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0))))))
(TINT_ADD_RID,(c! @ (^[V0]: ((c= @ ((cint_add @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ V0))))
(TINT_ADD_RINV,(c! @ (^[V0]: ((c= @ ((cint_add @ V0) @ (cint_neg @ V0))) @ (cint_of_num @ (cNUMERAL @ c_0))))))
(TINT_SGN_NEG,(c! @ (^[V0]: ((c= @ (cint_sgn @ (cint_neg @ V0))) @ (cint_neg @ (cint_sgn @ V0))))))
(TINT_SGN,(c! @ (^[V0]: ((c= @ (cint_sgn @ V0)) @ (((cCOND @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (((cCOND @ ((cint_lt @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cint_of_num @ (cNUMERAL @ c_0))))))))
(Tint_sgn,(c! @ (^[V0]: ((c= @ (cint_sgn @ V0)) @ (cint_of_real @ (creal_sgn @ (creal_of_int @ V0)))))))
(TINT_OF_REAL_OF_INT,(c! @ (^[V0]: ((c= @ (cint_of_real @ (creal_of_int @ V0))) @ V0))))
(TINT_NEGNEG,(c! @ (^[V0]: ((c= @ (cint_neg @ (cint_neg @ V0))) @ V0))))
(TINT_NEG_MINUS1,(c! @ (^[V0]: ((c= @ (cint_neg @ V0)) @ ((cint_mul @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)))))
(Tint_neg,(c! @ (^[V0]: ((c= @ (cint_neg @ V0)) @ (cint_of_real @ (creal_neg @ (creal_of_int @ V0)))))))
(TINT_GCD_1_conjunct1,(c! @ (^[V0]: ((c= @ (cint_gcd @ ((c__comma__ @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TINT_GCD_0_conjunct1,(c! @ (^[V0]: ((c= @ (cint_gcd @ ((c__comma__ @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0))) @ (cint_abs @ V0)))))
(TINT_GCD_1_conjunct0,(c! @ (^[V0]: ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TINT_GCD_0_conjunct0,(c! @ (^[V0]: ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ (cint_abs @ V0)))))
(TINT_GCD_REFL,(c! @ (^[V0]: ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ V0))) @ (cint_abs @ V0)))))
(TINT_ABS_SGN,(c! @ (^[V0]: ((c= @ (cint_abs @ (cint_sgn @ V0))) @ (cint_sgn @ (cint_abs @ V0))))))
(TINT_ABS_NEG,(c! @ (^[V0]: ((c= @ (cint_abs @ (cint_neg @ V0))) @ (cint_abs @ V0)))))
(TINT_ABS_ABS,(c! @ (^[V0]: ((c= @ (cint_abs @ (cint_abs @ V0))) @ (cint_abs @ V0)))))
(TINT_ABS,(c! @ (^[V0]: ((c= @ (cint_abs @ V0)) @ (((cCOND @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ V0) @ (cint_neg @ V0))))))
(Tint_abs,(c! @ (^[V0]: ((c= @ (cint_abs @ V0)) @ (cint_of_real @ (creal_abs @ (creal_of_int @ V0)))))))
(Tbset_conjunct3,(c! @ (^[V0]: ((c= @ (cbset @ (cNe @ V0))) @ ((cINSERT @ (cint_neg @ V0)) @ cEMPTY)))))
(Tbset_conjunct0,(c! @ (^[V0]: ((c= @ (cbset @ (cLt @ V0))) @ cEMPTY))))
(Tbset_conjunct1,(c! @ (^[V0]: ((c= @ (cbset @ (cGt @ V0))) @ ((cINSERT @ (cint_neg @ V0)) @ cEMPTY)))))
(Tbset_conjunct2,(c! @ (^[V0]: ((c= @ (cbset @ (cEq @ V0))) @ ((cINSERT @ (cint_neg @ ((cint_add @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ cEMPTY)))))
(Taset_conjunct3,(c! @ (^[V0]: ((c= @ (caset @ (cNe @ V0))) @ ((cINSERT @ (cint_neg @ V0)) @ cEMPTY)))))
(Taset_conjunct0,(c! @ (^[V0]: ((c= @ (caset @ (cLt @ V0))) @ ((cINSERT @ (cint_neg @ V0)) @ cEMPTY)))))
(Taset_conjunct1,(c! @ (^[V0]: ((c= @ (caset @ (cGt @ V0))) @ cEMPTY))))
(Taset_conjunct2,(c! @ (^[V0]: ((c= @ (caset @ (cEq @ V0))) @ ((cINSERT @ ((cint_add @ (cint_neg @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cEMPTY)))))
(Tplusinf_conjunct3,(c! @ (^[V0]: ((c= @ (cplusinf @ (cNe @ V0))) @ (cNox @ cT)))))
(Tplusinf_conjunct0,(c! @ (^[V0]: ((c= @ (cplusinf @ (cLt @ V0))) @ (cNox @ cF)))))
(Tplusinf_conjunct1,(c! @ (^[V0]: ((c= @ (cplusinf @ (cGt @ V0))) @ (cNox @ cT)))))
(Tplusinf_conjunct2,(c! @ (^[V0]: ((c= @ (cplusinf @ (cEq @ V0))) @ (cNox @ cF)))))
(Tmirror_conjunct3,(c! @ (^[V0]: ((c= @ (cmirror @ (cNe @ V0))) @ (cNe @ (cint_neg @ V0))))))
(Tmirror_conjunct0,(c! @ (^[V0]: ((c= @ (cmirror @ (cLt @ V0))) @ (cGt @ (cint_neg @ V0))))))
(Tmirror_conjunct1,(c! @ (^[V0]: ((c= @ (cmirror @ (cGt @ V0))) @ (cLt @ (cint_neg @ V0))))))
(Tmirror_conjunct2,(c! @ (^[V0]: ((c= @ (cmirror @ (cEq @ V0))) @ (cEq @ (cint_neg @ V0))))))
(Tminusinf_conjunct3,(c! @ (^[V0]: ((c= @ (cminusinf @ (cNe @ V0))) @ (cNox @ cT)))))
(Tminusinf_conjunct0,(c! @ (^[V0]: ((c= @ (cminusinf @ (cLt @ V0))) @ (cNox @ cT)))))
(Tminusinf_conjunct1,(c! @ (^[V0]: ((c= @ (cminusinf @ (cGt @ V0))) @ (cNox @ cF)))))
(Tminusinf_conjunct2,(c! @ (^[V0]: ((c= @ (cminusinf @ (cEq @ V0))) @ (cNox @ cF)))))
(TSIMPLEX_EMPTY,(c! @ (^[V0]: ((c= @ ((csimplex @ V0) @ cEMPTY)) @ ((c= @ V0) @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TINT_SGN_INEQS_conjunct6,(c! @ (^[V0]: ((c= @ ((cint_lt @ (cint_sgn @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((cint_lt @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_SGN_INEQS_conjunct1,(c! @ (^[V0]: ((c= @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_sgn @ V0))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_NEG_GT0,(c! @ (^[V0]: ((c= @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_neg @ V0))) @ ((cint_lt @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_NEG_LT0,(c! @ (^[V0]: ((c= @ ((cint_lt @ (cint_neg @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_SGN_INEQS_conjunct5,(c! @ (^[V0]: ((c= @ ((cint_le @ (cint_sgn @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((cint_le @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_LE_DOUBLE,(c! @ (^[V0]: ((c= @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_add @ V0) @ V0))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_SGN_INEQS_conjunct0,(c! @ (^[V0]: ((c= @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_sgn @ V0))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_NEG_GE0,(c! @ (^[V0]: ((c= @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_neg @ V0))) @ ((cint_le @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TNUM_OF_INT,(c! @ (^[V0]: ((c= @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ (cint_of_num @ (cnum_of_int @ V0))) @ V0)))))
(TLAGRANGE_INT,(c! @ (^[V0]: ((c= @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V0) @ ((cint_add @ ((cint_pow @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cint_add @ ((cint_pow @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cint_add @ ((cint_pow @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cint_pow @ V4) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))))))))))
(TINT_NEG_LE0,(c! @ (^[V0]: ((c= @ ((cint_le @ (cint_neg @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_LE_NEGL,(c! @ (^[V0]: ((c= @ ((cint_le @ (cint_neg @ V0)) @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_LE_NEGR,(c! @ (^[V0]: ((c= @ ((cint_le @ V0) @ (cint_neg @ V0))) @ ((cint_le @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_SGN_INEQS_conjunct8,(c! @ (^[V0]: ((c= @ ((cint_gt @ (cint_sgn @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((cint_gt @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_SGN_INEQS_conjunct3,(c! @ (^[V0]: ((c= @ ((cint_gt @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_sgn @ V0))) @ ((cint_gt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_SGN_INEQS_conjunct7,(c! @ (^[V0]: ((c= @ ((cint_ge @ (cint_sgn @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((cint_ge @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_SGN_INEQS_conjunct2,(c! @ (^[V0]: ((c= @ ((cint_ge @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_sgn @ V0))) @ ((cint_ge @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_DIVIDES_ZERO,(c! @ (^[V0]: ((c= @ ((cint_divides @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_DIVIDES_ONE,(c! @ (^[V0]: ((c= @ ((cint_divides @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c__caret__/ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ V0) @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TINT_DIVIDES_ONE_ABS,(c! @ (^[V0]: ((c= @ ((cint_divides @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cint_abs @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TINT_SGN_EQ_conjunct1,(c! @ (^[V0]: ((c= @ ((c= @ (cint_sgn @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cint_gt @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_SGN_EQ_conjunct0,(c! @ (^[V0]: ((c= @ ((c= @ (cint_sgn @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_SGN_EQ_conjunct2,(c! @ (^[V0]: ((c= @ ((c= @ (cint_sgn @ V0)) @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cint_lt @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_SGN_INEQS_conjunct4,(c! @ (^[V0]: ((c= @ ((c= @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_sgn @ V0))) @ ((c= @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_NEG_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cint_neg @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_ABS_ZERO,(c! @ (^[V0]: ((c= @ ((c= @ (cint_abs @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))))
(TINT_ABS_REFL,(c! @ (^[V0]: ((c= @ ((c= @ (cint_abs @ V0)) @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_ABS_NZ,(c! @ (^[V0]: ((c= @ (c~ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_abs @ V0))))))
(TINT_PRIME_NEG,(c! @ (^[V0]: ((c= @ (cint_prime @ (cint_neg @ V0))) @ (cint_prime @ V0)))))
(TINT_PRIME_ABS,(c! @ (^[V0]: ((c= @ (cint_prime @ (cint_abs @ V0))) @ (cint_prime @ V0)))))
(Tint_prime,(c! @ (^[V0]: ((c= @ (cint_prime @ V0)) @ ((c/__caret__ @ ((cint_gt @ (cint_abs @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V1]: ((c==> @ ((cint_divides @ V1) @ V0)) @ ((c__caret__/ @ ((c= @ (cint_abs @ V1)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cint_abs @ V1)) @ (cint_abs @ V0)))))))))))
(TINT_COPRIME_0_conjunct1,(c! @ (^[V0]: ((c= @ (cint_coprime @ ((c__comma__ @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0))) @ ((cint_divides @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TINT_COPRIME_0_conjunct0,(c! @ (^[V0]: ((c= @ (cint_coprime @ ((c__comma__ @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((cint_divides @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TINT_COPRIME_REFL,(c! @ (^[V0]: ((c= @ (cint_coprime @ ((c__comma__ @ V0) @ V0))) @ ((cint_divides @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TINT_OF_NUM_EXISTS,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ V0) @ (cint_of_num @ V1))))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)))))
(TINT_LT_REFL,(c! @ (^[V0]: (c~ @ ((cint_lt @ V0) @ V0)))))
(TINT_COPRIME_MINUS1_conjunct0,(c! @ (^[V0]: (cint_coprime @ ((c__comma__ @ ((cint_sub @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)))))
(TINT_COPRIME_PLUS1_conjunct0,(c! @ (^[V0]: (cint_coprime @ ((c__comma__ @ ((cint_add @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)))))
(TINT_COPRIME_1_conjunct1,(c! @ (^[V0]: (cint_coprime @ ((c__comma__ @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)))))
(TINT_COPRIME_MINUS1_conjunct1,(c! @ (^[V0]: (cint_coprime @ ((c__comma__ @ V0) @ ((cint_sub @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TINT_COPRIME_PLUS1_conjunct1,(c! @ (^[V0]: (cint_coprime @ ((c__comma__ @ V0) @ ((cint_add @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TINT_COPRIME_1_conjunct0,(c! @ (^[V0]: (cint_coprime @ ((c__comma__ @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(Tdest_int_rep,(c! @ (^[V0]: (c? @ (^[V1]: ((c__caret__/ @ ((c= @ (creal_of_int @ V0)) @ (creal_of_num @ V1))) @ ((c= @ (creal_of_int @ V0)) @ (creal_neg @ (creal_of_num @ V1)))))))))
(TINT_EUCLID,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (cint_prime @ V1)) @ ((cint_gt @ V1) @ V0)))))))
(TINT_POW_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_pow @ V0) @ V1))))))))
(TINT_POW_LE_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cint_pow @ V0) @ V1))))))))
(TINT_POW_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_pow @ V0) @ V1))))))))
(TINT_DIVIDES_FACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cint_abs @ V0))) @ ((cint_le @ (cint_abs @ V0)) @ (cint_of_num @ V1)))) @ ((cint_divides @ V0) @ (cint_of_num @ (cFACT @ V1)))))))))
(TINT_POW_1_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_le @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cint_le @ ((cint_pow @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TINT_POW_LT_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cint_pow @ V0) @ V1))))))))
(TINT_POW_1_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_lt @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((cint_lt @ ((cint_pow @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TINT_POW_NZ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ (c~ @ ((c= @ ((cint_pow @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0))))))))))
(TINT_DIVIDES_FACT_PRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cint_prime @ V0)) @ ((c= @ ((cint_divides @ V0) @ (cint_of_num @ (cFACT @ V1)))) @ ((cint_le @ (cint_abs @ V0)) @ (cint_of_num @ V1)))))))))
(Tint_pow_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (creal_of_int @ ((cint_pow @ V0) @ V1))) @ ((creal_pow @ (creal_of_int @ V0)) @ V1)))))))
(TINT_POW_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_pow @ (cint_neg @ V0)) @ V1)) @ (((cCOND @ (cEVEN @ V1)) @ ((cint_pow @ V0) @ V1)) @ (cint_neg @ ((cint_pow @ V0) @ V1)))))))))
(TINT_POW_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_pow @ V0) @ (cSUC @ V1))) @ ((cint_mul @ V0) @ ((cint_pow @ V0) @ V1))))))))
(Tint_pow,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_pow @ V0) @ V1)) @ (cint_of_real @ ((creal_pow @ (creal_of_int @ V0)) @ V1))))))))
(TINT_ABS_POW,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_abs @ ((cint_pow @ V0) @ V1))) @ ((cint_pow @ (cint_abs @ V0)) @ V1)))))))
(TINT_POW_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cint_pow @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0))))))))))
(TINT_DIVIDES_POW_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cint_abs @ V0))) @ ((c= @ ((cint_divides @ ((cint_pow @ V0) @ V1)) @ ((cint_pow @ V0) @ V2))) @ ((c<= @ V1) @ V2))))))))))
(TINT_POW_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_pow @ ((cint_pow @ V0) @ V1)) @ V2)) @ ((cint_pow @ V0) @ ((c* @ V1) @ V2))))))))))
(TINT_DIVISION_0,(c! @ (^[V0]: (c! @ (^[V1]: (((cCOND @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ ((cdiv @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ ((crem @ V0) @ V1)) @ V0))) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((crem @ V0) @ V1))) @ ((c/__caret__ @ ((cint_lt @ ((crem @ V0) @ V1)) @ (cint_abs @ V1))) @ ((c= @ V0) @ ((cint_add @ ((cint_mul @ ((cdiv @ V0) @ V1)) @ V1)) @ ((crem @ V0) @ V1)))))))))))
(TCONG_MULTIPLE,(c! @ (^[V0]: (c! @ (^[V1]: (((c== @ ((cint_mul @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_mod @ V1)))))))
(TCONG_MOD_1,(c! @ (^[V0]: (c! @ (^[V1]: (((c== @ V0) @ V1) @ (cint_mod @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TCONG_REFL,(c! @ (^[V0]: (c! @ (^[V1]: (((c== @ V0) @ V0) @ (cint_mod @ V1)))))))
(TINT_SUB_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((cint_le @ ((cint_sub @ (cint_abs @ V0)) @ (cint_abs @ V1))) @ (cint_abs @ ((cint_sub @ V0) @ V1))))))))
(TINT_MIN_MIN_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cint_le @ ((cint_min @ V1) @ V0)) @ V1))))))
(TINT_MIN_MIN_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cint_le @ ((cint_min @ V0) @ V1)) @ V1))))))
(TINT_GCD_POS,(c! @ (^[V0]: (c! @ (^[V1]: ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_ABS_SUB_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((cint_le @ (cint_abs @ ((cint_sub @ (cint_abs @ V0)) @ (cint_abs @ V1)))) @ (cint_abs @ ((cint_sub @ V0) @ V1))))))))
(TINT_ABS_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: ((cint_le @ (cint_abs @ ((cint_add @ V0) @ V1))) @ ((cint_add @ (cint_abs @ V0)) @ (cint_abs @ V1))))))))
(TINT_MAX_MAX_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cint_le @ V1) @ ((cint_max @ V0) @ V1)))))))
(TINT_MAX_MAX_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cint_le @ V0) @ ((cint_max @ V0) @ V1)))))))
(TINT_GCD_DIVIDES_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cint_divides @ (cint_gcd @ ((c__comma__ @ V1) @ V0))) @ V1))))))
(TINT_GCD_DIVIDES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cint_divides @ (cint_gcd @ ((c__comma__ @ V0) @ V1))) @ V1))))))
(TINT_LTE_TOTAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((cint_lt @ V1) @ V0)) @ ((cint_le @ V0) @ V1)))))))
(TINT_LET_TOTAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((cint_le @ V1) @ V0)) @ ((cint_lt @ V0) @ V1)))))))
(TINT_LE_TOTAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((cint_le @ V1) @ V0)) @ ((cint_le @ V0) @ V1)))))))
(TINT_LT_TOTAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((c= @ V1) @ V0)) @ ((c__caret__/ @ ((cint_lt @ V1) @ V0)) @ ((cint_lt @ V0) @ V1))))))))
(TINT_CONG_1_DIVIDES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (((c== @ V1) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cint_mod @ V0))) @ ((cint_divides @ V0) @ ((cint_sub @ V1) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TINT_LT_MUL_EQ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c= @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_mul @ V0) @ V1))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0))))))))
(TINT_LE_MUL_EQ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c= @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_mul @ V0) @ V1))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0))))))))
(TINT_MOD_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cint_add @ V0) @ ((cint_mul @ V2) @ V1)))) @ ((cint_le @ ((cint_add @ V0) @ ((cint_mul @ V2) @ V1))) @ V1))))))))))
(TINT_LT_MUL_EQ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_mul @ V0) @ V1))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))))))))
(TINT_LE_MUL_EQ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_mul @ V0) @ V1))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))))))))
(TINT_ABS_SIGN2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ (cint_abs @ ((cint_sub @ V1) @ V0))) @ (cint_neg @ V0))) @ ((cint_lt @ V1) @ (cint_of_num @ (cNUMERAL @ c_0)))))))))
(TINT_ABS_STILLNZ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ (cint_abs @ ((cint_sub @ V1) @ V0))) @ (cint_abs @ V0))) @ (c~ @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))))))))
(TINT_ABS_SIGN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ (cint_abs @ ((cint_sub @ V1) @ V0))) @ V0)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)))))))
(TINT_LT_GT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ V1) @ V0)) @ (c~ @ ((cint_lt @ V0) @ V1))))))))
(TINT_LT_IMP_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ V0) @ V1)) @ ((cint_le @ V0) @ V1)))))))
(TINT_LT_IMP_NE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_lt @ V0) @ V1)) @ (c~ @ ((c= @ V0) @ V1))))))))
(TINT_LT_ADD1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_le @ V0) @ V1)) @ ((cint_lt @ V0) @ ((cint_add @ V1) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TINT_DIVIDES_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cint_divides @ V0) @ V1)) @ ((c__caret__/ @ ((cint_le @ (cint_abs @ V0)) @ (cint_abs @ V1))) @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))))))))
(TINT_EQ_IMP_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ V0) @ V1)) @ ((cint_le @ V0) @ V1)))))))
(TINT_LT_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_mul @ V0) @ V1))))))))
(TINT_LT_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_add @ V0) @ V1))))))))
(TINT_LTE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_add @ V0) @ V1))))))))
(TINT_LET_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_add @ V0) @ V1))))))))
(TINT_LE_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_mul @ V0) @ V1))))))))
(TINT_LE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_add @ V0) @ V1))))))))
(TINT_DIVIDES_ANTISYM_POS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((c= @ ((c/__caret__ @ ((cint_divides @ V0) @ V1)) @ ((cint_divides @ V1) @ V0))) @ ((c= @ V0) @ V1))))))))
(TINT_PRIME_COPRIME_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cint_prime @ V1)) @ ((c/__caret__ @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_abs @ V0))) @ ((cint_lt @ (cint_abs @ V0)) @ (cint_abs @ V1))))) @ (cint_coprime @ ((c__comma__ @ V0) @ V1))))))))
(TINT_BEZOUT_PRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cint_prime @ V1)) @ (c~ @ ((cint_divides @ V1) @ V0)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ ((cint_mul @ V0) @ V2)) @ ((cint_add @ ((cint_mul @ V1) @ V3)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))))
(TINT_DISTINCT_PRIME_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cint_prime @ V0)) @ ((c/__caret__ @ (cint_prime @ V1)) @ (c~ @ ((c= @ (cint_abs @ V0)) @ (cint_abs @ V1)))))) @ (cint_coprime @ ((c__comma__ @ V0) @ V1))))))))
(TINT_DIVIDES_PRIME_PRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cint_prime @ V0)) @ (cint_prime @ V1))) @ ((c= @ ((cint_divides @ V0) @ V1)) @ ((c= @ (cint_abs @ V0)) @ (cint_abs @ V1)))))))))
(TINT_GCD_COPRIME_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ V1))) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ ((cint_mul @ V2) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))) @ ((c/__caret__ @ ((c= @ V1) @ ((cint_mul @ V3) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))) @ (cint_coprime @ ((c__comma__ @ V2) @ V3))))))))))))))
(TINT_DIVISION_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((cint_lt @ ((crem @ V0) @ V1)) @ (cint_abs @ V1))))))))
(TINT_DIVISION_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((crem @ V0) @ V1))))))))
(TINT_DIVISION_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ V0) @ ((cint_add @ ((cint_mul @ ((cdiv @ V0) @ V1)) @ V1)) @ ((crem @ V0) @ V1)))))))))
(TINT_ARCH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V2]: ((cint_lt @ V0) @ ((cint_mul @ V2) @ V1))))))))))
(TINT_PRIME_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cint_prime @ V0)) @ ((c__caret__/ @ ((cint_divides @ V0) @ V1)) @ (cint_coprime @ ((c__comma__ @ V0) @ V1)))))))))
(TINT_PRIME_COPRIME_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cint_prime @ V0)) @ ((c= @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ (c~ @ ((cint_divides @ V0) @ V1)))))))))
(TINT_COPRIME_SOS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ (cint_coprime @ ((c__comma__ @ ((cint_mul @ V0) @ V1)) @ ((cint_add @ ((cint_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cint_pow @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))
(TINT_COPRIME_BEZOUT_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ ((cint_mul @ V0) @ V2)) @ ((cint_add @ ((cint_mul @ V1) @ V3)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))))
(Tint_sub_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (creal_of_int @ ((cint_sub @ V0) @ V1))) @ ((creal_sub @ (creal_of_int @ V0)) @ (creal_of_int @ V1))))))))
(Tint_mul_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (creal_of_int @ ((cint_mul @ V0) @ V1))) @ ((creal_mul @ (creal_of_int @ V0)) @ (creal_of_int @ V1))))))))
(Tint_min_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (creal_of_int @ ((cint_min @ V0) @ V1))) @ ((creal_min @ (creal_of_int @ V0)) @ (creal_of_int @ V1))))))))
(Tint_max_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (creal_of_int @ ((cint_max @ V0) @ V1))) @ ((creal_max @ (creal_of_int @ V0)) @ (creal_of_int @ V1))))))))
(Tint_add_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (creal_of_int @ ((cint_add @ V0) @ V1))) @ ((creal_add @ (creal_of_int @ V0)) @ (creal_of_int @ V1))))))))
(TINT_SUB_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_sub @ ((cint_sub @ V0) @ V1)) @ V0)) @ (cint_neg @ V1)))))))
(TINT_ADD_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_sub @ ((cint_add @ V0) @ V1)) @ V0)) @ V1))))))
(TINT_SUB_NEG2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_sub @ (cint_neg @ V1)) @ (cint_neg @ V0))) @ ((cint_sub @ V0) @ V1)))))))
(TINT_SUB_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_sub @ (cint_neg @ V0)) @ V1)) @ (cint_neg @ ((cint_add @ V0) @ V1))))))))
(TINT_SUB_SUB2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_sub @ V0) @ ((cint_sub @ V0) @ V1))) @ V1))))))
(TINT_ADD_SUB2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_sub @ V0) @ ((cint_add @ V0) @ V1))) @ (cint_neg @ V1)))))))
(TINT_SUB_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_sub @ V0) @ (cint_neg @ V1))) @ ((cint_add @ V0) @ V1)))))))
(TINT_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_sub @ V0) @ V1)) @ ((cint_add @ V0) @ (cint_neg @ V1))))))))
(Tint_sub,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_sub @ V0) @ V1)) @ (cint_of_real @ ((creal_sub @ (creal_of_int @ V0)) @ (creal_of_int @ V1)))))))))
(TINT_DIFFSQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_mul @ ((cint_add @ V0) @ V1)) @ ((cint_sub @ V0) @ V1))) @ ((cint_sub @ ((cint_mul @ V0) @ V0)) @ ((cint_mul @ V1) @ V1))))))))
(TINT_NEG_MUL2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_mul @ (cint_neg @ V0)) @ (cint_neg @ V1))) @ ((cint_mul @ V0) @ V1)))))))
(TINT_MUL_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_mul @ (cint_neg @ V0)) @ V1)) @ (cint_neg @ ((cint_mul @ V0) @ V1))))))))
(TINT_MUL_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_mul @ V1) @ V0)) @ ((cint_mul @ V0) @ V1)))))))
(TINT_MUL_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_mul @ V0) @ (cint_neg @ V1))) @ (cint_neg @ ((cint_mul @ V0) @ V1))))))))
(Tint_mul,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_mul @ V0) @ V1)) @ (cint_of_real @ ((creal_mul @ (creal_of_int @ V0)) @ (creal_of_int @ V1)))))))))
(TINT_MIN_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_min @ V1) @ V0)) @ ((cint_min @ V0) @ V1)))))))
(TINT_MIN_ACI_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_min @ V0) @ ((cint_min @ V0) @ V1))) @ ((cint_min @ V0) @ V1)))))))
(TINT_MIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_min @ V0) @ V1)) @ (((cCOND @ ((cint_le @ V0) @ V1)) @ V0) @ V1)))))))
(Tint_min,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_min @ V0) @ V1)) @ (cint_of_real @ ((creal_min @ (creal_of_int @ V0)) @ (creal_of_int @ V1)))))))))
(TINT_MIN_MAX,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_min @ V0) @ V1)) @ (cint_neg @ ((cint_max @ (cint_neg @ V0)) @ (cint_neg @ V1)))))))))
(TINT_MAX,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_max @ V1) @ V0)) @ (((cCOND @ ((cint_le @ V1) @ V0)) @ V0) @ V1)))))))
(TINT_MAX_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_max @ V1) @ V0)) @ ((cint_max @ V0) @ V1)))))))
(TINT_MAX_ACI_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_max @ V0) @ ((cint_max @ V0) @ V1))) @ ((cint_max @ V0) @ V1)))))))
(Tint_max,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_max @ V0) @ V1)) @ (cint_of_real @ ((creal_max @ (creal_of_int @ V0)) @ (creal_of_int @ V1)))))))))
(TINT_MAX_MIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_max @ V0) @ V1)) @ (cint_neg @ ((cint_min @ (cint_neg @ V0)) @ (cint_neg @ V1)))))))))
(TINT_SUB_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_add @ ((cint_sub @ V1) @ V0)) @ V0)) @ V1))))))
(TINT_ADD_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_add @ V1) @ V0)) @ ((cint_add @ V0) @ V1)))))))
(TINT_SUB_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_add @ V0) @ ((cint_sub @ V1) @ V0))) @ V1))))))
(Tint_add,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_add @ V0) @ V1)) @ (cint_of_real @ ((creal_add @ (creal_of_int @ V0)) @ (creal_of_int @ V1)))))))))
(TINT_SGN_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_sgn @ ((cint_mul @ V0) @ V1))) @ ((cint_mul @ (cint_sgn @ V0)) @ (cint_sgn @ V1))))))))
(TINT_NEG_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_neg @ ((cint_sub @ V1) @ V0))) @ ((cint_sub @ V0) @ V1)))))))
(TINT_NEG_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_neg @ ((cint_mul @ V0) @ V1))) @ ((cint_mul @ (cint_neg @ V0)) @ V1)))))))
(TINT_NEG_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_neg @ ((cint_mul @ V0) @ V1))) @ ((cint_mul @ V0) @ (cint_neg @ V1))))))))
(TINT_NEG_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_neg @ ((cint_add @ V0) @ V1))) @ ((cint_add @ (cint_neg @ V0)) @ (cint_neg @ V1))))))))
(TINT_GCD_SUB_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ ((cint_sub @ V1) @ V0)) @ V1))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_GCD_SUB_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ ((cint_sub @ V0) @ V1)) @ V1))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_GCD_ADD_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ ((cint_add @ V1) @ V0)) @ V1))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_GCD_ADD_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ ((cint_add @ V0) @ V1)) @ V1))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_GCD_ABS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ (cint_abs @ V0)) @ V1))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_GCD_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ V1) @ V0))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_GCD_SUB_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ ((cint_sub @ V1) @ V0)))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_GCD_SUB_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ ((cint_sub @ V0) @ V1)))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_GCD_ADD_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ ((cint_add @ V1) @ V0)))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_GCD_ADD_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ ((cint_add @ V0) @ V1)))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_GCD_ABS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ (cint_abs @ V1)))) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))))
(TINT_ABS_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_abs @ ((cint_sub @ V1) @ V0))) @ (cint_abs @ ((cint_sub @ V0) @ V1))))))))
(TINT_ABS_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_abs @ ((cint_mul @ V0) @ V1))) @ ((cint_mul @ (cint_abs @ V0)) @ (cint_abs @ V1))))))))
(Tbset_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cbset @ ((cNdivides @ V0) @ V1))) @ cEMPTY))))))
(Tbset_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cbset @ ((cDivides @ V0) @ V1))) @ cEMPTY))))))
(Taset_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (caset @ ((cNdivides @ V0) @ V1))) @ cEMPTY))))))
(Taset_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (caset @ ((cDivides @ V0) @ V1))) @ cEMPTY))))))
(Tplusinf_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cplusinf @ ((cNdivides @ V0) @ V1))) @ ((cNdivides @ V0) @ V1)))))))
(Tplusinf_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cplusinf @ ((cDivides @ V0) @ V1))) @ ((cDivides @ V0) @ V1)))))))
(Tmirror_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmirror @ ((cNdivides @ V0) @ V1))) @ ((cNdivides @ V0) @ (cint_neg @ V1))))))))
(Tmirror_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmirror @ ((cDivides @ V0) @ V1))) @ ((cDivides @ V0) @ (cint_neg @ V1))))))))
(Tminusinf_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cminusinf @ ((cNdivides @ V0) @ V1))) @ ((cNdivides @ V0) @ V1)))))))
(Tminusinf_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cminusinf @ ((cDivides @ V0) @ V1))) @ ((cDivides @ V0) @ V1)))))))
(TINT_CONG_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((c== @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_mod @ V0))) @ ((cint_divides @ V0) @ V1)))))))
(TINT_CONG_TO_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((c== @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cint_mod @ V1))) @ (c? @ (^[V2]: ((c= @ V0) @ ((cint_add @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cint_mul @ V2) @ V1)))))))))))
(TCONG_MOD_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((c== @ V0) @ V1) @ (cint_mod @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ V0) @ V1)))))))
(Tinterp_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinterp @ V0) @ (cNe @ V1))) @ (c~ @ ((c= @ ((cint_add @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0))))))))))
(Tinterp_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinterp @ V0) @ (cLt @ V1))) @ ((cint_lt @ ((cint_add @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0)))))))))
(Tinterp_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinterp @ V0) @ (cGt @ V1))) @ ((cint_gt @ ((cint_add @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0)))))))))
(Tinterp_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinterp @ V0) @ (cEq @ V1))) @ ((c= @ ((cint_add @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0)))))))))
(TINT_SUB_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_sub @ V1) @ V0))) @ ((cint_lt @ V0) @ V1)))))))
(TINT_MUL_POS_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_mul @ V0) @ V1))) @ ((c__caret__/ @ ((c/__caret__ @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((c/__caret__ @ ((cint_lt @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((cint_lt @ V1) @ (cint_of_num @ (cNUMERAL @ c_0)))))))))))
(TINT_LT_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ (cint_neg @ V1)) @ (cint_neg @ V0))) @ ((cint_lt @ V0) @ V1)))))))
(TINT_LT_SQUARE_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ (cint_abs @ V0)) @ (cint_abs @ V1))) @ ((cint_lt @ ((cint_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cint_pow @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TINT_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ V1) @ V0)) @ (c~ @ ((cint_le @ V0) @ V1))))))))
(TINT_LT_ADDL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ V0) @ ((cint_add @ V1) @ V0))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)))))))
(TINT_LT_ADDR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ V0) @ ((cint_add @ V0) @ V1))) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)))))))
(Tint_lt,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ V0) @ V1)) @ ((creal_lt @ (creal_of_int @ V0)) @ (creal_of_int @ V1))))))))
(TINT_LT_DISCRETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ V0) @ V1)) @ ((cint_le @ ((cint_add @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V1)))))))
(TINT_LT_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_lt @ V0) @ V1)) @ ((c/__caret__ @ ((cint_le @ V0) @ V1)) @ (c~ @ ((c= @ V0) @ V1)))))))))
(TINT_SUB_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_sub @ V1) @ V0))) @ ((cint_le @ V0) @ V1)))))))
(TINT_MUL_POS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_mul @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c/__caret__ @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))) @ ((c/__caret__ @ ((cint_lt @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((cint_lt @ V1) @ (cint_of_num @ (cNUMERAL @ c_0)))))))))))))
(TINT_LE_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ (cint_neg @ V1)) @ (cint_neg @ V0))) @ ((cint_le @ V0) @ V1)))))))
(TINT_LE_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ (cint_neg @ V0)) @ V1)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((cint_add @ V0) @ V1))))))))
(TINT_LE_SQUARE_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ (cint_abs @ V0)) @ (cint_abs @ V1))) @ ((cint_le @ ((cint_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cint_pow @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TINT_LE_ADDL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ V0) @ ((cint_add @ V1) @ V0))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)))))))
(TINT_LE_ADDR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ V0) @ ((cint_add @ V0) @ V1))) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)))))))
(TINT_LE_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ V0) @ (cint_neg @ V1))) @ ((cint_le @ ((cint_add @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0)))))))))
(Tint_le,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ V0) @ V1)) @ ((creal_le @ (creal_of_int @ V0)) @ (creal_of_int @ V1))))))))
(TINT_LE_DISCRETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ V0) @ V1)) @ ((cint_lt @ V0) @ ((cint_add @ V1) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TINT_LE_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_le @ V0) @ V1)) @ ((c__caret__/ @ ((cint_lt @ V0) @ V1)) @ ((c= @ V0) @ V1))))))))
(TINT_GT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_gt @ V1) @ V0)) @ ((cint_lt @ V0) @ V1)))))))
(Tint_gt,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_gt @ V0) @ V1)) @ ((creal_gt @ (creal_of_int @ V0)) @ (creal_of_int @ V1))))))))
(TINT_GT_DISCRETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_gt @ V0) @ V1)) @ ((cint_ge @ V0) @ ((cint_add @ V1) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TINT_GE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_ge @ V1) @ V0)) @ ((cint_le @ V0) @ V1)))))))
(Tint_ge,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_ge @ V0) @ V1)) @ ((creal_ge @ (creal_of_int @ V0)) @ (creal_of_int @ V1))))))))
(TDIVIDES_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_divides @ (cint_neg @ V0)) @ V1)) @ ((cint_divides @ V0) @ V1)))))))
(TINT_DIVIDES_LABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_divides @ (cint_abs @ V0)) @ V1)) @ ((cint_divides @ V0) @ V1)))))))
(Tdivides,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_divides @ V1) @ V0)) @ (c? @ (^[V2]: ((c= @ V0) @ ((cint_mul @ V1) @ V2))))))))))
(TDIVIDES_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_divides @ V0) @ (cint_neg @ V1))) @ ((cint_divides @ V0) @ V1)))))))
(TINT_DIVIDES_RABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cint_divides @ V0) @ (cint_abs @ V1))) @ ((cint_divides @ V0) @ V1)))))))
(Talldivide_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((calldivide @ V0) @ (cNe @ V1))) @ cT))))))
(Talldivide_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((calldivide @ V0) @ (cLt @ V1))) @ cT))))))
(Talldivide_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((calldivide @ V0) @ (cGt @ V1))) @ cT))))))
(Talldivide_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((calldivide @ V0) @ (cEq @ V1))) @ cT))))))
(TINT_SUB_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cint_sub @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ V1)))))))
(TINT_ENTIRE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cint_mul @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))))))))
(TINT_SOS_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cint_add @ ((cint_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cint_pow @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))))))))
(TINT_RNEG_UNIQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cint_add @ V1) @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cint_neg @ V1))))))))
(TINT_EQ_ADD_RCANCEL_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cint_add @ V1) @ V0)) @ V0)) @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0)))))))))
(TINT_LNEG_UNIQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cint_add @ V0) @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cint_neg @ V1))))))))
(TINT_EQ_ADD_LCANCEL_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cint_add @ V0) @ V1)) @ V0)) @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0)))))))))
(TINT_EQ_NEG2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cint_neg @ V0)) @ (cint_neg @ V1))) @ ((c= @ V0) @ V1)))))))
(TINT_NEG_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cint_neg @ V0)) @ V1)) @ ((c= @ V0) @ (cint_neg @ V1))))))))
(TINT_GCD_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ V1))) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))))))))
(TINT_ABS_MUL_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cint_abs @ ((cint_mul @ V0) @ V1))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((c= @ (cint_abs @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cint_abs @ V1)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TINT_EQ_SQUARE_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cint_abs @ V0)) @ (cint_abs @ V1))) @ ((c= @ ((cint_pow @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cint_pow @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(Tint_eq,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ ((c= @ (creal_of_int @ V0)) @ (creal_of_int @ V1))))))))
(TINT_BOUNDS_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cint_lt @ (cint_neg @ V1)) @ V0)) @ ((cint_lt @ V0) @ V1))) @ ((cint_lt @ (cint_abs @ V0)) @ V1)))))))
(TINT_BOUNDS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cint_le @ (cint_neg @ V1)) @ V0)) @ ((cint_le @ V0) @ V1))) @ ((cint_le @ (cint_abs @ V0)) @ V1)))))))
(TINT_LE_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cint_le @ V0) @ V1)) @ ((cint_le @ V1) @ V0))) @ ((c= @ V0) @ V1)))))))
(TINT_DIVIDES_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cint_divides @ V0) @ V1)) @ ((cint_divides @ V1) @ V0))) @ ((c__caret__/ @ ((c= @ V0) @ V1)) @ ((c= @ V0) @ (cint_neg @ V1)))))))))
(TINT_DIVIDES_ANTISYM_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cint_divides @ V0) @ V1)) @ ((cint_divides @ V1) @ V0))) @ ((c= @ (cint_abs @ V0)) @ (cint_abs @ V1))))))))
(TINT_DIVIDES_ANTISYM_ASSOCIATED,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cint_divides @ V0) @ V1)) @ ((cint_divides @ V1) @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cint_divides @ V2) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ V0) @ ((cint_mul @ V1) @ V2)))))))))))
(TINT_NOT_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((cint_lt @ V1) @ V0))) @ ((cint_le @ V0) @ V1)))))))
(TINT_NOT_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((cint_le @ V1) @ V0))) @ ((cint_lt @ V0) @ V1)))))))
(TINT_NOT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c= @ V1) @ V0))) @ ((c__caret__/ @ ((cint_lt @ V1) @ V0)) @ ((cint_lt @ V0) @ V1))))))))
(TINT_COPRIME_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_coprime @ ((c__comma__ @ (cint_neg @ V0)) @ V1))) @ (cint_coprime @ ((c__comma__ @ V0) @ V1))))))))
(TINT_COPRIME_LABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_coprime @ ((c__comma__ @ (cint_abs @ V0)) @ V1))) @ (cint_coprime @ ((c__comma__ @ V0) @ V1))))))))
(TINT_COPRIME_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_coprime @ ((c__comma__ @ V1) @ V0))) @ (cint_coprime @ ((c__comma__ @ V0) @ V1))))))))
(TINT_COPRIME_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_coprime @ ((c__comma__ @ V0) @ (cint_neg @ V1)))) @ (cint_coprime @ ((c__comma__ @ V0) @ V1))))))))
(TINT_COPRIME_RABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_coprime @ ((c__comma__ @ V0) @ (cint_abs @ V1)))) @ (cint_coprime @ ((c__comma__ @ V0) @ V1))))))))
(TINT_COPRIME_GCD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ V1))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TINT_COPRIME_BEZOUT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ ((cint_add @ ((cint_mul @ V0) @ V2)) @ ((cint_mul @ V1) @ V3))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))
(Tint_coprime,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V2) @ V0)) @ ((cint_divides @ V2) @ V1))) @ ((cint_divides @ V2) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TINT_COPRIME_PRIME_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ (c! @ (^[V2]: (c~ @ ((c/__caret__ @ (cint_prime @ V2)) @ ((c/__caret__ @ ((cint_divides @ V2) @ V0)) @ ((cint_divides @ V2) @ V1))))))))))))
(TINT_LT_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c/__caret__ @ ((cint_lt @ V1) @ V0)) @ ((cint_lt @ V0) @ V1))))))))
(TINT_LTE_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c/__caret__ @ ((cint_lt @ V1) @ V0)) @ ((cint_le @ V0) @ V1))))))))
(TINT_LET_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c/__caret__ @ ((cint_le @ V1) @ V0)) @ ((cint_lt @ V0) @ V1))))))))
(TINT_GCD_EXISTS_POS,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c/__caret__ @ ((cint_divides @ V2) @ V0)) @ ((c/__caret__ @ ((cint_divides @ V2) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V2) @ ((cint_add @ ((cint_mul @ V0) @ V3)) @ ((cint_mul @ V1) @ V4)))))))))))))))))
(TINT_GCD_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cint_divides @ V2) @ V0)) @ ((c/__caret__ @ ((cint_divides @ V2) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V2) @ ((cint_add @ ((cint_mul @ V0) @ V3)) @ ((cint_mul @ V1) @ V4))))))))))))))))
(TINT_DIVMOD_EXIST_0,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (((cCOND @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ V2) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V3) @ V0))) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c/__caret__ @ ((cint_lt @ V3) @ (cint_abs @ V1))) @ ((c= @ V0) @ ((cint_add @ ((cint_mul @ V2) @ V1)) @ V3))))))))))))))
(TINT_GCD_BEZOUT,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ V1))) @ ((cint_add @ ((cint_mul @ V0) @ V2)) @ ((cint_mul @ V1) @ V3))))))))))))
(TINT_DOWN2,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cint_lt @ V3) @ V2)) @ ((c/__caret__ @ ((cint_lt @ V3) @ V0)) @ ((cint_lt @ V3) @ V1))))))))))))
(TINT_DIVIDES_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_divides @ V0) @ V1)) @ ((cint_divides @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V2))))))))))
(TINT_DIVIDES_RPOW_SUC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_divides @ V0) @ V1)) @ ((cint_divides @ V0) @ ((cint_pow @ V1) @ (cSUC @ V2)))))))))))
(TINT_POW_LE2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_le @ V0) @ V1))) @ ((cint_le @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V2))))))))))
(TINT_POW_LE2_ODD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_le @ V0) @ V1)) @ (cODD @ V2))) @ ((cint_le @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V2))))))))))
(TINT_DIVIDES_RPOW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V0) @ V1)) @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0))))) @ ((cint_divides @ V0) @ ((cint_pow @ V1) @ V2))))))))))
(TINT_POW_LT2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_lt @ V0) @ V1)))) @ ((cint_lt @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V2))))))))))
(TINT_PRIME_DIVPOW_N,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cint_prime @ V0)) @ ((cint_divides @ V0) @ ((cint_pow @ V1) @ V2)))) @ ((cint_divides @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V2))))))))))
(TINT_COPRIME_POW_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ (cint_coprime @ ((c__comma__ @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V2)))))))))))
(TINT_COPRIME_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ (cint_coprime @ ((c__comma__ @ V0) @ ((cint_pow @ V1) @ V2)))))))))))
(TINT_POW_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_pow @ ((cint_mul @ V0) @ V1)) @ V2)) @ ((cint_mul @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V2))))))))))
(TINT_COPRIME_POW2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cint_coprime @ ((c__comma__ @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V2)))) @ ((c__caret__/ @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TINT_COPRIME_LPOW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cint_coprime @ ((c__comma__ @ ((cint_pow @ V0) @ V2)) @ V1))) @ ((c__caret__/ @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TINT_COPRIME_RPOW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cint_coprime @ ((c__comma__ @ V0) @ ((cint_pow @ V1) @ V2)))) @ ((c__caret__/ @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ ((c= @ V2) @ (cNUMERAL @ c_0)))))))))))
(TINT_EQ_PRIME_POW_POS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_prime @ V0)) @ ((c/__caret__ @ (cint_prime @ V1)) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1))))) @ ((c= @ ((c= @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V3))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V2) @ (cNUMERAL @ c_0))) @ ((c= @ V3) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ V3))))))))))))))
(TINT_DIVIDES_PRIME_POW_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_prime @ V0)) @ (cint_prime @ V1))) @ ((c= @ ((cint_divides @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V3))) @ ((c__caret__/ @ ((c= @ V2) @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ ((c= @ (cint_abs @ V0)) @ (cint_abs @ V1))) @ ((c<= @ V2) @ V3))))))))))))))
(TINT_EQ_PRIME_POW_ABS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_prime @ V0)) @ (cint_prime @ V1))) @ ((c= @ ((c= @ ((cint_pow @ (cint_abs @ V0)) @ V2)) @ ((cint_pow @ (cint_abs @ V1)) @ V3))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V2) @ (cNUMERAL @ c_0))) @ ((c= @ V3) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ (cint_abs @ V0)) @ (cint_abs @ V1))) @ ((c= @ V2) @ V3))))))))))))))
(TINT_CONG_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((c== @ V0) @ V1) @ (cint_mod @ V3))) @ (((c== @ ((cint_pow @ V0) @ V2)) @ ((cint_pow @ V1) @ V2)) @ (cint_mod @ V3))))))))))))
(TINT_COPRIME_POW_DIVPROD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cint_divides @ ((cint_pow @ V1) @ V2)) @ ((cint_mul @ V0) @ V3))) @ (cint_coprime @ ((c__comma__ @ V1) @ V0)))) @ ((cint_divides @ ((cint_pow @ V1) @ V2)) @ V3)))))))))))
(TINT_PRIME_DIVPROD_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_prime @ V1)) @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V0) @ V3))) @ ((cint_divides @ ((cint_pow @ V1) @ V2)) @ ((cint_mul @ V0) @ V3))))) @ ((c__caret__/ @ ((cint_divides @ ((cint_pow @ V1) @ V2)) @ V0)) @ ((cint_divides @ ((cint_pow @ V1) @ V2)) @ V3))))))))))))
(TCONG_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c== @ V1) @ V0) @ (cint_mod @ V2))) @ (((c== @ V0) @ V1) @ (cint_mod @ V2))))))))))
(TINT_CONG_DIVIDES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c== @ V0) @ V2) @ (cint_mod @ V1))) @ ((c= @ ((cint_divides @ V1) @ V0)) @ ((cint_divides @ V1) @ V2))))))))))
(TINT_CONG_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c== @ V0) @ V2) @ (cint_mod @ V1))) @ ((c= @ (cint_coprime @ ((c__comma__ @ V1) @ V0))) @ (cint_coprime @ ((c__comma__ @ V1) @ V2)))))))))))
(TCONG_NEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c== @ V0) @ V1) @ (cint_mod @ V2))) @ (((c== @ (cint_neg @ V0)) @ (cint_neg @ V1)) @ (cint_mod @ V2))))))))))
(TINT_DOWN_MUL_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c? @ (^[V3]: ((cint_lt @ ((cint_add @ V0) @ ((cint_mul @ V3) @ V1))) @ V2)))))))))))
(TINT_LT_RMUL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ ((cint_lt @ ((cint_mul @ V1) @ V0)) @ ((cint_mul @ V2) @ V0))) @ ((cint_lt @ V1) @ V2))))))))))
(TINT_LT_LMUL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ ((cint_lt @ ((cint_mul @ V0) @ V1)) @ ((cint_mul @ V0) @ V2))) @ ((cint_lt @ V1) @ V2))))))))))
(TINT_ABS_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_lt @ (cint_abs @ ((cint_sub @ V1) @ V0))) @ V2)) @ ((cint_lt @ V0) @ ((cint_add @ V1) @ V2))))))))))
(TINT_ABS_CIRCLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_lt @ (cint_abs @ V1)) @ ((cint_sub @ (cint_abs @ V2)) @ (cint_abs @ V0)))) @ ((cint_lt @ (cint_abs @ ((cint_add @ V0) @ V1))) @ (cint_abs @ V2))))))))))
(TINT_LE_LADD_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_le @ V0) @ V2)) @ ((cint_le @ ((cint_add @ V1) @ V0)) @ ((cint_add @ V1) @ V2))))))))))
(TINT_DIVIDES_RMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_divides @ ((cint_mul @ V1) @ V0)) @ V2)) @ ((cint_divides @ V1) @ V2)))))))))
(TINT_DIVIDES_LMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_divides @ ((cint_mul @ V0) @ V1)) @ V2)) @ ((cint_divides @ V1) @ V2)))))))))
(TSOLVABLE_GCD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_divides @ (cint_gcd @ ((c__comma__ @ V0) @ V2))) @ V1)) @ (c? @ (^[V3]: (((c== @ ((cint_mul @ V0) @ V3)) @ V1) @ (cint_mod @ V2))))))))))))
(TINT_DIVISION_DECOMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_divides @ V0) @ ((cint_mul @ V1) @ V2))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((cint_mul @ V3) @ V4))) @ ((c/__caret__ @ ((cint_divides @ V3) @ V1)) @ ((cint_divides @ V4) @ V2)))))))))))))))
(TINT_DIVIDES_MUL_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_divides @ V0) @ V2)) @ ((cint_divides @ ((cint_mul @ V1) @ V0)) @ ((cint_mul @ V1) @ V2))))))))))
(TDIVIDES_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_divides @ V0) @ V2)) @ ((cint_divides @ V0) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_DIVIDES_MUL_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_divides @ V0) @ V1)) @ ((cint_divides @ ((cint_mul @ V0) @ V2)) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_DIVIDES_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_divides @ V0) @ V1)) @ ((cint_divides @ V0) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_EQ_IMP_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ V0) @ V1)) @ (((c== @ V0) @ V1) @ (cint_mod @ V2))))))))))
(TINT_CONG_IMP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_lt @ (cint_abs @ ((cint_sub @ V1) @ V2))) @ V0)) @ (((c== @ V1) @ V2) @ (cint_mod @ V0)))) @ ((c= @ V1) @ V2)))))))))
(TINT_LT_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_lt @ V1) @ V0)) @ ((cint_lt @ V0) @ V2))) @ ((cint_lt @ V1) @ V2)))))))))
(TINT_LTE_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_lt @ V1) @ V0)) @ ((cint_le @ V0) @ V2))) @ ((cint_lt @ V1) @ V2)))))))))
(TINT_ABS_BETWEEN1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_lt @ V0) @ V2)) @ ((cint_lt @ (cint_abs @ ((cint_sub @ V1) @ V0))) @ ((cint_sub @ V2) @ V0)))) @ ((cint_lt @ V1) @ V2)))))))))
(TINT_LE_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((cint_le @ V0) @ V2))) @ ((cint_le @ ((cint_mul @ V1) @ V0)) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_LET_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_le @ V1) @ V0)) @ ((cint_lt @ V0) @ V2))) @ ((cint_lt @ V1) @ V2)))))))))
(TINT_LE_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_le @ V1) @ V0)) @ ((cint_le @ V0) @ V2))) @ ((cint_le @ V1) @ V2)))))))))
(TINT_LE_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_le @ V0) @ V1)) @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V2))) @ ((cint_le @ ((cint_mul @ V0) @ V2)) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_DIVIDES_CMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ ((cint_mul @ V0) @ V1)) @ ((cint_mul @ V0) @ V2))) @ (c~ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))))) @ ((cint_divides @ V1) @ V2)))))))))
(TINT_GCD_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V2) @ V0)) @ ((cint_divides @ V2) @ V1))) @ ((cint_divides @ V2) @ (cint_gcd @ ((c__comma__ @ V0) @ V1)))))))))))
(TINT_COPRIME_DIVPROD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V1) @ ((cint_mul @ V0) @ V2))) @ (cint_coprime @ ((c__comma__ @ V1) @ V0)))) @ ((cint_divides @ V1) @ V2)))))))))
(TDIVIDES_ADD_REVL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V1) @ V0)) @ ((cint_divides @ V1) @ ((cint_add @ V2) @ V0)))) @ ((cint_divides @ V1) @ V2)))))))))
(TDIVIDES_ADD_REVR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V1) @ V0)) @ ((cint_divides @ V1) @ ((cint_add @ V0) @ V2)))) @ ((cint_divides @ V1) @ V2)))))))))
(TINT_DIVIDES_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V1) @ V0)) @ ((cint_divides @ V0) @ V2))) @ ((cint_divides @ V1) @ V2)))))))))
(TINT_DIVIDES_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V0) @ V2)) @ ((c/__caret__ @ ((cint_divides @ V1) @ V2)) @ (cint_coprime @ ((c__comma__ @ V0) @ V1))))) @ ((cint_divides @ ((cint_mul @ V0) @ V1)) @ V2)))))))))
(TDIVIDES_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V0) @ V1)) @ ((cint_divides @ V0) @ V2))) @ ((cint_divides @ V0) @ ((cint_sub @ V1) @ V2))))))))))
(TDIVIDES_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V0) @ V1)) @ ((cint_divides @ V0) @ V2))) @ ((cint_divides @ V0) @ ((cint_add @ V1) @ V2))))))))))
(TINT_PRIME_DIVPROD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cint_prime @ V1)) @ ((cint_divides @ V1) @ ((cint_mul @ V0) @ V2)))) @ ((c__caret__/ @ ((cint_divides @ V1) @ V0)) @ ((cint_divides @ V1) @ V2))))))))))
(TINT_PRIME_COPRIME_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cint_prime @ V1)) @ (cint_coprime @ ((c__comma__ @ V0) @ V2)))) @ ((c__caret__/ @ (cint_coprime @ ((c__comma__ @ V1) @ V0))) @ (cint_coprime @ ((c__comma__ @ V1) @ V2)))))))))))
(TINT_PRIME_FACTOR_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cint_prime @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ V2) @ ((cint_mul @ V0) @ V1))))) @ ((cint_lt @ (cint_abs @ V1)) @ (cint_abs @ V2))))))))))
(TINT_CONG_SOLVE_POS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V0) @ V2))) @ (c~ @ ((c/__caret__ @ ((c= @ V2) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ (cint_abs @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (((c== @ ((cint_mul @ V0) @ V3)) @ V1) @ (cint_mod @ V2)))))))))))))
(TINT_COPRIME_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ (cint_coprime @ ((c__comma__ @ V0) @ V2)))) @ (cint_coprime @ ((c__comma__ @ V0) @ ((cint_mul @ V1) @ V2)))))))))))
(TINT_LINEAR_CONG_POS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (((c== @ ((cint_mul @ V1) @ V0)) @ ((cint_mul @ V1) @ V3)) @ (cint_mod @ V2)))))))))))))
(TINT_DIVIDES_RMUL2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((cint_divides @ ((cint_mul @ V1) @ V0)) @ ((cint_mul @ V2) @ V0))) @ ((cint_divides @ V1) @ V2))))))))))
(TINT_DIVIDES_LMUL2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((cint_divides @ ((cint_mul @ V0) @ V1)) @ ((cint_mul @ V0) @ V2))) @ ((cint_divides @ V1) @ V2))))))))))
(TINT_PRIME_DIVPROD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cint_prime @ V1)) @ ((c= @ ((cint_divides @ V1) @ ((cint_mul @ V0) @ V2))) @ ((c__caret__/ @ ((cint_divides @ V1) @ V0)) @ ((cint_divides @ V1) @ V2)))))))))))
(TINT_COPRIME_RMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cint_coprime @ ((c__comma__ @ V1) @ ((cint_mul @ V2) @ V0)))) @ (cint_coprime @ ((c__comma__ @ V1) @ V2))))))))))
(TINT_COPRIME_LMUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cint_coprime @ ((c__comma__ @ V1) @ ((cint_mul @ V0) @ V2)))) @ (cint_coprime @ ((c__comma__ @ V1) @ V2))))))))))
(TINT_COPRIME_PRIME,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cint_coprime @ ((c__comma__ @ V0) @ V2))) @ (c~ @ ((c/__caret__ @ (cint_prime @ V1)) @ ((c/__caret__ @ ((cint_divides @ V1) @ V0)) @ ((cint_divides @ V1) @ V2))))))))))))
(TINT_CONG_SOLVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cint_coprime @ ((c__comma__ @ V0) @ V2))) @ (c? @ (^[V3]: (((c== @ ((cint_mul @ V0) @ V3)) @ V1) @ (cint_mod @ V2))))))))))))
(TINT_SUB_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_mul @ ((cint_sub @ V0) @ V1)) @ V2)) @ ((cint_sub @ ((cint_mul @ V0) @ V2)) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_MUL_AC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_mul @ ((cint_mul @ V0) @ V1)) @ V2)) @ ((cint_mul @ V0) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_ADD_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_mul @ ((cint_add @ V0) @ V1)) @ V2)) @ ((cint_add @ ((cint_mul @ V0) @ V2)) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_SUB_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_mul @ V1) @ ((cint_sub @ V0) @ V2))) @ ((cint_sub @ ((cint_mul @ V1) @ V0)) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_MUL_AC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_mul @ V1) @ ((cint_mul @ V0) @ V2))) @ ((cint_mul @ V0) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_ADD_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_mul @ V1) @ ((cint_add @ V0) @ V2))) @ ((cint_add @ ((cint_mul @ V1) @ V0)) @ ((cint_mul @ V1) @ V2))))))))))
(TINT_MUL_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_mul @ V0) @ ((cint_mul @ V1) @ V2))) @ ((cint_mul @ ((cint_mul @ V0) @ V1)) @ V2)))))))))
(TINT_MIN_ACI_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_min @ ((cint_min @ V0) @ V1)) @ V2)) @ ((cint_min @ V0) @ ((cint_min @ V1) @ V2))))))))))
(TINT_MIN_ACI_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_min @ V1) @ ((cint_min @ V0) @ V2))) @ ((cint_min @ V0) @ ((cint_min @ V1) @ V2))))))))))
(TINT_MIN_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_min @ V0) @ ((cint_min @ V1) @ V2))) @ ((cint_min @ ((cint_min @ V0) @ V1)) @ V2)))))))))
(TINT_MAX_ACI_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_max @ ((cint_max @ V0) @ V1)) @ V2)) @ ((cint_max @ V0) @ ((cint_max @ V1) @ V2))))))))))
(TINT_MAX_ACI_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_max @ V1) @ ((cint_max @ V0) @ V2))) @ ((cint_max @ V0) @ ((cint_max @ V1) @ V2))))))))))
(TINT_MAX_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_max @ V0) @ ((cint_max @ V1) @ V2))) @ ((cint_max @ ((cint_max @ V0) @ V1)) @ V2)))))))))
(TINT_SUB_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_add @ ((cint_sub @ V1) @ V0)) @ ((cint_sub @ V0) @ V2))) @ ((cint_sub @ V1) @ V2)))))))))
(TINT_ADD_AC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_add @ ((cint_add @ V0) @ V1)) @ V2)) @ ((cint_add @ V0) @ ((cint_add @ V1) @ V2))))))))))
(TINT_ADD_AC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_add @ V1) @ ((cint_add @ V0) @ V2))) @ ((cint_add @ V0) @ ((cint_add @ V1) @ V2))))))))))
(TINT_ADD_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_add @ V0) @ ((cint_add @ V1) @ V2))) @ ((cint_add @ ((cint_add @ V0) @ V1)) @ V2)))))))))
(TINT_GCD_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ (cint_gcd @ ((c__comma__ @ V1) @ V2))))) @ (cint_gcd @ ((c__comma__ @ (cint_gcd @ ((c__comma__ @ V0) @ V1))) @ V2))))))))))
(Tint_mod,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cint_mod @ V0) @ V1) @ V2)) @ ((cint_divides @ V0) @ ((cint_sub @ V1) @ V2))))))))))
(TINT_CONG_ADD_RCANCEL_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ ((cint_add @ V1) @ V0)) @ V0) @ (cint_mod @ V2))) @ (((c== @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_mod @ V2))))))))))
(TINT_CONG_ADD_LCANCEL_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ ((cint_add @ V0) @ V1)) @ V0) @ (cint_mod @ V2))) @ (((c== @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))) @ (cint_mod @ V2))))))))))
(TINT_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ V1) @ V2) @ (cint_mod @ V0))) @ ((cint_divides @ V0) @ ((cint_sub @ V1) @ V2))))))))))
(TINT_CONG_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ V1) @ V0) @ (cint_mod @ V2))) @ (((c== @ V0) @ V1) @ (cint_mod @ V2))))))))))
(TCONG_MOD_NEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ V0) @ V1) @ (cint_mod @ (cint_neg @ V2)))) @ (((c== @ V0) @ V1) @ (cint_mod @ V2))))))))))
(TCONG_MOD_ABS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ V0) @ V1) @ (cint_mod @ (cint_abs @ V2)))) @ (((c== @ V0) @ V1) @ (cint_mod @ V2))))))))))
(TCONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ V0) @ V1) @ (cint_mod @ V2))) @ (c? @ (^[V3]: ((c= @ ((cint_sub @ V0) @ V1)) @ ((cint_mul @ V3) @ V2))))))))))))
(Tint_congruent,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ V0) @ V1) @ (cint_mod @ V2))) @ (c? @ (^[V3]: ((c= @ ((cint_sub @ V0) @ V1)) @ ((cint_mul @ V2) @ V3))))))))))))
(Tinterp_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cinterp @ V1) @ ((cNdivides @ V0) @ V2))) @ (c~ @ ((cint_divides @ V0) @ ((cint_add @ V1) @ V2)))))))))))
(Tinterp_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cinterp @ V1) @ ((cDivides @ V0) @ V2))) @ ((cint_divides @ V0) @ ((cint_add @ V1) @ V2))))))))))
(TINT_LT_SUB_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ ((cint_sub @ V0) @ V2)) @ V1)) @ ((cint_lt @ V0) @ ((cint_add @ V1) @ V2))))))))))
(TINT_MIN_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ ((cint_min @ V0) @ V1)) @ V2)) @ ((c__caret__/ @ ((cint_lt @ V0) @ V2)) @ ((cint_lt @ V1) @ V2))))))))))
(TINT_MAX_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ ((cint_max @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((cint_lt @ V0) @ V2)) @ ((cint_lt @ V1) @ V2))))))))))
(TINT_LT_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ ((cint_add @ V1) @ V0)) @ ((cint_add @ V2) @ V0))) @ ((cint_lt @ V1) @ V2)))))))))
(TINT_LT_ADDNEG2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ ((cint_add @ V0) @ (cint_neg @ V2))) @ V1)) @ ((cint_lt @ V0) @ ((cint_add @ V1) @ V2))))))))))
(TINT_LT_ADD_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ ((cint_add @ V0) @ V2)) @ V1)) @ ((cint_lt @ V0) @ ((cint_sub @ V1) @ V2))))))))))
(TINT_LT_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ ((cint_add @ V0) @ V1)) @ ((cint_add @ V0) @ V2))) @ ((cint_lt @ V1) @ V2)))))))))
(TINT_LT_MIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ V1) @ ((cint_min @ V0) @ V2))) @ ((c/__caret__ @ ((cint_lt @ V1) @ V0)) @ ((cint_lt @ V1) @ V2))))))))))
(TINT_LT_MAX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ V1) @ ((cint_max @ V0) @ V2))) @ ((c__caret__/ @ ((cint_lt @ V1) @ V0)) @ ((cint_lt @ V1) @ V2))))))))))
(TINT_LT_SUB_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ V0) @ ((cint_sub @ V2) @ V1))) @ ((cint_lt @ ((cint_add @ V0) @ V1)) @ V2)))))))))
(TINT_LT_ADDNEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_lt @ V0) @ ((cint_add @ V2) @ (cint_neg @ V1)))) @ ((cint_lt @ ((cint_add @ V0) @ V1)) @ V2)))))))))
(TINT_LE_SUB_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_le @ ((cint_sub @ V0) @ V2)) @ V1)) @ ((cint_le @ V0) @ ((cint_add @ V1) @ V2))))))))))
(TINT_MIN_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_le @ ((cint_min @ V0) @ V1)) @ V2)) @ ((c__caret__/ @ ((cint_le @ V0) @ V2)) @ ((cint_le @ V1) @ V2))))))))))
(TINT_MAX_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_le @ ((cint_max @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((cint_le @ V0) @ V2)) @ ((cint_le @ V1) @ V2))))))))))
(TINT_LE_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_le @ ((cint_add @ V1) @ V0)) @ ((cint_add @ V2) @ V0))) @ ((cint_le @ V1) @ V2)))))))))
(TINT_LE_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_le @ ((cint_add @ V0) @ V1)) @ ((cint_add @ V0) @ V2))) @ ((cint_le @ V1) @ V2)))))))))
(TINT_LE_MIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_le @ V1) @ ((cint_min @ V0) @ V2))) @ ((c/__caret__ @ ((cint_le @ V1) @ V0)) @ ((cint_le @ V1) @ V2))))))))))
(TINT_LE_MAX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_le @ V1) @ ((cint_max @ V0) @ V2))) @ ((c__caret__/ @ ((cint_le @ V1) @ V0)) @ ((cint_le @ V1) @ V2))))))))))
(TINT_LE_SUB_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_le @ V0) @ ((cint_sub @ V2) @ V1))) @ ((cint_le @ ((cint_add @ V0) @ V1)) @ V2)))))))))
(TINT_DIVIDES_GCD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cint_divides @ V1) @ (cint_gcd @ ((c__comma__ @ V0) @ V2)))) @ ((c/__caret__ @ ((cint_divides @ V1) @ V0)) @ ((cint_divides @ V1) @ V2))))))))))
(Talldivide_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((calldivide @ V2) @ ((cNdivides @ V1) @ V0))) @ ((cint_divides @ V1) @ V2)))))))))
(Talldivide_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((calldivide @ V2) @ ((cDivides @ V1) @ V0))) @ ((cint_divides @ V1) @ V2)))))))))
(TINT_EQ_SUB_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cint_sub @ V0) @ V2)) @ V1)) @ ((c= @ V0) @ ((cint_add @ V1) @ V2))))))))))
(TINT_EQ_MUL_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cint_mul @ V0) @ V2)) @ ((cint_mul @ V1) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ (cint_of_num @ (cNUMERAL @ c_0))))))))))))
(TINT_EQ_MUL_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cint_mul @ V0) @ V1)) @ ((cint_mul @ V0) @ V2))) @ ((c__caret__/ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ V2))))))))))
(TINT_EQ_ADD_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cint_add @ V1) @ V0)) @ ((cint_add @ V2) @ V0))) @ ((c= @ V1) @ V2)))))))))
(TINT_EQ_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cint_add @ V0) @ V1)) @ ((cint_add @ V0) @ V2))) @ ((c= @ V1) @ V2)))))))))
(TINT_GCD_UNIQUE_ABS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ V1))) @ (cint_abs @ V2))) @ ((c/__caret__ @ ((cint_divides @ V2) @ V0)) @ ((c/__caret__ @ ((cint_divides @ V2) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V3) @ V0)) @ ((cint_divides @ V3) @ V1))) @ ((cint_divides @ V3) @ V2))))))))))))))
(TINT_GCD_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ V1))) @ V2)) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c/__caret__ @ ((cint_divides @ V2) @ V0)) @ ((c/__caret__ @ ((cint_divides @ V2) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V3) @ V0)) @ ((cint_divides @ V3) @ V1))) @ ((cint_divides @ V3) @ V2)))))))))))))))
(TINT_EQ_SUB_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ V0) @ ((cint_sub @ V2) @ V1))) @ ((c= @ ((cint_add @ V0) @ V1)) @ V2)))))))))
(TINT_ABS_BETWEEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c/__caret__ @ ((cint_lt @ ((cint_sub @ V1) @ V2)) @ V0)) @ ((cint_lt @ V0) @ ((cint_add @ V1) @ V2))))) @ ((cint_lt @ (cint_abs @ ((cint_sub @ V0) @ V1))) @ V2)))))))))
(TINT_COPRIME_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cint_coprime @ ((c__comma__ @ ((cint_mul @ V0) @ V1)) @ V2))) @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V0) @ V2))) @ (cint_coprime @ ((c__comma__ @ V1) @ V2)))))))))))
(TINT_COPRIME_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cint_coprime @ ((c__comma__ @ V1) @ ((cint_mul @ V0) @ V2)))) @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V1) @ V0))) @ (cint_coprime @ ((c__comma__ @ V1) @ V2)))))))))))
(TINT_POW_MUL_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((cint_mul @ ((cint_pow @ V0) @ V3)) @ V2)) @ ((cint_pow @ V1) @ V3)))) @ (c? @ (^[V4]: ((c= @ V2) @ ((cint_pow @ V4) @ V3))))))))))))))
(TINT_COPRIME_POW_ABS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V1) @ V2))) @ ((c= @ ((cint_mul @ V1) @ V2)) @ ((cint_pow @ V0) @ V3)))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ (cint_abs @ V1)) @ ((cint_pow @ V4) @ V3))) @ ((c= @ (cint_abs @ V2)) @ ((cint_pow @ V5) @ V3)))))))))))))))))
(TINT_COPRIME_POW_ODD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cODD @ V3)) @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V1) @ V2))) @ ((c= @ ((cint_mul @ V1) @ V2)) @ ((cint_pow @ V0) @ V3))))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V1) @ ((cint_pow @ V4) @ V3))) @ ((c= @ V2) @ ((cint_pow @ V5) @ V3)))))))))))))))))
(TINT_CONG_ADD_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((c== @ ((cint_add @ V1) @ V0)) @ ((cint_add @ V2) @ V0)) @ (cint_mod @ V3))) @ (((c== @ V1) @ V2) @ (cint_mod @ V3))))))))))))
(TINT_CONG_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((c== @ ((cint_add @ V0) @ V1)) @ ((cint_add @ V0) @ V2)) @ (cint_mod @ V3))) @ (((c== @ V1) @ V2) @ (cint_mod @ V3))))))))))))
(TINT_CRT_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((c== @ V0) @ V2) @ (cint_mod @ (cint_gcd @ ((c__comma__ @ V1) @ V3))))) @ (c? @ (^[V4]: ((c/__caret__ @ (((c== @ V4) @ V0) @ (cint_mod @ V1))) @ (((c== @ V4) @ V2) @ (cint_mod @ V3)))))))))))))))
(TINT_CONG_INT_DIVIDES_MODULUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((c== @ V1) @ V2) @ (cint_mod @ V0))) @ ((cint_divides @ V3) @ V0))) @ (((c== @ V1) @ V2) @ (cint_mod @ V3))))))))))))
(TCONG_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((c== @ V1) @ V0) @ (cint_mod @ V3))) @ (((c== @ V0) @ V2) @ (cint_mod @ V3)))) @ (((c== @ V1) @ V2) @ (cint_mod @ V3))))))))))))
(TINT_ABS_BETWEEN2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cint_lt @ V1) @ V0)) @ ((c/__caret__ @ ((cint_lt @ ((cint_mul @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cint_abs @ ((cint_sub @ V2) @ V1)))) @ ((cint_sub @ V0) @ V1))) @ ((cint_lt @ ((cint_mul @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cint_abs @ ((cint_sub @ V3) @ V0)))) @ ((cint_sub @ V0) @ V1))))) @ ((cint_lt @ V2) @ V3)))))))))))
(TINT_LT_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cint_lt @ V0) @ V2)) @ ((cint_lt @ V1) @ V3))) @ ((cint_lt @ ((cint_add @ V0) @ V1)) @ ((cint_add @ V2) @ V3))))))))))))
(TINT_LTE_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cint_lt @ V0) @ V2)) @ ((cint_le @ V1) @ V3))) @ ((cint_lt @ ((cint_add @ V0) @ V1)) @ ((cint_add @ V2) @ V3))))))))))))
(TINT_LET_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cint_le @ V0) @ V2)) @ ((cint_lt @ V1) @ V3))) @ ((cint_lt @ ((cint_add @ V0) @ V1)) @ ((cint_add @ V2) @ V3))))))))))))
(TINT_LE_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cint_le @ V0) @ V2)) @ ((cint_le @ V1) @ V3))) @ ((cint_le @ ((cint_add @ V0) @ V1)) @ ((cint_add @ V2) @ V3))))))))))))
(TINT_COPRIME_DIVISORS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V2) @ V0)) @ ((c/__caret__ @ ((cint_divides @ V3) @ V1)) @ (cint_coprime @ ((c__comma__ @ V0) @ V1))))) @ (cint_coprime @ ((c__comma__ @ V2) @ V3))))))))))))
(TINT_DIVIDES_MUL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cint_divides @ V0) @ V2)) @ ((cint_divides @ V1) @ V3))) @ ((cint_divides @ ((cint_mul @ V0) @ V1)) @ ((cint_mul @ V2) @ V3))))))))))))
(TINT_DIVMOD_UNIQ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ V1) @ ((cint_add @ ((cint_mul @ V3) @ V2)) @ V0))) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0)) @ ((cint_lt @ V0) @ (cint_abs @ V2))))) @ ((c= @ ((cdiv @ V1) @ V2)) @ V3)))))))))))
(TINT_DIVMOD_UNIQ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ V1) @ ((cint_add @ ((cint_mul @ V0) @ V2)) @ V3))) @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((cint_lt @ V3) @ (cint_abs @ V2))))) @ ((c= @ ((crem @ V1) @ V2)) @ V3)))))))))))
(TINT_GCD_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cint_gcd @ ((c__comma__ @ V0) @ V1))) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((c= @ V0) @ ((cint_mul @ V2) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))) @ ((c= @ V1) @ ((cint_mul @ V3) @ (cint_gcd @ ((c__comma__ @ V0) @ V1))))))) @ (cint_coprime @ ((c__comma__ @ V2) @ V3))))))))))))
(TINT_CONG_CHINESE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V2) @ V3))) @ ((c/__caret__ @ (((c== @ V0) @ V1) @ (cint_mod @ V2))) @ (((c== @ V0) @ V1) @ (cint_mod @ V3))))) @ (((c== @ V0) @ V1) @ (cint_mod @ ((cint_mul @ V2) @ V3)))))))))))))
(TINT_CHINESE_REMAINDER_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V1) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V0) @ V1))) @ (cint_coprime @ ((c__comma__ @ V2) @ V3))))))) @ (c? @ (^[V4]: ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V4) @ ((cint_mul @ V1) @ V3)))) @ ((c/__caret__ @ (((c== @ V4) @ V0) @ (cint_mod @ V1))) @ (((c== @ V4) @ V2) @ (cint_mod @ V3))))))))))))))))
(TINT_CHINESE_REMAINDER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V1) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ (c~ @ ((c= @ V3) @ (cint_of_num @ (cNUMERAL @ c_0))))))) @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((c= @ V4) @ ((cint_add @ V0) @ ((cint_mul @ V5) @ V1)))) @ ((c= @ V4) @ ((cint_add @ V2) @ ((cint_mul @ V6) @ V3))))))))))))))))))))
(TINT_CONG_MUL_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V0) @ V3))) @ (((c== @ ((cint_mul @ V1) @ V0)) @ ((cint_mul @ V2) @ V0)) @ (cint_mod @ V3)))) @ (((c== @ V1) @ V2) @ (cint_mod @ V3))))))))))))
(TINT_CONG_MUL_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V0) @ V3))) @ (((c== @ ((cint_mul @ V0) @ V1)) @ ((cint_mul @ V0) @ V2)) @ (cint_mod @ V3)))) @ (((c== @ V1) @ V2) @ (cint_mod @ V3))))))))))))
(TINT_CHINESE_REMAINDER_USUAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cint_coprime @ ((c__comma__ @ V1) @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ (((c== @ V4) @ V0) @ (cint_mod @ V1))) @ (((c== @ V4) @ V2) @ (cint_mod @ V3)))))))))))))))
(TINT_CONG_MUL_RCANCEL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cint_coprime @ ((c__comma__ @ V0) @ V3))) @ ((c= @ (((c== @ ((cint_mul @ V1) @ V0)) @ ((cint_mul @ V2) @ V0)) @ (cint_mod @ V3))) @ (((c== @ V1) @ V2) @ (cint_mod @ V3)))))))))))))
(TINT_CONG_MUL_LCANCEL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cint_coprime @ ((c__comma__ @ V0) @ V3))) @ ((c= @ (((c== @ ((cint_mul @ V0) @ V1)) @ ((cint_mul @ V0) @ V2)) @ (cint_mod @ V3))) @ (((c== @ V1) @ V2) @ (cint_mod @ V3)))))))))))))
(TINT_ADD2_SUB2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cint_sub @ ((cint_add @ V0) @ V2)) @ ((cint_add @ V1) @ V3))) @ ((cint_add @ ((cint_sub @ V0) @ V1)) @ ((cint_sub @ V2) @ V3))))))))))))
(TINT_CONG_ADD_RCANCEL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c== @ ((cint_add @ V1) @ V0)) @ ((cint_add @ V2) @ V0)) @ (cint_mod @ V3))) @ (((c== @ V1) @ V2) @ (cint_mod @ V3))))))))))))
(TINT_CONG_ADD_LCANCEL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c== @ ((cint_add @ V0) @ V1)) @ ((cint_add @ V0) @ V2)) @ (cint_mod @ V3))) @ (((c== @ V1) @ V2) @ (cint_mod @ V3))))))))))))
(TINT_CRT_STRONG_IFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (c? @ (^[V4]: ((c/__caret__ @ (((c== @ V4) @ V0) @ (cint_mod @ V2))) @ (((c== @ V4) @ V1) @ (cint_mod @ V3)))))) @ (((c== @ V0) @ V1) @ (cint_mod @ (cint_gcd @ ((c__comma__ @ V2) @ V3))))))))))))))
(TCONG_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c== @ V0) @ V2) @ (cint_mod @ V4))) @ (((c== @ V1) @ V3) @ (cint_mod @ V4)))) @ (((c== @ ((cint_sub @ V0) @ V1)) @ ((cint_sub @ V2) @ V3)) @ (cint_mod @ V4))))))))))))))
(TCONG_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c== @ V0) @ V2) @ (cint_mod @ V4))) @ (((c== @ V1) @ V3) @ (cint_mod @ V4)))) @ (((c== @ ((cint_mul @ V0) @ V1)) @ ((cint_mul @ V2) @ V3)) @ (cint_mod @ V4))))))))))))))
(TCONG_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c== @ V0) @ V2) @ (cint_mod @ V4))) @ (((c== @ V1) @ V3) @ (cint_mod @ V4)))) @ (((c== @ ((cint_add @ V0) @ V1)) @ ((cint_add @ V2) @ V3)) @ (cint_mod @ V4))))))))))))))
(TINT_CONG_SOLVE_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (cint_coprime @ ((c__comma__ @ V0) @ V4))) @ ((c==> @ ((c/__caret__ @ (((c== @ ((cint_mul @ V0) @ V2)) @ V1) @ (cint_mod @ V4))) @ (((c== @ ((cint_mul @ V0) @ V3)) @ V1) @ (cint_mod @ V4)))) @ (((c== @ V2) @ V3) @ (cint_mod @ V4)))))))))))))))
(TINT_CHINESE_REMAINDER_COPRIME_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cint_coprime @ ((c__comma__ @ V4) @ V5))) @ ((c/__caret__ @ (((c== @ V2) @ V0) @ (cint_mod @ V4))) @ ((c/__caret__ @ (((c== @ V2) @ V1) @ (cint_mod @ V5))) @ ((c/__caret__ @ (((c== @ V3) @ V0) @ (cint_mod @ V4))) @ (((c== @ V3) @ V1) @ (cint_mod @ V5))))))) @ (((c== @ V2) @ V3) @ (cint_mod @ ((cint_mul @ V4) @ V5)))))))))))))))))
(TMINUSINF_REPEATS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((calldivide @ V2) @ V3)) @ ((c= @ ((cinterp @ V0) @ (cminusinf @ V3))) @ ((cinterp @ ((cint_add @ V0) @ ((cint_mul @ V1) @ V2))) @ (cminusinf @ V3)))))))))))))
(TEXISTS_MOD_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (V1 @ ((cint_add @ V3) @ ((cint_mul @ V2) @ V0)))) @ (V1 @ V3))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2)) @ ((c/__caret__ @ ((cint_le @ V2) @ V0)) @ (V1 @ (cint_neg @ V2)))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2)) @ ((c/__caret__ @ ((cint_le @ V2) @ V0)) @ (V1 @ V2)))))))))))
(TEXISTS_MOD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (V1 @ ((cint_add @ V3) @ ((cint_mul @ V2) @ V0)))) @ (V1 @ V3))))))) @ ((c= @ (c? @ (^[V2]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2)) @ ((c/__caret__ @ ((cint_le @ V2) @ V0)) @ (V1 @ (cint_neg @ V2))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2)) @ ((c/__caret__ @ ((cint_le @ V2) @ V0)) @ (V1 @ V2))))))))))))
(TEXISTS_MULTIPLE_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (V1 @ ((cint_mul @ V0) @ V2))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cint_divides @ V0) @ V2)) @ (V1 @ V2))))))))))
(TSIMPLEX_EXTREME_POINTS_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V0) @ V1)) @ ((c= @ V1) @ ((chull @ cconvex) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cextreme_point_of @ V3) @ V1)) @ V3)))))))))))))
(TSIMPLEX_EXTREME_POINTS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V0) @ V1)) @ (c~ @ (caffine_dependent @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cextreme_point_of @ V3) @ V1)) @ V3)))))))))))))
(TSIMPLEX_EXTREME_POINTS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V0) @ V1)) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cextreme_point_of @ V3) @ V1)) @ V3))))))))))))
(TSUBSET_FACE_OF_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csimplex @ V0) @ V2)) @ ((cSUBSET @ V1) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cextreme_point_of @ V4) @ V2)) @ V4)))))))) @ ((cface_of @ ((chull @ cconvex) @ V1)) @ V2)))))))))
(TFACE_OF_SIMPLEX_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csimplex @ V0) @ V1)) @ ((cface_of @ V2) @ V1))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cextreme_point_of @ V5) @ V1)) @ V5))))))) @ ((c= @ V2) @ ((chull @ cconvex) @ V3)))))))))))))
(TFINITE_FACES_OF_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V0) @ V1)) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cface_of @ V3) @ V1)) @ V3))))))))))))
(TFACES_OF_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V0) @ V1)) @ ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cface_of @ V3) @ V1)) @ V3)))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cSUBSET @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cextreme_point_of @ V5) @ V1)) @ V5))))))) @ ((chull @ cconvex) @ V3)))))))))))))
(TSIMPLEX_IMP_POLYTOPE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V0) @ V1)) @ (cpolytope @ V1)))))))
(TCLOSED_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V0) @ V1)) @ (cclosed @ V1)))))))
(TCOMPACT_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V0) @ V1)) @ (ccompact @ V1)))))))
(TCONVEX_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V0) @ V1)) @ (cconvex @ V1)))))))
(TSIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((csimplex @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V2))) @ ((c/__caret__ @ ((c= @ (cint_of_num @ (cCARD @ V2))) @ ((cint_add @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c= @ V1) @ ((chull @ cconvex) @ V2)))))))))))))
(Tsimplex,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((csimplex @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ (c~ @ (caffine_dependent @ V2))) @ ((c/__caret__ @ ((c= @ (cint_of_num @ (cCARD @ V2))) @ ((cint_add @ V0) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c= @ V1) @ ((chull @ cconvex) @ V2))))))))))))
(TMAINTHM_A,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((calldivide @ V0) @ V1)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0))) @ ((c= @ (c? @ (^[V2]: ((cinterp @ V2) @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2)) @ ((c/__caret__ @ ((cint_le @ V2) @ V0)) @ ((c__caret__/ @ ((cinterp @ V2) @ (cplusinf @ V1))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ (caset @ V1))) @ ((cinterp @ ((cint_sub @ V3) @ V2)) @ V1))))))))))))))))
(TMAINTHM_B,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((calldivide @ V0) @ V1)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0))) @ ((c= @ (c? @ (^[V2]: ((cinterp @ V2) @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2)) @ ((c/__caret__ @ ((cint_le @ V2) @ V0)) @ ((c__caret__/ @ ((cinterp @ V2) @ (cminusinf @ V1))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ (cbset @ V1))) @ ((cinterp @ ((cint_add @ V3) @ V2)) @ V1))))))))))))))))
(TNOMINIMAL_EQUIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((calldivide @ V0) @ V1)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0))) @ ((c= @ (c! @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cint_lt @ V3) @ V2)) @ ((cinterp @ V3) @ V1))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2)) @ ((c/__caret__ @ ((cint_le @ V2) @ V0)) @ ((cinterp @ V2) @ (cminusinf @ V1)))))))))))))
(TINTERP_MIRROR_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinterp @ (cint_neg @ V0)) @ (cmirror @ V1))) @ ((cinterp @ V0) @ V1)))))))
(TINTERP_MIRROR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinterp @ V0) @ (cmirror @ V1))) @ ((cinterp @ (cint_neg @ V0)) @ V1)))))))
(TALLDIVIDE_MIRROR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((calldivide @ V0) @ (cmirror @ V1))) @ ((calldivide @ V0) @ V1)))))))
(TBDISJ_REPEATS_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((calldivide @ V0) @ V1)) @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ V0))) @ ((c==> @ ((c/__caret__ @ ((cinterp @ V2) @ V1)) @ (c~ @ ((cinterp @ ((cint_sub @ V2) @ V0)) @ V1)))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3)) @ ((c/__caret__ @ ((cint_le @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ (cbset @ V1))) @ ((c= @ V2) @ ((cint_add @ V4) @ V3))))))))))))))))))
(Tinterp_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinterp @ V0) @ (cNox @ V1))) @ V1))))))
(Talldivide_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((calldivide @ V0) @ (cNox @ V1))) @ cT))))))
(Tind_model_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (cmk_ind @ (cdest_ind @ V0))) @ V0))))
(TI_IND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cI_IND @ V0)) @ (cI_IND @ V1))) @ ((c= @ V0) @ V1)))))))
(TNUM_REP_RULES_conjunct1,(c! @ (^[V0]: ((c==> @ (cNUM_REP @ V0)) @ (cNUM_REP @ (cIND_SUC @ V0))))))
(TNUM_REP_CASES,(c! @ (^[V0]: ((c= @ (cNUM_REP @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ cIND_0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((c= @ V0) @ (cIND_SUC @ V1))) @ (cNUM_REP @ V1)))))))))
(TIND_SUC_0,(c! @ (^[V0]: (c~ @ ((c= @ (cIND_SUC @ V0)) @ cIND_0)))))
(TIND_SUC_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cIND_SUC @ V0)) @ (cIND_SUC @ V1))) @ ((c= @ V0) @ V1)))))))
(THREAL_LE_REFL,(c! @ (^[V0]: ((chreal_le @ V0) @ V0))))
(THREAL_MUL_LINV,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (chreal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((chreal_mul @ (chreal_inv @ V0)) @ V0)) @ (chreal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(THREAL_MUL_LID,(c! @ (^[V0]: ((c= @ ((chreal_mul @ (chreal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ V0))))
(THREAL_MUL_LZERO,(c! @ (^[V0]: ((c= @ ((chreal_mul @ (chreal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (chreal_of_num @ (cNUMERAL @ c_0))))))
(THREAL_MUL_RZERO,(c! @ (^[V0]: ((c= @ ((chreal_mul @ V0) @ (chreal_of_num @ (cNUMERAL @ c_0)))) @ (chreal_of_num @ (cNUMERAL @ c_0))))))
(THREAL_ADD_LID,(c! @ (^[V0]: ((c= @ ((chreal_add @ (chreal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ V0))))
(THREAL_ADD_RID,(c! @ (^[V0]: ((c= @ ((chreal_add @ V0) @ (chreal_of_num @ (cNUMERAL @ c_0)))) @ V0))))
(Threal_inv,(c! @ (^[V0]: ((c= @ (chreal_inv @ V0)) @ (cmk_hreal @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cnadd_eq @ (cnadd_inv @ V2)) @ V1)) @ ((cdest_hreal @ V0) @ V2))))))))))
(THREAL_ARCH,(c! @ (^[V0]: (c? @ (^[V1]: ((chreal_le @ V0) @ (chreal_of_num @ V1)))))))
(THREAL_LE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((chreal_le @ V0) @ ((chreal_add @ V0) @ V1)))))))
(THREAL_LE_TOTAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((chreal_le @ V1) @ V0)) @ ((chreal_le @ V0) @ V1)))))))
(THREAL_LE_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chreal_le @ V1) @ V0)) @ (c? @ (^[V2]: ((c= @ V0) @ ((chreal_add @ V1) @ V2))))))))))
(Ttreal_neg,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctreal_neg @ ((c__comma__ @ V1) @ V0))) @ ((c__comma__ @ V0) @ V1)))))))
(Ttreal_inv,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctreal_inv @ ((c__comma__ @ V1) @ V0))) @ (((cCOND @ ((c= @ V1) @ V0)) @ ((c__comma__ @ (chreal_of_num @ (cNUMERAL @ c_0))) @ (chreal_of_num @ (cNUMERAL @ c_0)))) @ (((cCOND @ ((chreal_le @ V0) @ V1)) @ ((c__comma__ @ (chreal_inv @ (c__at__ @ (^[V2]: ((c= @ V1) @ ((chreal_add @ V0) @ V2)))))) @ (chreal_of_num @ (cNUMERAL @ c_0)))) @ ((c__comma__ @ (chreal_of_num @ (cNUMERAL @ c_0))) @ (chreal_inv @ (c__at__ @ (^[V2]: ((c= @ V0) @ ((chreal_add @ V1) @ V2))))))))))))))
(THREAL_MUL_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chreal_mul @ V1) @ V0)) @ ((chreal_mul @ V0) @ V1)))))))
(Threal_mul,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chreal_mul @ V0) @ V1)) @ (cmk_hreal @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cnadd_eq @ ((cnadd_mul @ V3) @ V4)) @ V2)) @ ((c/__caret__ @ ((cdest_hreal @ V0) @ V3)) @ ((cdest_hreal @ V1) @ V4)))))))))))))))
(THREAL_ADD_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chreal_add @ V1) @ V0)) @ ((chreal_add @ V0) @ V1)))))))
(Threal_add,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chreal_add @ V0) @ V1)) @ (cmk_hreal @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cnadd_eq @ ((cnadd_add @ V3) @ V4)) @ V2)) @ ((c/__caret__ @ ((cdest_hreal @ V0) @ V3)) @ ((cdest_hreal @ V1) @ V4)))))))))))))))
(THREAL_LE_EXISTS_DEF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chreal_le @ V1) @ V0)) @ (c? @ (^[V2]: ((c= @ V0) @ ((chreal_add @ V1) @ V2))))))))))
(Threal_le,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chreal_le @ V0) @ V1)) @ (c__at__ @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ ((cnadd_le @ V3) @ V4)) @ V2)) @ ((c/__caret__ @ ((cdest_hreal @ V0) @ V3)) @ ((cdest_hreal @ V1) @ V4)))))))))))))))
(THREAL_LE_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((chreal_le @ V0) @ V1)) @ ((chreal_le @ V1) @ V0))) @ ((c= @ V0) @ V1)))))))
(THREAL_LE_MUL_RCANCEL_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chreal_le @ V0) @ V1)) @ ((chreal_le @ ((chreal_mul @ V0) @ V2)) @ ((chreal_mul @ V1) @ V2))))))))))
(THREAL_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ ((chreal_add @ V0) @ V1)) @ ((chreal_add @ V0) @ V2))) @ ((c= @ V1) @ V2)))))))))
(THREAL_LE_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chreal_le @ V1) @ V0)) @ ((chreal_le @ V0) @ V2))) @ ((chreal_le @ V1) @ V2)))))))))
(THREAL_ADD_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chreal_mul @ ((chreal_add @ V0) @ V1)) @ V2)) @ ((chreal_add @ ((chreal_mul @ V0) @ V2)) @ ((chreal_mul @ V1) @ V2))))))))))
(THREAL_ADD_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chreal_mul @ V1) @ ((chreal_add @ V0) @ V2))) @ ((chreal_add @ ((chreal_mul @ V1) @ V0)) @ ((chreal_mul @ V1) @ V2))))))))))
(THREAL_MUL_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chreal_mul @ V0) @ ((chreal_mul @ V1) @ V2))) @ ((chreal_mul @ ((chreal_mul @ V0) @ V1)) @ V2)))))))))
(THREAL_ADD_AC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chreal_add @ ((chreal_add @ V0) @ V1)) @ V2)) @ ((chreal_add @ V0) @ ((chreal_add @ V1) @ V2))))))))))
(THREAL_ADD_AC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chreal_add @ V1) @ ((chreal_add @ V0) @ V2))) @ ((chreal_add @ V0) @ ((chreal_add @ V1) @ V2))))))))))
(THREAL_ADD_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chreal_add @ V0) @ ((chreal_add @ V1) @ V2))) @ ((chreal_add @ ((chreal_add @ V0) @ V1)) @ V2)))))))))
(THREAL_LE_ADD_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chreal_le @ ((chreal_add @ V1) @ V0)) @ ((chreal_add @ V2) @ V0))) @ ((chreal_le @ V1) @ V2)))))))))
(THREAL_LE_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chreal_le @ ((chreal_add @ V0) @ V1)) @ ((chreal_add @ V0) @ V2))) @ ((chreal_le @ V1) @ V2)))))))))
(THREAL_EQ_ADD_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((chreal_add @ V1) @ V0)) @ ((chreal_add @ V2) @ V0))) @ ((c= @ V1) @ V2)))))))))
(THREAL_EQ_ADD_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((chreal_add @ V0) @ V1)) @ ((chreal_add @ V0) @ V2))) @ ((c= @ V1) @ V2)))))))))
(THREAL_LE_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chreal_le @ V0) @ V2)) @ ((chreal_le @ V1) @ V3))) @ ((chreal_le @ ((chreal_add @ V0) @ V1)) @ ((chreal_add @ V2) @ V3))))))))))))
(Ttreal_mul,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((ctreal_mul @ ((c__comma__ @ V0) @ V2)) @ ((c__comma__ @ V3) @ V1))) @ ((c__comma__ @ ((chreal_add @ ((chreal_mul @ V0) @ V3)) @ ((chreal_mul @ V2) @ V1))) @ ((chreal_add @ ((chreal_mul @ V0) @ V1)) @ ((chreal_mul @ V2) @ V3)))))))))))))
(Ttreal_add,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((ctreal_add @ ((c__comma__ @ V0) @ V2)) @ ((c__comma__ @ V1) @ V3))) @ ((c__comma__ @ ((chreal_add @ V0) @ V1)) @ ((chreal_add @ V2) @ V3))))))))))))
(Ttreal_le,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((ctreal_le @ ((c__comma__ @ V0) @ V3)) @ ((c__comma__ @ V2) @ V1))) @ ((chreal_le @ ((chreal_add @ V0) @ V1)) @ ((chreal_add @ V2) @ V3))))))))))))
(Ttreal_eq,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((ctreal_eq @ ((c__comma__ @ V0) @ V3)) @ ((c__comma__ @ V2) @ V1))) @ ((c= @ ((chreal_add @ V0) @ V1)) @ ((chreal_add @ V2) @ V3))))))))))))
(Ttype_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cTyvar @ V2))))) @ ((c/__caret__ @ (V0 @ cBool)) @ ((c/__caret__ @ (V0 @ cInd)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cFun @ V2) @ V3))))))))))) @ (V0 @ V1)))))))
(Thas_type_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((V0 @ ((cVar @ V3) @ V4)) @ V4)))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ (cEqual @ V3)) @ ((cFun @ V3) @ ((cFun @ V3) @ cBool)))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ (cSelect @ V3)) @ ((cFun @ ((cFun @ V3) @ cBool)) @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ ((cFun @ V5) @ V6))) @ ((V0 @ V4) @ V5))) @ ((V0 @ ((cComb @ V3) @ V4)) @ V6))))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((V0 @ V5) @ V6)) @ ((V0 @ (((cAbs @ V3) @ V4) @ V5)) @ ((cFun @ V4) @ V6)))))))))))))))) @ ((c==> @ ((chas_type @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))
(Tterm_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (V0 @ ((cVar @ V2) @ V3))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cEqual @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cSelect @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cComb @ V2) @ V3)))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (V0 @ V4)) @ (V0 @ (((cAbs @ V2) @ V3) @ V4)))))))))))))) @ (V0 @ V1)))))))
(Tresult_RECURSION,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: ((c= @ (V2 @ (cClash @ V3))) @ (V0 @ V3))))) @ (c! @ (^[V3]: ((c= @ (V2 @ (cResult @ V3))) @ (V1 @ V3))))))))))))
(Tsum_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cINL @ V2))))) @ (c! @ (^[V2]: (V0 @ (cINR @ V2)))))) @ (V0 @ V1)))))))
(TEXISTS_SUM_THM,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ ((c__caret__/ @ (c? @ (^[V1]: (V0 @ (cINL @ V1))))) @ (c? @ (^[V1]: (V0 @ (cINR @ V1)))))))))
(TFORALL_SUM_THM,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ ((c/__caret__ @ (c! @ (^[V1]: (V0 @ (cINL @ V1))))) @ (c! @ (^[V1]: (V0 @ (cINR @ V1)))))))))
(Tstring_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (V0 @ (cString @ V2))))) @ (V0 @ V1)))))))
(Tsetlevel_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cUr_bool)) @ ((c/__caret__ @ (V0 @ cUr_ind)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cPowerset @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cCartprod @ V2) @ V3))))))))))) @ (V0 @ V1)))))))
(Tresult_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cClash @ V2))))) @ (c! @ (^[V2]: (V0 @ (cResult @ V2)))))) @ (V0 @ V1)))))))
(TCONSTR_IND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cBOTTOM)) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: (V0 @ (V4 @ V5))))) @ (V0 @ (((cCONSTR @ V2) @ V3) @ V4))))))))))) @ (V0 @ V1)))))))
(TPOLYFUN_N_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c? @ (^[V3]: (c! @ (^[V4]: ((c= @ (V0 @ V4)) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V5]: ((creal_mul @ (V3 @ V5)) @ ((creal_pow @ V4) @ V5)))))))))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c= @ (V1 @ V4)) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V5]: ((creal_mul @ (V3 @ V5)) @ ((creal_pow @ V4) @ V5))))))))))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c= @ ((creal_add @ (V0 @ V4)) @ (V1 @ V4))) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V5]: ((creal_mul @ (V3 @ V5)) @ ((creal_pow @ V4) @ V5)))))))))))))))))
(TREAL_WLOG_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ V3) @ V3)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((creal_lt @ V3) @ V4)) @ ((V0 @ V3) @ V4))))))))) @ ((V0 @ V1) @ V2)))))))))
(TREAL_WLOG_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((creal_le @ V3) @ V4)) @ ((V0 @ V3) @ V4)))))))) @ ((V0 @ V1) @ V2)))))))))
(TREAL_SUP_EQ_INF,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_abs @ V2)) @ V1)))))))) @ ((c= @ ((c= @ (csup @ V0)) @ (cinf @ V0))) @ (c? @ (^[V1]: ((c= @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))))
(TSUP_conjunct0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1)))))))) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((creal_le @ V1) @ (csup @ V0)))))))))
(TSUP_conjunct1,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1)))))))) @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1))))) @ ((creal_le @ (csup @ V0)) @ V1))))))))
(TINF_conjunct0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2)))))))) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((creal_le @ (cinf @ V0)) @ V1))))))))
(TINF_conjunct1,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2)))))))) @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2))))) @ ((creal_le @ V1) @ (cinf @ V0)))))))))
(TREAL_COMPACT_ATTAINS_SUP,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (creal_compact @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1)))))))))))
(TREAL_COMPACT_ATTAINS_INF,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (creal_compact @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2)))))))))))
(TCOMPACT_ATTAINS_SUP,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (ccompact @ ((cIMAGE @ clift) @ V0))) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1)))))))))))
(TCOMPACT_ATTAINS_INF,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (ccompact @ ((cIMAGE @ clift) @ V0))) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2)))))))))))
(TBOUNDED_HAS_INF_conjunct0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ ((cIMAGE @ clift) @ V0))) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((creal_le @ (cinf @ V0)) @ V1))))))))
(TBOUNDED_HAS_SUP_conjunct0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ ((cIMAGE @ clift) @ V0))) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((creal_le @ V1) @ (csup @ V0)))))))))
(TBOUNDED_HAS_SUP_conjunct1,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ ((cIMAGE @ clift) @ V0))) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1))))) @ ((creal_le @ (csup @ V0)) @ V1))))))))
(TBOUNDED_HAS_INF_conjunct1,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ ((cIMAGE @ clift) @ V0))) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2))))) @ ((creal_le @ V1) @ (cinf @ V0)))))))))
(TSUP_FINITE_conjunct0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((cIN @ (csup @ V0)) @ V0)))))
(TINF_FINITE_conjunct0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((cIN @ (cinf @ V0)) @ V0)))))
(TSUP_FINITE_LEMMA,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1)))))))))))
(TINF_FINITE_LEMMA,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2)))))))))))
(TINF_FINITE_conjunct1,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((creal_le @ (cinf @ V0)) @ V1))))))))
(TSUP_FINITE_conjunct1,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((creal_le @ V1) @ (csup @ V0)))))))))
(TREAL_COMPLETE_SOMEPOS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c? @ (^[V1]: ((c/__caret__ @ (V0 @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((creal_le @ V2) @ V1)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((creal_le @ V2) @ V1))))) @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((creal_le @ V3) @ V2))))) @ ((creal_le @ V1) @ V2)))))))))))
(TREAL_SUP_EXISTS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((creal_lt @ V2) @ V1)))))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ (V0 @ V3)) @ ((creal_lt @ V2) @ V3))))) @ ((creal_lt @ V2) @ V1))))))))))
(TREAL_COMPLETE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((creal_le @ V2) @ V1)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((creal_le @ V2) @ V1))))) @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((creal_le @ V3) @ V2))))) @ ((creal_le @ V1) @ V2)))))))))))
(TREAL_COMPACT_IMP_CLOSED,(c! @ (^[V0]: ((c==> @ (creal_compact @ V0)) @ (creal_closed @ V0)))))
(TREAL_COMPACT_IMP_BOUNDED,(c! @ (^[V0]: ((c==> @ (creal_compact @ V0)) @ (creal_bounded @ V0)))))
(Tsup_def,(c! @ (^[V0]: ((c= @ (csup @ V0)) @ (c__at__ @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1))))) @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V3) @ V2))))) @ ((creal_le @ V1) @ V2)))))))))))
(Tsup,(c! @ (^[V0]: ((c= @ (csup @ V0)) @ (c__at__ @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ (V0 @ V3)) @ ((creal_lt @ V2) @ V3))))) @ ((creal_lt @ V2) @ V1))))))))))
(Tinf,(c! @ (^[V0]: ((c= @ (cinf @ V0)) @ (c__at__ @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2))))) @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V2) @ V3))))) @ ((creal_le @ V2) @ V1)))))))))))
(TIMAGE_LIFT_DROP_conjunct1,(c! @ (^[V0]: ((c= @ ((cIMAGE @ ((co @ cdrop) @ clift)) @ V0)) @ V0))))
(TTOPSPACE_EUCLIDEANREAL_SUBTOPOLOGY,(c! @ (^[V0]: ((c= @ (ctopspace @ ((csubtopology @ ceuclideanreal) @ V0))) @ V0))))
(TSETOK_LE_LT,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((creal_le @ V2) @ V1)))))))) @ ((c/__caret__ @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((creal_lt @ V2) @ V1)))))))))))
(TREAL_OPEN_IN,(c! @ (^[V0]: ((c= @ (creal_open @ V0)) @ ((copen_in @ ceuclideanreal) @ V0)))))
(TREAL_OPEN_REAL_CLOSED,(c! @ (^[V0]: ((c= @ (creal_open @ V0)) @ (creal_closed @ ((cDIFF @ cUNIV) @ V0))))))
(TREAL_OPEN,(c! @ (^[V0]: ((c= @ (creal_open @ V0)) @ (copen @ ((cIMAGE @ clift) @ V0))))))
(Treal_open,(c! @ (^[V0]: ((c= @ (creal_open @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_abs @ ((creal_sub @ V3) @ V1))) @ V2)) @ ((cIN @ V3) @ V0))))))))))))))
(TREAL_OPEN_SUBREAL_OPEN,(c! @ (^[V0]: ((c= @ (creal_open @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (creal_open @ V2)) @ ((c/__caret__ @ ((cIN @ V1) @ V2)) @ ((cSUBSET @ V2) @ V0))))))))))))
(TREAL_COMPACT_EQ_BOUNDED_CLOSED,(c! @ (^[V0]: ((c= @ (creal_compact @ V0)) @ ((c/__caret__ @ (creal_bounded @ V0)) @ (creal_closed @ V0))))))
(Treal_compact,(c! @ (^[V0]: ((c= @ (creal_compact @ V0)) @ (ccompact @ ((cIMAGE @ clift) @ V0))))))
(TREAL_CLOSED_IN,(c! @ (^[V0]: ((c= @ (creal_closed @ V0)) @ ((cclosed_in @ ceuclideanreal) @ V0)))))
(Treal_closed,(c! @ (^[V0]: ((c= @ (creal_closed @ V0)) @ (creal_open @ ((cDIFF @ cUNIV) @ V0))))))
(TREAL_CLOSED,(c! @ (^[V0]: ((c= @ (creal_closed @ V0)) @ (cclosed @ ((cIMAGE @ clift) @ V0))))))
(TREAL_BOUNDED,(c! @ (^[V0]: ((c= @ (creal_bounded @ V0)) @ (cbounded @ ((cIMAGE @ clift) @ V0))))))
(TREAL_BOUNDED_POS_LT,(c! @ (^[V0]: ((c= @ (creal_bounded @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_lt @ (creal_abs @ V2)) @ V1)))))))))))
(TREAL_BOUNDED_POS,(c! @ (^[V0]: ((c= @ (creal_bounded @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_abs @ V2)) @ V1)))))))))))
(Treal_bounded,(c! @ (^[V0]: ((c= @ (creal_bounded @ V0)) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_abs @ V2)) @ V1))))))))))
(TOPEN_LIFT,(c! @ (^[V0]: ((c= @ (copen @ ((cIMAGE @ clift) @ V0))) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_abs @ ((creal_sub @ V3) @ V1))) @ V2)) @ ((cIN @ V3) @ V0))))))))))))))
(TCLOSED_LIFT,(c! @ (^[V0]: ((c= @ (cclosed @ ((cIMAGE @ clift) @ V0))) @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V1))) @ ((creal_lt @ (creal_abs @ ((creal_sub @ V3) @ V1))) @ V2))))))))) @ ((cIN @ V1) @ V0))))))))
(TBOUNDED_LIFT,(c! @ (^[V0]: ((c= @ (cbounded @ ((cIMAGE @ clift) @ V0))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_abs @ V2)) @ V1))))))))))
(TEXISTS_DROP,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (V0 @ (cdrop @ V1))))))))
(TFORALL_DROP,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (V0 @ (cdrop @ V1))))))))
(TREAL_SUP_LE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V3) @ V2)))))))) @ ((c= @ ((creal_le @ (csup @ V0)) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1)))))))))))
(TREAL_LE_INF_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V2) @ V3)))))))) @ ((c= @ ((creal_le @ V1) @ (cinf @ V0))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2)))))))))))
(TREAL_ABS_SUP_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_abs @ V2)) @ V1)))))) @ ((creal_le @ (creal_abs @ (csup @ V0))) @ V1)))))))
(TREAL_ABS_INF_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_abs @ V2)) @ V1)))))) @ ((creal_le @ (creal_abs @ (cinf @ V0))) @ V1)))))))
(TREAL_SUP_LT_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((creal_lt @ (csup @ V0)) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_lt @ V2) @ V1)))))))))))
(TREAL_INF_LT_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((creal_lt @ (cinf @ V0)) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((creal_lt @ V2) @ V1)))))))))))
(TREAL_LT_SUP_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((creal_lt @ V1) @ (csup @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((creal_lt @ V1) @ V2)))))))))))
(TREAL_LT_INF_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((creal_lt @ V1) @ (cinf @ V0))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_lt @ V1) @ V2)))))))))))
(TREAL_SUP_LE_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((creal_le @ (csup @ V0)) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1)))))))))))
(TREAL_INF_LE_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((creal_le @ (cinf @ V0)) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1)))))))))))
(TREAL_LE_SUP_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((creal_le @ V1) @ (csup @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2)))))))))))
(TREAL_LE_INF_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((creal_le @ V1) @ (cinf @ V0))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2)))))))))))
(TSUP_UNIQUE_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((c= @ (csup @ V0)) @ V1)) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1))))))))))))
(TINF_UNIQUE_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((c= @ (cinf @ V0)) @ V1)) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2))))))))))))
(TREAL_SUP_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V2) @ V1))))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ V2) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((creal_lt @ V2) @ V3))))))))) @ ((c= @ (csup @ V0)) @ V1)))))))
(TREAL_INF_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ V1) @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ V1) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((creal_lt @ V3) @ V2))))))))) @ ((c= @ (cinf @ V0)) @ V1)))))))
(Tradical_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (crational @ V2)) @ (V0 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (creal_neg @ V2)))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (c~ @ ((c= @ V2) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ (V0 @ (creal_inv @ V2)))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((creal_add @ V2) @ V3)))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((creal_mul @ V2) @ V3)))))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2))) @ (V0 @ (csqrt @ V2))))))))))) @ ((c==> @ (cradical @ V1)) @ (V0 @ V1))))))))
(TFORALL_POS_MONO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ V2) @ V3)) @ (V0 @ V2))) @ (V0 @ V3))))))) @ (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ (V0 @ (creal_inv @ (creal_of_num @ V2)))))))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (V0 @ V1))))))))
(TFORALL_POS_MONO_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ V2) @ V3)) @ (V0 @ V2))) @ (V0 @ V3))))))) @ (c! @ (^[V2]: (V0 @ (creal_inv @ ((creal_add @ (creal_of_num @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (V0 @ V1))))))))
(TFORALL_INTEGER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (creal_of_num @ V2))))) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (creal_neg @ V2))))))) @ ((c==> @ (cinteger @ V1)) @ (V0 @ V1))))))))
(TSUP_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V3) @ V2))))) @ ((creal_le @ V1) @ V2))))) @ ((c= @ (csup @ V0)) @ V1)))))))
(TINF_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V2) @ V3))))) @ ((creal_le @ V2) @ V1))))) @ ((c= @ (cinf @ V0)) @ V1)))))))
(TLIMPT_APPROACHABLE_LIFT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((climit_point_of @ (clift @ V1)) @ ((cIMAGE @ clift) @ V0))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V1))) @ ((creal_lt @ (creal_abs @ ((creal_sub @ V3) @ V1))) @ V2))))))))))))))
(TCOSMALL_APPROXIMATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<_c @ ((cDIFF @ cUNIV) @ V0)) @ cUNIV)) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((creal_lt @ (creal_abs @ ((creal_sub @ V3) @ V1))) @ V2)))))))))))))
(TREAL_SUP_ASCLOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (creal_abs @ ((creal_sub @ V3) @ V1))) @ V2)))))) @ ((creal_le @ (creal_abs @ ((creal_sub @ (csup @ V0)) @ V1))) @ V2)))))))))
(TREAL_INF_ASCLOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (creal_abs @ ((creal_sub @ V3) @ V1))) @ V2)))))) @ ((creal_le @ (creal_abs @ ((creal_sub @ (cinf @ V0)) @ V1))) @ V2)))))))))
(TCOCOUNTABLE_APPROXIMATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cCOUNTABLE @ ((cDIFF @ cUNIV) @ V0))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((creal_lt @ (creal_abs @ ((creal_sub @ V3) @ V1))) @ V2)))))))))))))
(TREAL_LE_INF_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V2) @ V3))))))))) @ ((creal_le @ (cinf @ V0)) @ (cinf @ V1))))))))
(TREAL_SUP_LE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ V3) @ V2))))))))) @ ((creal_le @ (csup @ V0)) @ (csup @ V1))))))))
(TSUP_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V3) @ V2))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ V3) @ V2)))))))))) @ ((c= @ (csup @ ((cUNION @ V0) @ V1))) @ ((creal_max @ (csup @ V0)) @ (csup @ V1)))))))))
(TINF_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V2) @ V3))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ V2) @ V3)))))))))) @ ((c= @ (cinf @ ((cUNION @ V0) @ V1))) @ ((creal_min @ (cinf @ V0)) @ (cinf @ V1)))))))))
(TREAL_OPEN_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (creal_open @ V0)) @ (creal_open @ V1))) @ (creal_open @ ((cUNION @ V0) @ V1))))))))
(TREAL_OPEN_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (creal_open @ V0)) @ (creal_open @ V1))) @ (creal_open @ ((cINTER @ V0) @ V1))))))))
(TREAL_OPEN_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (creal_open @ V0)) @ (creal_closed @ V1))) @ (creal_open @ ((cDIFF @ V0) @ V1))))))))
(TREAL_COMPACT_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (creal_compact @ V0)) @ (creal_compact @ V1))) @ (creal_compact @ ((cUNION @ V0) @ V1))))))))
(TREAL_CLOSED_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (creal_closed @ V0)) @ (creal_open @ V1))) @ (creal_closed @ ((cDIFF @ V0) @ V1))))))))
(TREAL_CLOSED_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (creal_closed @ V0)) @ (creal_closed @ V1))) @ (creal_closed @ ((cUNION @ V0) @ V1))))))))
(TREAL_CLOSED_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (creal_closed @ V0)) @ (creal_closed @ V1))) @ (creal_closed @ ((cINTER @ V0) @ V1))))))))
(TREAL_BOUNDED_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (creal_bounded @ V0)) @ ((cSUBSET @ V1) @ V0))) @ (creal_bounded @ V1)))))))
(TSUP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V3) @ V2))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ V3) @ V2)))))))) @ ((c= @ (csup @ V0)) @ (csup @ V1))))))))
(TINF_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V2) @ V3))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ V2) @ V3)))))))) @ ((c= @ (cinf @ V0)) @ (cinf @ V1))))))))
(TSUBSET_LIFT_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cSUBSET @ ((cIMAGE @ clift) @ V0)) @ ((cIMAGE @ clift) @ V1))) @ ((cSUBSET @ V0) @ V1)))))))
(TREAL_BOUNDED_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (creal_bounded @ ((cUNION @ V0) @ V1))) @ ((c/__caret__ @ (creal_bounded @ V0)) @ (creal_bounded @ V1))))))))
(TPRODUCT_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (V0 @ V4))) @ (V0 @ ((creal_mul @ V3) @ V4)))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (V0 @ (V2 @ V3)))))))) @ (V0 @ ((cproduct @ V1) @ V2))))))))))
(TSUM_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (V0 @ V4))) @ (V0 @ ((creal_add @ V3) @ V4)))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (V0 @ (V2 @ V3)))))))) @ (V0 @ ((csum @ V1) @ V2))))))))))
(Texpression_RECURSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ (c! @ (^[V7]: ((c= @ (V6 @ (cConstant @ V7))) @ (V0 @ V7))))) @ ((c/__caret__ @ (c! @ (^[V7]: ((c= @ (V6 @ (cNegation @ V7))) @ ((V1 @ V7) @ (V6 @ V7)))))) @ ((c/__caret__ @ (c! @ (^[V7]: ((c= @ (V6 @ (cInverse @ V7))) @ ((V2 @ V7) @ (V6 @ V7)))))) @ ((c/__caret__ @ (c! @ (^[V7]: (c! @ (^[V8]: ((c= @ (V6 @ ((cAddition @ V7) @ V8))) @ ((((V3 @ V7) @ V8) @ (V6 @ V7)) @ (V6 @ V8)))))))) @ ((c/__caret__ @ (c! @ (^[V7]: (c! @ (^[V8]: ((c= @ (V6 @ ((cMultiplication @ V7) @ V8))) @ ((((V4 @ V7) @ V8) @ (V6 @ V7)) @ (V6 @ V8)))))))) @ (c! @ (^[V7]: ((c= @ (V6 @ (cSqrt @ V7))) @ ((V5 @ V7) @ (V6 @ V7)))))))))))))))))))))))))
(Tquat_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cX)) @ ((c/__caret__ @ (V0 @ cZERO)) @ ((c/__caret__ @ (V0 @ cONE)) @ (V0 @ cTOP))))) @ (V0 @ V1)))))))
(Tpropform_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (V0 @ (cPropform @ V2))))) @ (V0 @ V1)))))))
(TPASSOC_DEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cPASSOC @ V0) @ ((c__comma__ @ V1) @ ((c__comma__ @ V2) @ V3)))) @ (V0 @ ((c__comma__ @ ((c__comma__ @ V1) @ V2)) @ V3))))))))))))
(Teulerian_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cvertices @ V4))) @ ((c= @ (cedges @ V4)) @ cEMPTY))) @ (((V0 @ V4) @ cNIL) @ ((c__comma__ @ V5) @ V5)))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((cIN @ V8) @ (cedges @ V4))) @ ((c/__caret__ @ (((cconnects @ V4) @ V8) @ ((c__comma__ @ V5) @ V6))) @ (((V0 @ ((cdelete_edge @ V8) @ V4)) @ V9) @ ((c__comma__ @ V6) @ V7))))) @ (((V0 @ V4) @ ((cCONS @ V8) @ V9)) @ ((c__comma__ @ V5) @ V7))))))))))))))))) @ ((c==> @ (((ceulerian @ V1) @ V2) @ V3)) @ (((V0 @ V1) @ V2) @ V3))))))))))))
(TADDITIVE_TAGGED_DIVISION_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V1))) @ ((ctagged_division_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V1)) @ cNIL))))) @ ((c= @ ((cvsum @ V0) @ (cGABS @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((cGEQ @ (V4 @ ((c__comma__ @ V5) @ V6))) @ ((cvector_sub @ (V2 @ (cinterval_upperbound @ V6))) @ (V2 @ (cinterval_lowerbound @ V6)))))))))))) @ ((cvector_sub @ (V2 @ V1)) @ (V2 @ V3)))))))))))))
(THYPERPLANE_CELLCOMPLEX_UNIV,(c! @ (^[V0]: ((chyperplane_cellcomplex @ V0) @ cUNIV))))
(THYPERPLANE_CELLCOMPLEX_EMPTY,(c! @ (^[V0]: ((chyperplane_cellcomplex @ V0) @ cEMPTY))))
(TFINITE_HYPERPLANE_CELLCOMPLEXES,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((chyperplane_cellcomplex @ V0) @ V2)) @ V2))))))))))
(TFINITE_HYPERPLANE_CELLS,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((chyperplane_cell @ V0) @ V2)) @ V2))))))))))
(TUNIONS_HYPERPLANE_CELLS,(c! @ (^[V0]: ((c= @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((chyperplane_cell @ V0) @ V2)) @ V2))))))) @ cUNIV))))
(THYPERPLANE_CELLCOMPLEX_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chyperplane_cellcomplex @ V0) @ V2)) @ ((cSUBSET @ V0) @ V1))) @ ((chyperplane_cellcomplex @ V1) @ V2)))))))))
(THYPERPLANE_CELL_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chyperplane_cell @ ((cUNION @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((chyperplane_cell @ V0) @ V3)) @ ((c/__caret__ @ ((chyperplane_cell @ V1) @ V4)) @ ((c= @ V2) @ ((cINTER @ V3) @ V4)))))))))))))))))
(TFINITE_SET_OF_HYPERPLANE_CELLS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((chyperplane_cellcomplex @ V0) @ V2)))))) @ (cFINITE @ V1)))))))
(THYPERPLANE_CELL_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((chyperplane_cell @ V0) @ V2))))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY))))) @ ((chyperplane_cell @ V0) @ (cINTERS @ V1))))))))
(TFINITE_RESTRICT_HYPERPLANE_CELLCOMPLEXES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((chyperplane_cellcomplex @ V0) @ V3)) @ (V1 @ V3))) @ V3))))))))))))
(TFINITE_RESTRICT_HYPERPLANE_CELLS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((chyperplane_cell @ V0) @ V3)) @ (V1 @ V3))) @ V3))))))))))))
(THYPERPLANE_CELLCOMPLEX_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((chyperplane_cellcomplex @ V0) @ V2))))) @ ((chyperplane_cellcomplex @ V0) @ (cUNIONS @ V1))))))))
(THYPERPLANE_CELLCOMPLEX_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((chyperplane_cellcomplex @ V0) @ V2))))) @ ((chyperplane_cellcomplex @ V0) @ (cINTERS @ V1))))))))
(THYPERPLANE_CELLCOMPLEX_COMPL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chyperplane_cellcomplex @ V0) @ V1)) @ ((chyperplane_cellcomplex @ V0) @ ((cDIFF @ cUNIV) @ V1))))))))
(THYPERPLANE_CELL_CELLCOMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chyperplane_cell @ V0) @ V1)) @ ((chyperplane_cellcomplex @ V0) @ V1)))))))
(THYPERPLANE_CELL_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chyperplane_cell @ V0) @ V1)) @ (cconvex @ V1)))))))
(THYPERPLANE_CELL_RELATIVELY_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((chyperplane_cell @ V0) @ V1))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((chull @ caffine) @ V1))) @ V1)))))))
(THYPERPLANE_CELL_RELATIVE_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((chyperplane_cell @ V0) @ V1))) @ ((c= @ (crelative_interior @ V1)) @ V1)))))))
(THYPERPLANE_CELL_INTER_OPEN_AFFINE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((chyperplane_cell @ V0) @ V1))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ (caffine @ V3)) @ ((c= @ V1) @ ((cINTER @ V2) @ V3))))))))))))))
(Teuler_characteristic,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ceuler_characteristic @ V0) @ V1)) @ ((csum @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((chyperplane_cell @ V0) @ V3)) @ ((cSUBSET @ V3) @ V1))) @ V3)))))) @ (^[V2]: ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cnum_of_int @ (caff_dim @ V2)))))))))))
(TCELL_SUBSET_CELLCOMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chyperplane_cell @ V0) @ V1)) @ ((chyperplane_cellcomplex @ V0) @ V2))) @ ((c= @ ((cSUBSET @ V1) @ V2)) @ (c~ @ ((cDISJOINT @ V1) @ V2)))))))))))
(THYPERPLANE_CELL_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chyperplane_cell @ V0) @ V1)) @ ((c/__caret__ @ ((chyperplane_cell @ V0) @ V2)) @ (c~ @ ((c= @ ((cINTER @ V1) @ V2)) @ cEMPTY))))) @ ((chyperplane_cell @ V0) @ ((cINTER @ V1) @ V2))))))))))
(TTAGGED_DIVISION_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V0) @ V2)) @ ((c/__caret__ @ ((ctagged_division_of @ V1) @ V3)) @ ((c= @ ((cINTER @ (cinterior @ V2)) @ (cinterior @ V3))) @ cEMPTY)))) @ ((ctagged_division_of @ ((cUNION @ V0) @ V1)) @ ((cUNION @ V2) @ V3))))))))))))
(TADDITIVE_CONTENT_TAGGED_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ctagged_division_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c= @ ((csum @ V0) @ (cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ (ccontent @ V5)))))))))) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))
(TTAGGED_DIVISION_OF_NONTRIVIAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (c~ @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((ctagged_division_of @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ ((c__comma__ @ V4) @ V5)) @ V0)) @ (c~ @ ((c= @ (ccontent @ V5)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((c__comma__ @ V4) @ V5))))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TRSUM_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ ((creal_le @ (cvector_norm @ (V1 @ V5))) @ V2)))))) @ ((creal_le @ (cvector_norm @ ((cvsum @ V0) @ (cGABS @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((cGEQ @ (V5 @ ((c__comma__ @ V6) @ V7))) @ ((c% @ (ccontent @ V7)) @ (V1 @ V6)))))))))))) @ ((creal_mul @ V2) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))))
(THAS_INTEGRAL_COMBINE_TAGGED_DIVISION_TOPDOWN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((ctagged_division_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ (((chas_integral @ V1) @ ((cvsum @ V0) @ (cGABS @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((cGEQ @ (V4 @ ((c__comma__ @ V5) @ V6))) @ ((cintegral @ V6) @ V1)))))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(THYPERPLANE_CELLCOMPLEX_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chyperplane_cellcomplex @ V0) @ V1)) @ ((chyperplane_cellcomplex @ V0) @ V2))) @ ((chyperplane_cellcomplex @ V0) @ ((cDIFF @ V1) @ V2))))))))))
(THYPERPLANE_CELLCOMPLEX_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chyperplane_cellcomplex @ V0) @ V1)) @ ((chyperplane_cellcomplex @ V0) @ V2))) @ ((chyperplane_cellcomplex @ V0) @ ((cINTER @ V1) @ V2))))))))))
(THYPERPLANE_CELLCOMPLEX_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chyperplane_cellcomplex @ V0) @ V1)) @ ((chyperplane_cellcomplex @ V0) @ V2))) @ ((chyperplane_cellcomplex @ V0) @ ((cUNION @ V1) @ V2))))))))))
(Thyperplane_cellcomplex,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chyperplane_cellcomplex @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((chyperplane_cell @ V0) @ V3))))) @ ((c= @ V1) @ (cUNIONS @ V2)))))))))))
(TPAIRWISE_DISJOINT_HYPERPLANE_CELLS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((chyperplane_cell @ V0) @ V2))))) @ ((cpairwise @ cDISJOINT) @ V1)))))))
(TDISJOINT_HYPERPLANE_CELLS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chyperplane_cell @ V0) @ V1)) @ ((chyperplane_cell @ V0) @ V2))) @ ((c= @ ((cDISJOINT @ V1) @ V2)) @ (c~ @ ((c= @ V1) @ V2)))))))))))
(TDISJOINT_HYPERPLANE_CELLS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chyperplane_cell @ V0) @ V1)) @ ((c/__caret__ @ ((chyperplane_cell @ V0) @ V2)) @ (c~ @ ((c= @ V1) @ V2))))) @ ((cDISJOINT @ V1) @ V2)))))))))
(TNONEMPTY_HYPERPLANE_CELL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chyperplane_cell @ V0) @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY))))))))
(TNOT_HYPERPLANE_CELL_EMPTY,(c! @ (^[V0]: (c~ @ ((chyperplane_cell @ V0) @ cEMPTY)))))
(THYPERPLANE_EQUIV_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((chyperplane_equiv @ ((cUNION @ V0) @ V1)) @ V2) @ V3)) @ ((c/__caret__ @ (((chyperplane_equiv @ V0) @ V2) @ V3)) @ (((chyperplane_equiv @ V1) @ V2) @ V3))))))))))))
(THYPERPLANE_EQUIV_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chyperplane_equiv @ V0) @ V2) @ V1)) @ (((chyperplane_equiv @ V0) @ V1) @ V2)))))))))
(THYPERPLANE_EQUIV_REFL,(c! @ (^[V0]: (c! @ (^[V1]: (((chyperplane_equiv @ V0) @ V1) @ V1))))))
(Thyperplane_equiv,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chyperplane_equiv @ V0) @ V1) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ ((chyperplane_side @ V3) @ V1)) @ ((chyperplane_side @ V3) @ V2)))))))))))))
(TTAGGED_DIVISION_OF_TRIVIAL,(c! @ (^[V0]: ((c= @ ((ctagged_division_of @ V0) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TTAGGED_PARTIAL_DIVISION_OF_TRIVIAL,(c! @ (^[V0]: ((c= @ ((ctagged_partial_division_of @ V0) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TTAGGED_PARTIAL_DIVISION_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ctagged_partial_division_of @ V0) @ V2)) @ ((cSUBSET @ V1) @ V0))) @ ((ctagged_partial_division_of @ V1) @ V2)))))))))
(TDIVISION_OF_TAGGED_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ctagged_division_of @ V0) @ V1)) @ ((cdivision_of @ ((cIMAGE @ cSND) @ V0)) @ V1)))))))
(TTAGGED_DIVISION_OF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ctagged_division_of @ V0) @ V1)) @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ ((c__comma__ @ V2) @ V3)) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V1)) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c= @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))))))))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ ((c__comma__ @ V2) @ V3)) @ V0)) @ ((c/__caret__ @ ((cIN @ ((c__comma__ @ V4) @ V5)) @ V0)) @ (c~ @ ((c= @ ((c__comma__ @ V2) @ V3)) @ ((c__comma__ @ V4) @ V5)))))) @ ((c= @ ((cINTER @ (cinterior @ V3)) @ (cinterior @ V5))) @ cEMPTY))))))))))) @ ((c= @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((cIN @ ((c__comma__ @ V4) @ V3)) @ V0)))) @ V3))))))) @ V1))))))))))
(Ttagged_division_of,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ctagged_division_of @ V0) @ V1)) @ ((c/__caret__ @ ((ctagged_partial_division_of @ V0) @ V1)) @ ((c= @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((cIN @ ((c__comma__ @ V4) @ V3)) @ V0)))) @ V3))))))) @ V1))))))))
(TPAIRED_EXT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (V0 @ ((c__comma__ @ V2) @ V3))) @ (V1 @ ((c__comma__ @ V2) @ V3)))))))) @ ((c= @ V0) @ V1)))))))
(TCURRY_DEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cCURRY @ V0) @ V1) @ V2)) @ (V0 @ ((c__comma__ @ V1) @ V2))))))))))
(TZL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cposet @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cchain @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cfl @ V0) @ V2)) @ (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ (V0 @ ((c__comma__ @ V3) @ V2))))))))))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cfl @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ (V0 @ ((c__comma__ @ V1) @ V2))) @ ((c= @ V1) @ V2)))))))))))
(TORDINAL_SUC,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cordinal @ V0)) @ (c? @ (^[V1]: (c~ @ ((cfl @ V0) @ V1)))))) @ (cordinal @ (cGABS @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((cGEQ @ (V1 @ ((c__comma__ @ V2) @ V3))) @ ((c__caret__/ @ (V0 @ ((c__comma__ @ V2) @ V3))) @ ((c/__caret__ @ ((c= @ V3) @ (c__at__ @ (^[V4]: (c~ @ ((cfl @ V0) @ V4)))))) @ ((c__caret__/ @ ((cfl @ V0) @ V2)) @ ((c= @ V2) @ (c__at__ @ (^[V4]: (c~ @ ((cfl @ V0) @ V4))))))))))))))))))))
(TWOSET_POSET,(c! @ (^[V0]: ((c==> @ (cwoset @ V0)) @ (cposet @ V0)))))
(TOEP,(c! @ (^[V0]: ((c==> @ (cposet @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (ctoset @ V1)) @ ((c/__caret__ @ ((c= @ (cfl @ V1)) @ (cfl @ V0))) @ ((cSUBSET @ V0) @ V1)))))))))
(THP,(c! @ (^[V0]: ((c==> @ (cposet @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((cchain @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cchain @ V0) @ V2)) @ ((cSUBSET @ V1) @ V2))) @ ((c= @ V2) @ V1)))))))))))
(TORDINAL_UP,(c! @ (^[V0]: ((c==> @ (cordinal @ V0)) @ ((c__caret__/ @ (c! @ (^[V1]: ((cfl @ V0) @ V1)))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cordinal @ V1)) @ ((c/__caret__ @ ((cfl @ V1) @ V2)) @ (c~ @ ((cfl @ V0) @ V2)))))))))))))
(Twoset,(c! @ (^[V0]: ((c= @ (cwoset @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cfl @ V0) @ V1)) @ (V0 @ ((c__comma__ @ V1) @ V1)))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ ((c__comma__ @ V1) @ V2))) @ (V0 @ ((c__comma__ @ V2) @ V3)))) @ (V0 @ ((c__comma__ @ V1) @ V3)))))))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ ((c__comma__ @ V1) @ V2))) @ (V0 @ ((c__comma__ @ V2) @ V1)))) @ ((c= @ V1) @ V2))))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cfl @ V0) @ V1)) @ ((cfl @ V0) @ V2))) @ ((c__caret__/ @ (V0 @ ((c__comma__ @ V1) @ V2))) @ (V0 @ ((c__comma__ @ V2) @ V1))))))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V1 @ V2)) @ ((cfl @ V0) @ V2))))) @ (c? @ (^[V2]: (V1 @ V2))))) @ (c? @ (^[V2]: ((c/__caret__ @ (V1 @ V2)) @ (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ (V0 @ ((c__comma__ @ V2) @ V3)))))))))))))))))))
(TWOSET,(c! @ (^[V0]: ((c= @ (cwoset @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ ((c__comma__ @ V1) @ V2))) @ (V0 @ ((c__comma__ @ V2) @ V1)))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V1 @ V2)) @ ((cfl @ V0) @ V2))))) @ (c? @ (^[V2]: (V1 @ V2))))) @ (c? @ (^[V2]: ((c/__caret__ @ (V1 @ V2)) @ (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ (V0 @ ((c__comma__ @ V2) @ V3))))))))))))))))
(Ttoset,(c! @ (^[V0]: ((c= @ (ctoset @ V0)) @ ((c/__caret__ @ (cposet @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ (cfl @ V0))) @ ((cIN @ V2) @ (cfl @ V0)))) @ ((c__caret__/ @ (V0 @ ((c__comma__ @ V1) @ V2))) @ (V0 @ ((c__comma__ @ V2) @ V1)))))))))))))
(Tposet,(c! @ (^[V0]: ((c= @ (cposet @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cfl @ V0) @ V1)) @ (V0 @ ((c__comma__ @ V1) @ V1)))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ ((c__comma__ @ V1) @ V2))) @ (V0 @ ((c__comma__ @ V2) @ V3)))) @ (V0 @ ((c__comma__ @ V1) @ V3)))))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ ((c__comma__ @ V1) @ V2))) @ (V0 @ ((c__comma__ @ V2) @ V1)))) @ ((c= @ V1) @ V2))))))))))))
(Tordinal,(c! @ (^[V0]: ((c= @ (cordinal @ V0)) @ ((c/__caret__ @ (cwoset @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cfl @ V0) @ V1)) @ ((c= @ V1) @ (c__at__ @ (^[V2]: (c~ @ ((cless @ V0) @ ((c__comma__ @ V2) @ V1))))))))))))))
(TINSEG_PROPER_SUBSET_FL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cinseg @ V1) @ V0)) @ (c~ @ ((c= @ V0) @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cfl @ V0) @ V2)) @ (c~ @ ((cfl @ V1) @ V2)))))))))))
(TINSEG_PROPER_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cinseg @ V1) @ V0)) @ (c~ @ ((c= @ V0) @ V1)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (V0 @ ((c__comma__ @ V2) @ V3))) @ (c~ @ (V1 @ ((c__comma__ @ V2) @ V3))))))))))))))
(TINSEG_WOSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cinseg @ V1) @ V0)) @ (cwoset @ V0))) @ (cwoset @ V1)))))))
(TORDINAL_CHAINED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cordinal @ V0)) @ (cordinal @ V1))) @ ((c__caret__/ @ ((cinseg @ V1) @ V0)) @ ((cinseg @ V0) @ V1))))))))
(TINSEG_LINSEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cwoset @ V1)) @ ((c= @ ((cinseg @ V0) @ V1)) @ ((c__caret__/ @ ((c= @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cfl @ V1) @ V2)) @ ((c= @ V0) @ ((clinseg @ V1) @ V2)))))))))))))
(Tinseg,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinseg @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (V1 @ ((c__comma__ @ V2) @ V3))) @ ((c/__caret__ @ (V0 @ ((c__comma__ @ V2) @ V3))) @ ((cfl @ V1) @ V3)))))))))))))
(TORDINAL_CHAINED_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cinseg @ V1) @ V0)) @ ((cinseg @ V1) @ V2))) @ ((c==> @ ((c/__caret__ @ (cordinal @ V0)) @ (cordinal @ V2))) @ ((c__caret__/ @ ((c= @ V1) @ V0)) @ ((c__caret__/ @ ((c= @ V1) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cfl @ V0) @ V3)) @ ((c/__caret__ @ ((cfl @ V2) @ V3)) @ ((c/__caret__ @ ((c= @ V1) @ ((clinseg @ V0) @ V3))) @ ((c= @ V1) @ ((clinseg @ V2) @ V3))))))))))))))))))
(TINSEG_SUBSET_FL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cinseg @ V0) @ V1)) @ ((c==> @ ((cfl @ V0) @ V2)) @ ((cfl @ V1) @ V2))))))))))
(TINSEG_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cinseg @ V0) @ V1)) @ ((c==> @ (V0 @ ((c__comma__ @ V2) @ V3))) @ (V1 @ ((c__comma__ @ V2) @ V3)))))))))))))
(TWOSET_WELL_CONTRAPOS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cwoset @ V0)) @ ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V1 @ V2)) @ ((cfl @ V0) @ V2))))) @ (c? @ (^[V2]: (V1 @ V2))))) @ (c? @ (^[V2]: ((c/__caret__ @ (V1 @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cless @ V0) @ ((c__comma__ @ V3) @ V2))) @ (c~ @ (V1 @ V3)))))))))))))))
(TORDINAL_UNION_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cfl @ V0) @ V1)) @ ((c==> @ (cordinal @ V0)) @ ((cfl @ (cUNIONS @ cordinal)) @ V1))))))))
(TWOSET_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cwoset @ V0)) @ ((c==> @ ((cfl @ V0) @ V1)) @ (V0 @ ((c__comma__ @ V1) @ V1)))))))))
(TWOSET_FLEQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cwoset @ V0)) @ ((c= @ ((cfl @ V0) @ V1)) @ (V0 @ ((c__comma__ @ V1) @ V1)))))))))
(TLINSEG_WOSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cwoset @ V0)) @ (cwoset @ ((clinseg @ V0) @ V1))))))))
(TPOSET_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cposet @ V0)) @ ((c==> @ ((cfl @ V0) @ V1)) @ (V0 @ ((c__comma__ @ V1) @ V1)))))))))
(TPOSET_FLEQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cposet @ V0)) @ ((c= @ ((cfl @ V0) @ V1)) @ (V0 @ ((c__comma__ @ V1) @ V1)))))))))
(Tlinseg,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((clinseg @ V0) @ V1)) @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ ((c/__caret__ @ (V0 @ ((c__comma__ @ V3) @ V4))) @ ((cless @ V0) @ ((c__comma__ @ V4) @ V1))))))))))))))))
(Tfl,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cfl @ V0) @ V1)) @ (c? @ (^[V2]: ((c__caret__/ @ (V0 @ ((c__comma__ @ V1) @ V2))) @ (V0 @ ((c__comma__ @ V2) @ V1)))))))))))
(TWOSET_TOTAL_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cwoset @ V0)) @ ((c==> @ ((c/__caret__ @ ((cfl @ V0) @ V2)) @ ((cfl @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V2) @ V1)) @ ((c__caret__/ @ ((cless @ V0) @ ((c__comma__ @ V2) @ V1))) @ ((cless @ V0) @ ((c__comma__ @ V1) @ V2)))))))))))))
(TWOSET_TOTAL_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cwoset @ V0)) @ ((c==> @ ((c/__caret__ @ ((cfl @ V0) @ V2)) @ ((cfl @ V0) @ V1))) @ ((c__caret__/ @ (V0 @ ((c__comma__ @ V2) @ V1))) @ ((cless @ V0) @ ((c__comma__ @ V1) @ V2))))))))))))
(TWOSET_TOTAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cwoset @ V0)) @ ((c==> @ ((c/__caret__ @ ((cfl @ V0) @ V2)) @ ((cfl @ V0) @ V1))) @ ((c__caret__/ @ (V0 @ ((c__comma__ @ V2) @ V1))) @ (V0 @ ((c__comma__ @ V1) @ V2))))))))))))
(TWOSET_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cwoset @ V0)) @ ((c==> @ ((c/__caret__ @ (V0 @ ((c__comma__ @ V1) @ V2))) @ (V0 @ ((c__comma__ @ V2) @ V1)))) @ ((c= @ V1) @ V2))))))))))
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(TVARIATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3)))))) @ ((c= @ ((cvariation @ V1) @ V0)) @ ((cvariation @ V1) @ V2))))))))))
(TSUMMABLE_COMPARISON,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V1) @ ((co @ clift) @ V0))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c>= @ V4) @ V3)) @ ((cIN @ V4) @ V1))) @ ((creal_le @ (cvector_norm @ (V2 @ V4))) @ (V0 @ V4))))))))) @ ((csummable @ V1) @ V2)))))))))
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(TBASIS_EXPANSION_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V2]: ((c% @ (V0 @ V2)) @ (cbasis @ V2))))) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ (V0 @ V2)) @ ((c$ @ V1) @ V2)))))))))))
(TSTRETCH_GALOIS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (c~ @ ((c= @ (V0 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((c= @ V1) @ (clambda @ (^[V3]: ((creal_mul @ (V0 @ V3)) @ ((c$ @ V2) @ V3)))))) @ ((c= @ (clambda @ (^[V3]: ((creal_mul @ (creal_inv @ (V0 @ V3))) @ ((c$ @ V1) @ V3))))) @ V2))))))))))
(TCONTENT_IMAGE_STRETCH_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (ccontent @ ((cIMAGE @ (^[V3]: (clambda @ (^[V4]: ((creal_mul @ (V0 @ V4)) @ ((c$ @ V3) @ V4)))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))) @ ((creal_mul @ (creal_abs @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ V0))) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))
(TINTERVAL_IMAGE_STRETCH_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ ((cIMAGE @ (^[V5]: (clambda @ (^[V6]: ((creal_mul @ (V0 @ V6)) @ ((c$ @ V5) @ V6)))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))))))
(THAS_MEASURE_IMAGE_STD_SIMPLEX,(c! @ (^[V0]: ((c==> @ ((cpermutes @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((chas_measure @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V2) @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V2) @ (V0 @ (cdimindex @ cUNIV)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c< @ V3) @ (cdimindex @ cUNIV)))) @ ((creal_le @ ((c$ @ V2) @ (V0 @ V3))) @ ((c$ @ V2) @ (V0 @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))) @ V2)))))) @ (cmeasure @ ((chull @ cconvex) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (cbasis @ V2))))))))))))))
(TCONGRUENT_IMAGE_STD_SIMPLEX,(c! @ (^[V0]: ((c==> @ ((cpermutes @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V2) @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V2) @ (V0 @ (cdimindex @ cUNIV)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c< @ V3) @ (cdimindex @ cUNIV)))) @ ((creal_le @ ((c$ @ V2) @ (V0 @ V3))) @ ((c$ @ V2) @ (V0 @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))) @ V2)))))) @ ((cIMAGE @ (^[V1]: (clambda @ (^[V2]: ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((cinverse @ V0) @ V2))) @ (^[V3]: ((c$ @ V1) @ V3))))))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V2) @ V3)))))) @ ((creal_le @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V3]: ((c$ @ V2) @ V3)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ V2)))))))))))
(TMULTIPLICATIVE_1,(c! @ (^[V0]: ((c==> @ (cmultiplicative @ V0)) @ ((c= @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TMULTIPLICATIVE_DIVISORSUM,(c! @ (^[V0]: ((c==> @ (cmultiplicative @ V0)) @ (cmultiplicative @ (^[V1]: ((cnsum @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cnum_divides @ V3) @ V1)) @ V3)))))) @ V0)))))))
(TMULTIPLICATIVE,(c! @ (^[V0]: ((c= @ (cmultiplicative @ V0)) @ ((c/__caret__ @ ((c= @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ (cnum_coprime @ ((c__comma__ @ V1) @ V2))))) @ ((c= @ (V0 @ ((c* @ V1) @ V2))) @ ((c* @ (V0 @ V1)) @ (V0 @ V2)))))))))))))
(Tmultiplicative,(c! @ (^[V0]: ((c= @ (cmultiplicative @ V0)) @ ((c/__caret__ @ ((c= @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnum_coprime @ ((c__comma__ @ V1) @ V2))) @ ((c= @ (V0 @ ((c* @ V1) @ V2))) @ ((c* @ (V0 @ V1)) @ (V0 @ V2)))))))))))))
(Tnadd_rep,(c! @ (^[V0]: ((c= @ (cis_nadd @ V0)) @ ((c= @ (cdest_nadd @ (cmk_nadd @ V0))) @ V0)))))
(Tis_nadd,(c! @ (^[V0]: ((c= @ (cis_nadd @ V0)) @ (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c<= @ (cdist @ ((c__comma__ @ ((c* @ V2) @ (V0 @ V3))) @ ((c* @ V3) @ (V0 @ V2))))) @ ((c* @ V1) @ ((c+ @ V2) @ V3)))))))))))))
(TBOUNDS_DIVIDED,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (c! @ (^[V2]: ((c<= @ (V0 @ V2)) @ V1)))))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: ((c<= @ ((c* @ V3) @ (V0 @ V3))) @ ((c+ @ ((c* @ V1) @ V3)) @ V2))))))))))))
(TREFLECT_INJ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ V1)) @ ((c< @ (V0 @ V2)) @ V1))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ V1)) @ ((c/__caret__ @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V3)) @ V1)) @ ((c= @ (V0 @ V2)) @ (V0 @ V3))))) @ ((c= @ V2) @ V3)))))))) @ (c! @ (^[V2]: ((c==> @ ((c< @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ V1)) @ ((c< @ ((c- @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (V0 @ V2))) @ V1))))))))))
(TFORSTER_PUZZLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c> @ (V0 @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V0 @ (V0 @ V2)))))) @ ((c= @ (V0 @ V1)) @ V1)))))))
(TMONOTONE_BIGGER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c< @ V2) @ V3)) @ ((c< @ (V0 @ V2)) @ (V0 @ V3)))))))) @ ((c<= @ V1) @ (V0 @ V1))))))))
(TNSUM_CLAUSES_NUMSEG_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnsum @ ((c.. @ V1) @ (cNUMERAL @ c_0))) @ V0)) @ (((cCOND @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ (V0 @ (cNUMERAL @ c_0))) @ (cNUMERAL @ c_0))))))))
(TNSUM_SING_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnsum @ ((c.. @ V1) @ V1)) @ V0)) @ (V0 @ V1)))))))
(TNPRODUCT_CLAUSES_NUMSEG_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnproduct @ ((c.. @ V1) @ (cNUMERAL @ c_0))) @ V0)) @ (((cCOND @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ (V0 @ (cNUMERAL @ c_0))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TNPRODUCT_SING_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnproduct @ ((c.. @ V1) @ V1)) @ V0)) @ (V0 @ V1)))))))
(Tpartitions,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpartitions @ V0) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ (V0 @ V2)) @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ V1)))))) @ ((c= @ ((cnsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ (^[V2]: ((c* @ (V0 @ V2)) @ V2)))) @ V1))))))))
(TPERMUTES_IN_NUMSEG_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpermutes @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2))) @ ((cIN @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)))) @ ((c<= @ (V0 @ V1)) @ V2)))))))))
(TPSEQ_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ (c! @ (^[V3]: ((c==> @ ((c< @ V3) @ V2)) @ ((c< @ (V0 @ V3)) @ V1)))))) @ ((c< @ ((((cPSEQ @ V1) @ V0) @ (cNUMERAL @ c_0)) @ V2)) @ ((cEXP @ V1) @ V2))))))))))
(TNSUM_CLAUSES_NUMSEG_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnsum @ ((c.. @ V1) @ (cSUC @ V2))) @ V0)) @ (((cCOND @ ((c<= @ V1) @ (cSUC @ V2))) @ ((c+ @ ((cnsum @ ((c.. @ V1) @ V2)) @ V0)) @ (V0 @ (cSUC @ V2)))) @ ((cnsum @ ((c.. @ V1) @ V2)) @ V0))))))))))
(TNPRODUCT_CLAUSES_NUMSEG_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnproduct @ ((c.. @ V1) @ (cSUC @ V2))) @ V0)) @ (((cCOND @ ((c<= @ V1) @ (cSUC @ V2))) @ ((c* @ ((cnproduct @ ((c.. @ V1) @ V2)) @ V0)) @ (V0 @ (cSUC @ V2)))) @ ((cnproduct @ ((c.. @ V1) @ V2)) @ V0))))))))))
(TKLE_RANGE_COMBINE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((ckle @ V3) @ V4) @ V0)) @ ((c/__caret__ @ (((ckle @ V3) @ V0) @ V5)) @ ((c/__caret__ @ ((c__caret__/ @ (((ckle @ V3) @ V4) @ V5)) @ (((ckle @ V3) @ V5) @ V4))) @ ((c/__caret__ @ ((c<= @ V1) @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3))) @ ((c< @ (V4 @ V7)) @ (V0 @ V7)))) @ V7)))))))) @ ((c<= @ V2) @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3))) @ ((c< @ (V0 @ V7)) @ (V5 @ V7)))) @ V7)))))))))))) @ ((c<= @ ((c+ @ V1) @ V2)) @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3))) @ ((c< @ (V4 @ V7)) @ (V5 @ V7)))) @ V7)))))))))))))))))))))
(TRELPOW_LEMMA_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c= @ (V0 @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((c= @ (V0 @ V3)) @ V2)) @ (c! @ (^[V5]: ((c==> @ ((c< @ V5) @ V3)) @ ((V4 @ (V0 @ V5)) @ (V0 @ (cSUC @ V5))))))))) @ (c? @ (^[V5]: ((c/__caret__ @ (c? @ (^[V6]: ((c/__caret__ @ ((c<= @ V6) @ V3)) @ ((c<= @ V5) @ (cSUC @ (cFACT @ (V0 @ V6)))))))) @ ((c/__caret__ @ (cprime @ V5)) @ (c? @ (^[V6]: ((c/__caret__ @ ((c< @ V6) @ ((cEXP @ V5) @ (cSUC @ V3)))) @ ((c/__caret__ @ ((c< @ V1) @ V5)) @ ((c/__caret__ @ ((c< @ V2) @ V5)) @ ((c/__caret__ @ (c? @ (^[V7]: ((c= @ V6) @ ((c+ @ V1) @ ((c* @ V5) @ V7)))))) @ ((c/__caret__ @ (c? @ (^[V7]: ((c/__caret__ @ ((c< @ V7) @ ((cEXP @ V5) @ V3))) @ ((c= @ V6) @ ((c+ @ V7) @ ((c* @ ((cEXP @ V5) @ V3)) @ V2))))))) @ (c! @ (^[V7]: ((c==> @ ((c< @ V7) @ ((cEXP @ V5) @ V3))) @ ((c==> @ ((cprimepow @ V5) @ V7)) @ (c? @ (^[V8]: ((c/__caret__ @ ((c< @ V8) @ V7)) @ (c? @ (^[V9]: ((c/__caret__ @ ((c< @ V9) @ V5)) @ (c? @ (^[V10]: ((c/__caret__ @ ((c< @ V10) @ V5)) @ ((c/__caret__ @ ((V4 @ V9) @ V10)) @ (c? @ (^[V11]: ((c/__caret__ @ ((c<= @ V11) @ V6)) @ ((c= @ V6) @ ((c+ @ V8) @ ((c* @ V7) @ ((c+ @ V9) @ ((c* @ V5) @ ((c+ @ V10) @ ((c* @ V5) @ V11)))))))))))))))))))))))))))))))))))))))))))))))
(TNSUM_EQ_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V4)) @ ((c<= @ V4) @ V2))) @ ((c= @ (V0 @ V4)) @ (V3 @ V4)))))) @ ((c= @ ((cnsum @ ((c.. @ V1) @ V2)) @ V0)) @ ((cnsum @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TNPRODUCT_EQ_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V4)) @ ((c<= @ V4) @ V2))) @ ((c= @ (V0 @ V4)) @ (V3 @ V4)))))) @ ((c= @ ((cnproduct @ ((c.. @ V1) @ V2)) @ V0)) @ ((cnproduct @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TNSUM_LE_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V4)) @ ((c<= @ V4) @ V2))) @ ((c<= @ (V0 @ V4)) @ (V3 @ V4)))))) @ ((c<= @ ((cnsum @ ((c.. @ V1) @ V2)) @ V0)) @ ((cnsum @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TNPRODUCT_LE_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V4)) @ ((c<= @ V4) @ V2))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ c_0)) @ (V0 @ V4))) @ ((c<= @ (V0 @ V4)) @ (V3 @ V4))))))) @ ((c<= @ ((cnproduct @ ((c.. @ V1) @ V2)) @ V0)) @ ((cnproduct @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TNSUM_ADD_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cnsum @ ((c.. @ V1) @ V2)) @ (^[V4]: ((c+ @ (V0 @ V4)) @ (V3 @ V4))))) @ ((c+ @ ((cnsum @ ((c.. @ V1) @ V2)) @ V0)) @ ((cnsum @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TNPRODUCT_MUL_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cnproduct @ ((c.. @ V1) @ V2)) @ (^[V4]: ((c* @ (V0 @ V4)) @ (V3 @ V4))))) @ ((c* @ ((cnproduct @ ((c.. @ V1) @ V2)) @ V0)) @ ((cnproduct @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TKLE_RANGE_COMBINE_R_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((ckle @ V2) @ V3) @ V0)) @ ((c/__caret__ @ (((ckle @ V2) @ V0) @ V4)) @ ((c/__caret__ @ ((c__caret__/ @ (((ckle @ V2) @ V3) @ V4)) @ (((ckle @ V2) @ V4) @ V3))) @ ((c<= @ V1) @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2))) @ ((c< @ (V3 @ V6)) @ (V0 @ V6)))) @ V6))))))))))) @ ((c<= @ V1) @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2))) @ ((c< @ (V3 @ V6)) @ (V4 @ V6)))) @ V6)))))))))))))))))))
(TKLE_RANGE_COMBINE_L_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((ckle @ V2) @ V3) @ V0)) @ ((c/__caret__ @ (((ckle @ V2) @ V0) @ V4)) @ ((c/__caret__ @ ((c__caret__/ @ (((ckle @ V2) @ V3) @ V4)) @ (((ckle @ V2) @ V4) @ V3))) @ ((c<= @ V1) @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2))) @ ((c< @ (V0 @ V6)) @ (V4 @ V6)))) @ V6))))))))))) @ ((c<= @ V1) @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2))) @ ((c< @ (V3 @ V6)) @ (V4 @ V6)))) @ V6)))))))))))))))))))
(TNPRODUCT_CANCEL_PRIME_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ ((c* @ ((cEXP @ V2) @ V4)) @ ((cnproduct @ ((cDELETE @ V3) @ V2)) @ (^[V5]: ((cEXP @ V5) @ (V0 @ V5)))))) @ ((c* @ V2) @ V1))) @ ((c==> @ ((c/__caret__ @ (cprime @ V2)) @ ((c/__caret__ @ (cFINITE @ V3)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ (cprime @ V5))))))) @ (c~ @ ((c= @ V4) @ (cNUMERAL @ c_0))))))))))))))))
(TKLE_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((ckle @ V1) @ V2) @ V0)) @ ((c/__caret__ @ (((ckle @ V1) @ V0) @ V3)) @ ((c__caret__/ @ (((ckle @ V1) @ V2) @ V3)) @ (((ckle @ V1) @ V3) @ V2))))) @ (((ckle @ V1) @ V2) @ V3)))))))))))
(TKLE_TRANS_2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((ckle @ V1) @ V2) @ V0)) @ ((c/__caret__ @ (((ckle @ V1) @ V0) @ V3)) @ (c! @ (^[V4]: ((c<= @ (V3 @ V4)) @ ((c+ @ (V2 @ V4)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ (((ckle @ V1) @ V2) @ V3)))))))))))
(TMULTIPLICATIVE_CONVOLUTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmultiplicative @ V0)) @ (cmultiplicative @ V1))) @ (cmultiplicative @ (^[V2]: ((cnsum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cnum_divides @ V4) @ V2)) @ V4)))))) @ (^[V3]: ((c* @ (V0 @ V3)) @ (V1 @ ((cDIV @ V2) @ V3)))))))))))))
(TMULTIPLICATIVE_IGNOREZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ (V1 @ V2)) @ (V0 @ V2)))))) @ (cmultiplicative @ V0))) @ (cmultiplicative @ V1)))))))
(TPOINTWISE_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ (c! @ (^[V2]: ((c<= @ (V0 @ V2)) @ (V1 @ V2))))) @ (c! @ (^[V2]: ((c<= @ (V1 @ V2)) @ (V0 @ V2)))))) @ ((c= @ V0) @ V1)))))))
(TBOUNDS_IGNORE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (c! @ (^[V3]: ((c<= @ (V0 @ V3)) @ ((c+ @ (V1 @ V3)) @ V2))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c<= @ V3) @ V4)) @ ((c<= @ (V0 @ V4)) @ ((c+ @ (V1 @ V4)) @ V2)))))))))))))))
(TMULTIPLICATIVE_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cmultiplicative @ V0)) @ ((c/__caret__ @ (cmultiplicative @ V1)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (cprime @ V3)) @ ((c= @ (V0 @ ((cEXP @ V3) @ V4))) @ (V1 @ ((cEXP @ V3) @ V4))))))))))) @ ((c==> @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0)))) @ ((c= @ (V0 @ V2)) @ (V1 @ V2)))))))))))
(TKLE_BETWEEN_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((ckle @ V2) @ V0) @ V4)) @ ((c/__caret__ @ (((ckle @ V2) @ V4) @ V1)) @ ((c/__caret__ @ (((ckle @ V2) @ V3) @ V0)) @ (((ckle @ V2) @ V3) @ V1))))) @ (((ckle @ V2) @ V3) @ V4)))))))))))))
(TKLE_BETWEEN_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((ckle @ V2) @ V0) @ V3)) @ ((c/__caret__ @ (((ckle @ V2) @ V3) @ V1)) @ ((c/__caret__ @ (((ckle @ V2) @ V0) @ V4)) @ (((ckle @ V2) @ V1) @ V4))))) @ (((ckle @ V2) @ V3) @ V4)))))))))))))
(TSERIES_REARRANGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((csummable @ V3) @ (^[V4]: (clift @ (cvector_norm @ (V1 @ V4)))))) @ ((cpermutes @ V0) @ V3))) @ ((c= @ (((csums @ ((co @ V1) @ V0)) @ V2) @ V3)) @ (((csums @ V1) @ V2) @ V3))))))))))))
(TBOUNDED_FUNCTIONS_BIJECTIONS_2_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cSUC @ V2)))) @ ((cIN @ (V4 @ V5)) @ V1))))) @ (c! @ (^[V5]: ((c==> @ (c~ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cSUC @ V2))))) @ ((c= @ (V4 @ V5)) @ V5)))))) @ V4))))))) @ ((cIN @ ((^[V3]: ((c__comma__ @ (V3 @ (cSUC @ V2))) @ (^[V4]: (((cCOND @ ((c= @ V4) @ (cSUC @ V2))) @ V4) @ (V3 @ V4))))) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ V5) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V8)) @ ((c<= @ V8) @ V2))) @ ((cIN @ (V7 @ V8)) @ V1))))) @ (c! @ (^[V8]: ((c==> @ (c~ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V8)) @ ((c<= @ V8) @ V2)))) @ ((c= @ (V7 @ V8)) @ V8)))))) @ V7)))))))) @ ((c__comma__ @ V4) @ V5)))))))))))))))))
(TDET_PERMUTE_ROWS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdet @ (clambda @ (^[V2]: ((c$ @ V1) @ (V0 @ V2)))))) @ ((creal_mul @ (csign @ V0)) @ (cdet @ V1)))))))))
(TDET_PERMUTE_COLUMNS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdet @ (clambda @ (^[V2]: (clambda @ (^[V3]: ((c$ @ ((c$ @ V1) @ V2)) @ (V0 @ V3)))))))) @ ((creal_mul @ (csign @ V0)) @ (cdet @ V1)))))))))
(TCLOSURE_COSMALL_COORDINATES,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c<_c @ ((cDIFF @ cUNIV) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((V0 @ V1) @ V3)) @ V3))))))) @ cUNIV))))) @ ((c= @ (cclosure @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((V0 @ V3) @ ((c$ @ V2) @ V3)))))) @ V2))))))) @ cUNIV)))))
(TCLOSURE_COCOUNTABLE_COORDINATES,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cCOUNTABLE @ ((cDIFF @ cUNIV) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((V0 @ V1) @ V3)) @ V3))))))))))) @ ((c= @ (cclosure @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((V0 @ V3) @ ((c$ @ V2) @ V3)))))) @ V2))))))) @ cUNIV)))))
(TINJF,(c! @ (^[V0]: ((c= @ (cINJF @ V0)) @ (^[V1]: ((V0 @ (cNUMFST @ V1)) @ (cNUMSND @ V1)))))))
(TINJF_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cINJF @ V0)) @ (cINJF @ V1))) @ ((c= @ V0) @ V1)))))))
(TTRANSITIVE_STEPWISE_LE_EQ,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((V0 @ V1) @ V1)))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V3))) @ ((V0 @ V1) @ V3)))))))))) @ ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))) @ (c! @ (^[V1]: ((V0 @ V1) @ (cSUC @ V1)))))))))
(TTRANSITIVE_STEPWISE_LT_EQ,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V3))) @ ((V0 @ V1) @ V3))))))))) @ ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c< @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))) @ (c! @ (^[V1]: ((V0 @ V1) @ (cSUC @ V1)))))))))
(TBINOM_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ V3) @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ (cNUMERAL @ c_0)) @ (cSUC @ V3))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ (cSUC @ V4))) @ ((V0 @ V3) @ V4))) @ ((V0 @ (cSUC @ V3)) @ (cSUC @ V4)))))))))) @ ((V0 @ V1) @ V2)))))))))
(TWLOG_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ V3) @ V3)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c< @ V3) @ V4)) @ ((V0 @ V3) @ V4))))))))) @ ((V0 @ V1) @ V2)))))))))
(TTRANSITIVE_STEPWISE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ V3) @ V3)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V5))) @ ((V0 @ V3) @ V5))))))))) @ (c! @ (^[V3]: ((V0 @ V3) @ (cSUC @ V3))))))) @ ((c==> @ ((c<= @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))
(TIND_EUCLID,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ V3) @ (cNUMERAL @ c_0))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ ((c+ @ V3) @ V4)))))))))) @ ((V0 @ V1) @ V2)))))))))
(TWLOG_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c<= @ V3) @ V4)) @ ((V0 @ V3) @ V4)))))))) @ ((V0 @ V1) @ V2)))))))))
(TTRANSITIVE_STEPWISE_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V5))) @ ((V0 @ V3) @ V5))))))))) @ (c! @ (^[V3]: ((V0 @ V3) @ (cSUC @ V3)))))) @ ((c==> @ ((c< @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))
(TSUBSEQUENCE_DIAGONALIZATION_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c< @ V5) @ V6)) @ ((c< @ (V4 @ V5)) @ (V4 @ V6)))))))) @ ((V0 @ V2) @ ((co @ V3) @ V4)))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V0 @ V2) @ ((co @ V3) @ V4))) @ (c! @ (^[V7]: ((c==> @ ((c<= @ V6) @ V7)) @ (c? @ (^[V8]: ((c/__caret__ @ ((c<= @ V7) @ V8)) @ ((c= @ (V5 @ V7)) @ (V4 @ V8)))))))))) @ ((V0 @ V2) @ ((co @ V3) @ V5))))))))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c< @ V3) @ V4)) @ ((c< @ (V2 @ V3)) @ (V2 @ V4)))))))) @ (c! @ (^[V3]: ((V0 @ V3) @ ((co @ V1) @ V2)))))))))))))
(Tswapseq_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((V0 @ (cNUMERAL @ c_0)) @ cI)) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V0 @ V6) @ V5)) @ (c~ @ ((c= @ V3) @ V4)))) @ ((V0 @ (cSUC @ V6)) @ ((co @ (cswap @ ((c__comma__ @ V3) @ V4))) @ V5))))))))))))) @ ((c==> @ ((cswapseq @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))
(TMONOTONE_CONVERGENCE_DECREASING_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((cintegrable_on @ (V0 @ V3)) @ V2)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((creal_le @ (cdrop @ ((V0 @ (cSUC @ V3)) @ V4))) @ (cdrop @ ((V0 @ V3) @ V4))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (((c--> @ (^[V4]: ((V0 @ V4) @ V3))) @ (V1 @ V3)) @ csequentially))))) @ (cbounded @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ cUNIV)) @ ((cintegral @ V2) @ (V0 @ V4)))))))))))) @ ((cintegrable_on @ V1) @ V2)))))))))
(TMONOTONE_CONVERGENCE_INCREASING_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((cintegrable_on @ (V0 @ V3)) @ V2)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((creal_le @ (cdrop @ ((V0 @ V3) @ V4))) @ (cdrop @ ((V0 @ (cSUC @ V3)) @ V4))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (((c--> @ (^[V4]: ((V0 @ V4) @ V3))) @ (V1 @ V3)) @ csequentially))))) @ (cbounded @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ cUNIV)) @ ((cintegral @ V2) @ (V0 @ V4)))))))))))) @ ((cintegrable_on @ V1) @ V2)))))))))
(TMONOTONE_CONVERGENCE_INTERVAL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((cintegrable_on @ (V0 @ V4)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((creal_le @ (cdrop @ ((V0 @ V4) @ V5))) @ (cdrop @ ((V0 @ (cSUC @ V4)) @ V5))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (((c--> @ (^[V5]: ((V0 @ V5) @ V4))) @ (V1 @ V4)) @ csequentially))))) @ (cbounded @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ cUNIV)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (V0 @ V5)))))))))))) @ ((cintegrable_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(TBEPPO_LEVI_MONOTONE_CONVERGENCE_DECREASING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((cintegrable_on @ (V0 @ V2)) @ V1)))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (cdrop @ ((V0 @ (cSUC @ V2)) @ V3))) @ (cdrop @ ((V0 @ V2) @ V3))))))))) @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ ((cintegral @ V1) @ (V0 @ V3))))))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (cnegligible @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ V1) @ V3))) @ (((c--> @ (^[V5]: ((V0 @ V5) @ V4))) @ (V2 @ V4)) @ csequentially))))) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (((c--> @ (^[V4]: ((cintegral @ V1) @ (V0 @ V4)))) @ ((cintegral @ V1) @ V2)) @ csequentially))))))))))))))
(TBEPPO_LEVI_MONOTONE_CONVERGENCE_INCREASING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((cintegrable_on @ (V0 @ V2)) @ V1)))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (cdrop @ ((V0 @ V2) @ V3))) @ (cdrop @ ((V0 @ (cSUC @ V2)) @ V3))))))))) @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ ((cintegral @ V1) @ (V0 @ V3))))))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (cnegligible @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ V1) @ V3))) @ (((c--> @ (^[V5]: ((V0 @ V5) @ V4))) @ (V2 @ V4)) @ csequentially))))) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (((c--> @ (^[V4]: ((cintegral @ V1) @ (V0 @ V4)))) @ ((cintegral @ V1) @ V2)) @ csequentially))))))))))))))
(TMONOTONE_CONVERGENCE_DECREASING_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((cintegrable_on @ (V0 @ V3)) @ V1)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((creal_le @ (cdrop @ ((V0 @ (cSUC @ V3)) @ V4))) @ (cdrop @ ((V0 @ V3) @ V4))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (((c--> @ (^[V4]: ((V0 @ V4) @ V3))) @ (V2 @ V3)) @ csequentially))))) @ (cbounded @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ cUNIV)) @ ((cintegral @ V1) @ (V0 @ V4)))))))))))) @ (((c--> @ (^[V3]: ((cintegral @ V1) @ (V0 @ V3)))) @ ((cintegral @ V1) @ V2)) @ csequentially)))))))))
(TMONOTONE_CONVERGENCE_INCREASING_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((cintegrable_on @ (V0 @ V3)) @ V1)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((creal_le @ (cdrop @ ((V0 @ V3) @ V4))) @ (cdrop @ ((V0 @ (cSUC @ V3)) @ V4))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (((c--> @ (^[V4]: ((V0 @ V4) @ V3))) @ (V2 @ V3)) @ csequentially))))) @ (cbounded @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ cUNIV)) @ ((cintegral @ V1) @ (V0 @ V4)))))))))))) @ (((c--> @ (^[V3]: ((cintegral @ V1) @ (V0 @ V3)))) @ ((cintegral @ V1) @ V2)) @ csequentially)))))))))
(TMONOTONE_CONVERGENCE_INTERVAL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((cintegrable_on @ (V0 @ V4)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_le @ (cdrop @ ((V0 @ V4) @ V5))) @ (cdrop @ ((V0 @ (cSUC @ V4)) @ V5))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (((c--> @ (^[V5]: ((V0 @ V5) @ V4))) @ (V3 @ V4)) @ csequentially))))) @ (cbounded @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ cUNIV)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ (V0 @ V5)))))))))))) @ (((c--> @ (^[V4]: ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ (V0 @ V4)))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V3)) @ csequentially)))))))))))
(THAS_MEASURE_COUNTABLE_NEGLIGIBLE_UNIONS_BOUNDED_conjunct1,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: (cmeasurable @ (V0 @ V1))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V1) @ V2))) @ (cnegligible @ ((cINTER @ (V0 @ V1)) @ (V0 @ V2))))))))) @ (cbounded @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))) @ (((csums @ (^[V1]: (clift @ (cmeasure @ (V0 @ V1))))) @ (clift @ (cmeasure @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2)))))))))) @ (cfrom @ (cNUMERAL @ c_0)))))))
(THAS_MEASURE_COUNTABLE_NEGLIGIBLE_UNIONS_BOUNDED_conjunct0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: (cmeasurable @ (V0 @ V1))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V1) @ V2))) @ (cnegligible @ ((cINTER @ (V0 @ V1)) @ (V0 @ V2))))))))) @ (cbounded @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))) @ (cmeasurable @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))))
(TMEASURABLE_COUNTABLE_UNIONS_BOUNDED,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: (cmeasurable @ (V0 @ V1))))) @ (cbounded @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2)))))))))) @ (cmeasurable @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))))
(THAS_MEASURE_NESTED_INTERS_conjunct1,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: (cmeasurable @ (V0 @ V1))))) @ (c! @ (^[V1]: ((cSUBSET @ (V0 @ (cSUC @ V1))) @ (V0 @ V1)))))) @ (((c--> @ (^[V1]: (clift @ (cmeasure @ (V0 @ V1))))) @ (clift @ (cmeasure @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2)))))))))) @ csequentially)))))
(THAS_MEASURE_NESTED_INTERS_conjunct0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: (cmeasurable @ (V0 @ V1))))) @ (c! @ (^[V1]: ((cSUBSET @ (V0 @ (cSUC @ V1))) @ (V0 @ V1)))))) @ (cmeasurable @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))))
(TBOUNDED_CLOSED_NEST,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: (cclosed @ (V0 @ V1))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c~ @ ((c= @ (V0 @ V1)) @ cEMPTY))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ ((cSUBSET @ (V0 @ V2)) @ (V0 @ V1)))))))) @ (cbounded @ (V0 @ (cNUMERAL @ c_0))))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((cIN @ V1) @ (V0 @ V2))))))))))
(TDECREASING_CLOSED_NEST_SING,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: (cclosed @ (V0 @ V1))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c~ @ ((c= @ (V0 @ V1)) @ cEMPTY))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ ((cSUBSET @ (V0 @ V2)) @ (V0 @ V1)))))))) @ (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (V0 @ V2))) @ ((cIN @ V4) @ (V0 @ V2)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V3) @ V4))) @ V1))))))))))))))) @ (c? @ (^[V1]: ((c= @ (cINTERS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c= @ V3) @ (V0 @ V4))))) @ V3))))))) @ ((cINSERT @ V1) @ cEMPTY))))))))
(TDECREASING_CLOSED_NEST,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: (cclosed @ (V0 @ V1))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c~ @ ((c= @ (V0 @ V1)) @ cEMPTY))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ ((cSUBSET @ (V0 @ V2)) @ (V0 @ V1)))))))) @ (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (V0 @ V2))) @ ((cIN @ V4) @ (V0 @ V2)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V3) @ V4))) @ V1))))))))))))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((cIN @ V1) @ (V0 @ V2))))))))))
(TNEGLIGIBLE_COUNTABLE_UNIONS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (cnegligible @ (V0 @ V1))))) @ (cnegligible @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))))
(TMEASURABLE_COUNTABLE_INTERS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (cmeasurable @ (V0 @ V1))))) @ (cmeasurable @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))))
(TLEBESGUE_MEASURABLE_COUNTABLE_UNIONS_EXPLICIT,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (clebesgue_measurable @ (V0 @ V1))))) @ (clebesgue_measurable @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))))
(TLEBESGUE_MEASURABLE_COUNTABLE_INTERS_EXPLICIT,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (clebesgue_measurable @ (V0 @ V1))))) @ (clebesgue_measurable @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))))
(TMEASURE_COUNTABLE_UNIONS_LE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (cmeasurable @ (V0 @ V2))))) @ (c! @ (^[V2]: ((creal_le @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V3]: (cmeasure @ (V0 @ V3))))) @ V1))))) @ ((creal_le @ (cmeasure @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (V0 @ V3))))))))) @ V1)))))))
(TMEASURE_COUNTABLE_UNIONS_LE_STRONG_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (cmeasurable @ (V0 @ V2))))) @ (c! @ (^[V2]: ((creal_le @ (cmeasure @ (cUNIONS @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c<= @ V4) @ V2)) @ (V0 @ V4))))))))) @ V1))))) @ ((creal_le @ (cmeasure @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (V0 @ V3))))))))) @ V1)))))))
(THAS_DERIVATIVE_SERIES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cconvex @ V4)) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V4)) @ (((chas_derivative @ (V1 @ V5)) @ ((V0 @ V5) @ V6)) @ ((cwithin @ (cat @ V6)) @ V4)))))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c? @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((c>= @ V7) @ V6)) @ ((cIN @ V8) @ V4))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ ((cvsum @ ((cINTER @ V2) @ ((c.. @ (cNUMERAL @ c_0)) @ V7))) @ (^[V10]: (((V0 @ V10) @ V8) @ V9)))) @ ((V3 @ V8) @ V9)))) @ ((creal_mul @ V5) @ (cvector_norm @ V9)))))))))))))))) @ (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V5) @ V4)) @ (((csums @ (^[V7]: ((V1 @ V7) @ V5))) @ V6) @ V2)))))))))) @ (c? @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V4)) @ ((c/__caret__ @ (((csums @ (^[V7]: ((V1 @ V7) @ V6))) @ (V5 @ V6)) @ V2)) @ (((chas_derivative @ V5) @ (V3 @ V6)) @ ((cwithin @ (cat @ V6)) @ V4))))))))))))))))))))
(THAS_DERIVATIVE_SEQUENCE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconvex @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ (((chas_derivative @ (V1 @ V4)) @ ((V0 @ V4) @ V5)) @ ((cwithin @ (cat @ V5)) @ V3)))))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((c>= @ V6) @ V5)) @ ((cIN @ V7) @ V3))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ (((V0 @ V6) @ V7) @ V8)) @ ((V2 @ V7) @ V8)))) @ ((creal_mul @ V4) @ (cvector_norm @ V8)))))))))))))))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V4) @ V3)) @ (((c--> @ (^[V6]: ((V1 @ V6) @ V4))) @ V5) @ csequentially)))))))))) @ (c? @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((c/__caret__ @ (((c--> @ (^[V6]: ((V1 @ V6) @ V5))) @ (V4 @ V5)) @ csequentially)) @ (((chas_derivative @ V4) @ (V2 @ V5)) @ ((cwithin @ (cat @ V5)) @ V3))))))))))))))))))
(THAS_DERIVATIVE_SEQUENCE_LIPSCHITZ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cconvex @ V2)) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ (((chas_derivative @ (V3 @ V5)) @ ((V0 @ V5) @ V6)) @ ((cwithin @ (cat @ V6)) @ V2)))))))) @ (c! @ (^[V5]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c? @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((c>= @ V7) @ V6)) @ ((cIN @ V8) @ V2))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ (((V0 @ V7) @ V8) @ V9)) @ ((V1 @ V8) @ V9)))) @ ((creal_mul @ V5) @ (cvector_norm @ V9)))))))))))))))))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((c>= @ V6) @ V5)) @ ((c/__caret__ @ ((c>= @ V7) @ V5)) @ ((c/__caret__ @ ((cIN @ V8) @ V2)) @ ((cIN @ V9) @ V2))))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ ((cvector_sub @ ((V3 @ V6) @ V8)) @ ((V3 @ V7) @ V8))) @ ((cvector_sub @ ((V3 @ V6) @ V9)) @ ((V3 @ V7) @ V9))))) @ ((creal_mul @ V4) @ (cvector_norm @ ((cvector_sub @ V8) @ V9))))))))))))))))))))))))))))
(THAS_ANTIDERIVATIVE_SEQUENCE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconvex @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ (((chas_derivative @ (V0 @ V4)) @ ((V1 @ V4) @ V5)) @ ((cwithin @ (cat @ V5)) @ V3)))))))) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((c>= @ V6) @ V5)) @ ((cIN @ V7) @ V3))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ (((V1 @ V6) @ V7) @ V8)) @ ((V2 @ V7) @ V8)))) @ ((creal_mul @ V4) @ (cvector_norm @ V8)))))))))))))))))) @ (c? @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ (((chas_derivative @ V4) @ (V2 @ V5)) @ ((cwithin @ (cat @ V5)) @ V3)))))))))))))))))
(TEQUIINTEGRABLE_LIMIT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cequiintegrable_on @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ cUNIV)) @ (V0 @ V5))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (((c--> @ (^[V5]: ((V0 @ V5) @ V4))) @ (V1 @ V4)) @ csequentially)))))) @ ((cintegrable_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(TEQUIINTEGRABLE_LIMIT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cequiintegrable_on @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ cUNIV)) @ (V0 @ V5))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (((c--> @ (^[V5]: ((V0 @ V5) @ V4))) @ (V3 @ V4)) @ csequentially)))))) @ (((c--> @ (^[V4]: ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ (V0 @ V4)))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V3)) @ csequentially)))))))))))
(THAS_DERIVATIVE_VSUM_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V5)) @ ((c<= @ V5) @ V2))) @ (((chas_derivative @ (V0 @ V5)) @ (V3 @ V5)) @ V4))))) @ (((chas_derivative @ (^[V5]: ((cvsum @ ((c.. @ V1) @ V2)) @ (^[V6]: ((V0 @ V6) @ V5))))) @ (^[V5]: ((cvsum @ ((c.. @ V1) @ V2)) @ (^[V6]: ((V3 @ V6) @ V5))))) @ V4)))))))))))))
(TCONNECTED_NEST_GEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c/__caret__ @ (cclosed @ (V0 @ V1))) @ (cconnected @ (V0 @ V1)))))) @ ((c/__caret__ @ (c? @ (^[V1]: (ccompact @ (V0 @ V1))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ ((cSUBSET @ (V0 @ V2)) @ (V0 @ V1)))))))))) @ (cconnected @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))))
(TCONNECTED_NEST,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c/__caret__ @ (ccompact @ (V0 @ V1))) @ (cconnected @ (V0 @ V1)))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ ((cSUBSET @ (V0 @ V2)) @ (V0 @ V1))))))))) @ (cconnected @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2))))))))))))
(TCOMPACT_NEST,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c/__caret__ @ (ccompact @ (V0 @ V1))) @ (c~ @ ((c= @ (V0 @ V1)) @ cEMPTY)))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ ((cSUBSET @ (V0 @ V2)) @ (V0 @ V1))))))))) @ (c~ @ ((c= @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2)))))))) @ cEMPTY))))))
(TCONSTR_REC,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (V1 @ (((cCONSTR @ V2) @ V3) @ V4))) @ ((((V0 @ V2) @ V3) @ V4) @ (^[V5]: (V1 @ (V4 @ V5))))))))))))))))
(TFINITE_CART,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((V0 @ V1) @ V3)) @ V3)))))))))) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((V0 @ V3) @ ((c$ @ V2) @ V3)))))) @ V2))))))))))
(TCOUNTABLE_CART,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cCOUNTABLE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((V0 @ V1) @ V3)) @ V3)))))))))) @ (cCOUNTABLE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((V0 @ V3) @ ((c$ @ V2) @ V3)))))) @ V2))))))))))
(TZRECSPACE_CASES,(c! @ (^[V0]: ((c= @ (cZRECSPACE @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ cZBOT)) @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ (((cZCONSTR @ V1) @ V2) @ V3))) @ (c! @ (^[V4]: (cZRECSPACE @ (V3 @ V4))))))))))))))))
(TLAMBDA_SKOLEM,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (c? @ (^[V2]: ((V0 @ V1) @ V2))))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((V0 @ V2) @ ((c$ @ V1) @ V2)))))))))))
(TDEPENDENT_CHOICE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c? @ (^[V2]: ((V0 @ (cNUMERAL @ c_0)) @ V2)))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((V0 @ V2) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((V0 @ (cSUC @ V2)) @ V4)) @ (((V1 @ V2) @ V3) @ V4))))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ V3) @ (V2 @ V3))))) @ (c! @ (^[V3]: (((V1 @ V3) @ (V2 @ V3)) @ (V2 @ (cSUC @ V3))))))))))))))
(TMK_REC_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (c_mk_rec @ V0)) @ (c_mk_rec @ V1))) @ ((c==> @ ((c/__caret__ @ (cZRECSPACE @ V0)) @ (cZRECSPACE @ V1))) @ ((c= @ V0) @ V1))))))))
(TINJP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINJP @ V0) @ V1)) @ (^[V2]: (^[V3]: (((cCOND @ (cNUMLEFT @ V2)) @ ((V0 @ (cNUMRIGHT @ V2)) @ V3)) @ ((V1 @ (cNUMRIGHT @ V2)) @ V3))))))))))
(TINJP_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cINJP @ V0) @ V2)) @ ((cINJP @ V1) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ V3))))))))))))
(TBOUNDED_DECREASING_CONVERGENT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2)))))))) @ (c! @ (^[V1]: ((creal_le @ (cdrop @ (V0 @ (cSUC @ V1)))) @ (cdrop @ (V0 @ V1))))))) @ (c? @ (^[V1]: (((c--> @ V0) @ V1) @ csequentially)))))))
(TBOUNDED_INCREASING_CONVERGENT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ (V0 @ V2)))))))) @ (c! @ (^[V1]: ((creal_le @ (cdrop @ (V0 @ V1))) @ (cdrop @ (V0 @ (cSUC @ V1)))))))) @ (c? @ (^[V1]: (((c--> @ V0) @ V1) @ csequentially)))))))
(TSERIES_COMPARISON_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((csums @ V0) @ V3) @ V2)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((creal_le @ (cvector_norm @ (V1 @ V4))) @ (cdrop @ (V0 @ V4)))))))) @ (c? @ (^[V4]: ((c/__caret__ @ (((csums @ V1) @ V4) @ V2)) @ ((creal_le @ (cvector_norm @ V4)) @ (cdrop @ V3)))))))))))))))
(TSUMMABLE_TRIVIAL,(c! @ (^[V0]: ((csummable @ cEMPTY) @ V0))))
(TCAUCHY_IMP_BOUNDED,(c! @ (^[V0]: ((c==> @ (ccauchy @ V0)) @ (cbounded @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c= @ V2) @ (V0 @ V3))))) @ V2))))))))))
(TCAUCHY,(c! @ (^[V0]: ((c= @ (ccauchy @ V0)) @ (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c>= @ V3) @ V2)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V0 @ V3)) @ (V0 @ V2)))) @ V1)))))))))))))
(Tcauchy,(c! @ (^[V0]: ((c= @ (ccauchy @ V0)) @ (c! @ (^[V1]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c>= @ V3) @ V2)) @ ((c>= @ V4) @ V2))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V0 @ V3)) @ (V0 @ V4)))) @ V1)))))))))))))))
(TSERIES_DIFFS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (((c--> @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ csequentially)) @ (((csums @ (^[V2]: ((cvector_sub @ (V0 @ V2)) @ (V0 @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (V0 @ V1)) @ (cfrom @ V1))))))))
(TSERIES_REARRANGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((csummable @ V3) @ (^[V4]: (clift @ (cvector_norm @ (V0 @ V4)))))) @ ((c/__caret__ @ ((cpermutes @ V1) @ V3)) @ (((csums @ V0) @ V2) @ V3)))) @ (((csums @ ((co @ V0) @ V1)) @ V2) @ V3)))))))))))
(TSUMMABLE_IMP_BOUNDED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csummable @ V1) @ V0)) @ (cbounded @ ((cIMAGE @ V0) @ V1))))))))
(TSUMS_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c= @ (V0 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))))) @ (((csums @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ V1)))))))
(TSERIES_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((csums @ V0) @ V2) @ V1)) @ (((csums @ V0) @ V3) @ V1))) @ ((c= @ V2) @ V3)))))))))))
(TLIMPT_OF_SEQUENCE_SUBSEQUENCE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((climit_point_of @ V1) @ ((cIMAGE @ V0) @ cUNIV))) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c< @ V3) @ V4)) @ ((c< @ (V2 @ V3)) @ (V2 @ V4)))))))) @ (((c--> @ ((co @ V0) @ V2)) @ V1) @ csequentially))))))))))
(TSERIES_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((csums @ V0) @ V1) @ V3)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV))))) @ (((csums @ (^[V4]: (clift @ ((c$ @ (V0 @ V4)) @ V2)))) @ (clift @ ((c$ @ V1) @ V2))) @ V3)))))))))))
(TSERIES_INJECTIVE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((csummable @ ((cIMAGE @ V2) @ V3)) @ (^[V4]: (clift @ (cvector_norm @ (V0 @ V4)))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V3)) @ ((c/__caret__ @ ((cIN @ V5) @ V3)) @ ((c= @ (V2 @ V4)) @ (V2 @ V5))))) @ ((c= @ V4) @ V5)))))))) @ ((c= @ (((csums @ ((co @ V0) @ V2)) @ V1) @ V3)) @ (((csums @ V0) @ V1) @ ((cIMAGE @ V2) @ V3)))))))))))))
(TSERIES_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((csums @ (^[V3]: (((cCOND @ ((cIN @ V3) @ V2)) @ (V0 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))) @ V1) @ cUNIV)) @ (((csums @ V0) @ V1) @ V2)))))))))
(TCLOSED_CONTAINS_SEQUENTIAL_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cclosed @ V2)) @ ((c/__caret__ @ (c! @ (^[V3]: ((cIN @ (V0 @ V3)) @ V2)))) @ (((c--> @ V0) @ V1) @ csequentially)))) @ ((cIN @ V1) @ V2)))))))))
(TSEQUENCE_UNIQUE_LIMPT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ csequentially)) @ ((climit_point_of @ V1) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ (c? @ (^[V5]: ((c= @ V4) @ (V0 @ V5))))) @ V4)))))))) @ ((c= @ V1) @ V2)))))))))
(TCAUCHY_CONTINUOUS_UNIQUENESS_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (ccauchy @ V4)) @ (c! @ (^[V5]: ((cIN @ (V4 @ V5)) @ V1))))) @ (ccauchy @ ((co @ V3) @ V4)))))) @ ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((cIN @ (V0 @ V4)) @ V1)))) @ (((c--> @ V0) @ V2) @ csequentially))) @ (c? @ (^[V4]: ((c/__caret__ @ (((c--> @ ((co @ V3) @ V0)) @ V4) @ csequentially)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c! @ (^[V6]: ((cIN @ (V5 @ V6)) @ V1)))) @ (((c--> @ V5) @ V2) @ csequentially))) @ (((c--> @ ((co @ V3) @ V5)) @ V4) @ csequentially))))))))))))))))))
(TSUMMABLE_EQ_EVENTUALLY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V3) @ V4)) @ ((cIN @ V4) @ V1))) @ ((c= @ (V0 @ V4)) @ (V2 @ V4)))))))) @ ((csummable @ V1) @ V0))) @ ((csummable @ V1) @ V2)))))))))
(TSUMMABLE_IFF_EVENTUALLY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V3) @ V4)) @ ((cIN @ V4) @ V1))) @ ((c= @ (V0 @ V4)) @ (V2 @ V4)))))))) @ ((c= @ ((csummable @ V1) @ V0)) @ ((csummable @ V1) @ V2))))))))))
(TINFSUM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V1) @ V0)) @ ((c/__caret__ @ ((csummable @ V1) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3)))))))) @ ((c= @ ((cinfsum @ V1) @ V0)) @ ((cinfsum @ V1) @ V2))))))))))
(TINFSUM_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V1) @ V0)) @ ((csummable @ V1) @ V2))) @ ((c= @ ((cinfsum @ V1) @ (^[V3]: ((cvector_sub @ (V0 @ V3)) @ (V2 @ V3))))) @ ((cvector_sub @ ((cinfsum @ V1) @ V0)) @ ((cinfsum @ V1) @ V2)))))))))))
(TINFSUM_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V1) @ V0)) @ ((csummable @ V1) @ V2))) @ ((c= @ ((cinfsum @ V1) @ (^[V3]: ((cvector_add @ (V0 @ V3)) @ (V2 @ V3))))) @ ((cvector_add @ ((cinfsum @ V1) @ V0)) @ ((cinfsum @ V1) @ V2)))))))))))
(TSUMMABLE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3)))))) @ ((csummable @ V1) @ V0))) @ ((csummable @ V1) @ V2)))))))))
(TSUMMABLE_IFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3)))))) @ ((c= @ ((csummable @ V1) @ V0)) @ ((csummable @ V1) @ V2))))))))))
(TSUMS_REINDEX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csums @ (^[V4]: (V0 @ ((c+ @ V4) @ V3)))) @ V1) @ (cfrom @ V2))) @ (((csums @ V0) @ V1) @ (cfrom @ ((c+ @ V2) @ V3)))))))))))))
(TSERIES_TRIVIAL,(c! @ (^[V0]: (((csums @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ cEMPTY))))
(TSUMS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((c= @ (V0 @ V4)) @ (V1 @ V4)))))) @ (((csums @ V0) @ V2) @ V3))) @ (((csums @ V1) @ V2) @ V3)))))))))))
(TSUMS_IFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((c= @ (V0 @ V4)) @ (V1 @ V4)))))) @ ((c= @ (((csums @ V0) @ V2) @ V3)) @ (((csums @ V1) @ V2) @ V3))))))))))))
(TSERIES_NEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((csums @ V0) @ V1) @ V2)) @ (((csums @ (^[V3]: (cvector_neg @ (V0 @ V3)))) @ (cvector_neg @ V1)) @ V2)))))))))
(TSERIES_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((csums @ V0) @ V2) @ V3)) @ (((csums @ (^[V4]: ((c% @ V1) @ (V0 @ V4)))) @ ((c% @ V1) @ V2)) @ V3)))))))))))
(TSERIES_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((csums @ V0) @ V2) @ V4)) @ (((csums @ V1) @ V3) @ V4))) @ (((csums @ (^[V5]: ((cvector_sub @ (V0 @ V5)) @ (V1 @ V5)))) @ ((cvector_sub @ V2) @ V3)) @ V4)))))))))))))
(TSERIES_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((csums @ V0) @ V2) @ V4)) @ (((csums @ V1) @ V3) @ V4))) @ (((csums @ (^[V5]: ((cvector_add @ (V0 @ V5)) @ (V1 @ V5)))) @ ((cvector_add @ V2) @ V3)) @ V4)))))))))))))
(TSERIES_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((csums @ V0) @ V2) @ V3)) @ (clinear @ V1))) @ (((csums @ (^[V4]: (V1 @ (V0 @ V4)))) @ (V1 @ V2)) @ V3)))))))))))
(TSERIES_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ (((csums @ V0) @ ((cvsum @ V1) @ V0)) @ V1)))))))
(Tsummable,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((csummable @ V1) @ V0)) @ (c? @ (^[V2]: (((csums @ V0) @ V2) @ V1)))))))))
(Tinfsum,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinfsum @ V1) @ V0)) @ (c__at__ @ (^[V2]: (((csums @ V0) @ V2) @ V1)))))))))
(TCONVERGENT_EQ_CAUCHY,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (((c--> @ V0) @ V1) @ csequentially)))) @ (ccauchy @ V0)))))
(TLIM_SUBSEQUENCE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c< @ V3) @ V4)) @ ((c< @ (V1 @ V3)) @ (V1 @ V4)))))))) @ (((c--> @ V0) @ V2) @ csequentially))) @ (((c--> @ ((co @ V0) @ V1)) @ V2) @ csequentially)))))))))
(TSEQ_OFFSET_NEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c--> @ V0) @ V2) @ csequentially)) @ (((c--> @ (^[V3]: (V0 @ ((c- @ V3) @ V1)))) @ V2) @ csequentially)))))))))
(TSEQ_OFFSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c--> @ V0) @ V2) @ csequentially)) @ (((c--> @ (^[V3]: (V0 @ ((c+ @ V3) @ V1)))) @ V2) @ csequentially)))))))))
(TLIM_SEQUENTIALLY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((c--> @ V0) @ V1) @ csequentially)) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c<= @ V3) @ V4)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V0 @ V4)) @ V1))) @ V2)))))))))))))))
(TVSUM_4,(c! @ (^[V0]: ((c= @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V0)) @ ((cvector_add @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cvector_add @ (V0 @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cvector_add @ (V0 @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (V0 @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TVSUM_3,(c! @ (^[V0]: ((c= @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ V0)) @ ((cvector_add @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cvector_add @ (V0 @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (V0 @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))))))
(TVSUM_2,(c! @ (^[V0]: ((c= @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V0)) @ ((cvector_add @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (V0 @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))
(TVSUM_1,(c! @ (^[V0]: ((c= @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TVSUM_SING_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ ((c.. @ V1) @ V1)) @ V0)) @ (V0 @ V1)))))))
(TVSUM_SUB_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cvsum @ ((c.. @ V1) @ V2)) @ (^[V4]: ((cvector_sub @ (V0 @ V4)) @ (V3 @ V4))))) @ ((cvector_sub @ ((cvsum @ ((c.. @ V1) @ V2)) @ V0)) @ ((cvsum @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TVSUM_ADD_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cvsum @ ((c.. @ V1) @ V2)) @ (^[V4]: ((cvector_add @ (V0 @ V4)) @ (V3 @ V4))))) @ ((cvector_add @ ((cvsum @ ((c.. @ V1) @ V2)) @ V0)) @ ((cvsum @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TVSUM_EQ_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V4)) @ ((c<= @ V4) @ V2))) @ ((c= @ (V0 @ V4)) @ (V3 @ V4)))))) @ ((c= @ ((cvsum @ ((c.. @ V1) @ V2)) @ V0)) @ ((cvsum @ ((c.. @ V1) @ V2)) @ V3))))))))))))
(TVSUM_CLAUSES_NUMSEG_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ ((c.. @ V1) @ (cNUMERAL @ c_0))) @ V0)) @ (((cCOND @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ (V0 @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TVSUM_CLAUSES_NUMSEG_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvsum @ ((c.. @ V1) @ (cSUC @ V2))) @ V0)) @ (((cCOND @ ((c<= @ V1) @ (cSUC @ V2))) @ ((cvector_add @ ((cvsum @ ((c.. @ V1) @ V2)) @ V0)) @ (V0 @ (cSUC @ V2)))) @ ((cvsum @ ((c.. @ V1) @ V2)) @ V0))))))))))
(TMSUM_CLAUSES_NUMSEG_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmsum @ ((c.. @ V1) @ (cNUMERAL @ c_0))) @ V0)) @ (((cCOND @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ (V0 @ (cNUMERAL @ c_0))) @ (cmat @ (cNUMERAL @ c_0)))))))))
(TMSUM_CLAUSES_NUMSEG_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmsum @ ((c.. @ V1) @ (cSUC @ V2))) @ V0)) @ (((cCOND @ ((c<= @ V1) @ (cSUC @ V2))) @ ((cmatrix_add @ ((cmsum @ ((c.. @ V1) @ V2)) @ V0)) @ (V0 @ (cSUC @ V2)))) @ ((cmsum @ ((c.. @ V1) @ V2)) @ V0))))))))))
(TSERIES_0,(c! @ (^[V0]: (((csums @ (^[V1]: (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))) @ V0))))
(TSUMMABLE_0,(c! @ (^[V0]: ((csummable @ V0) @ (^[V1]: (cvec @ (cNUMERAL @ c_0)))))))
(TSCHNIRELMANN_BOUNDS_conjunct1,(c! @ (^[V0]: ((creal_le @ (cschnirelmann @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TSCHNIRELMANN_BOUNDS_conjunct0,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cschnirelmann @ V0)))))
(TDEST_MK_MULTIVECTOR,(c! @ (^[V0]: ((c==> @ ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdest_multivector @ (cmk_multivector @ V0))) @ V0)))))
(TMBASIS_NONZERO,(c! @ (^[V0]: ((c==> @ ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ (c~ @ ((c= @ (cmbasis @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))))
(TSCHNIRELMANN_SENSITIVE_1,(c! @ (^[V0]: ((c==> @ (c~ @ ((cIN @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0))) @ ((c= @ (cschnirelmann @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TFINITE_MAX,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c==> @ (cFINITE @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c<= @ V2) @ V1))))))))))))
(TINFINITE_ENUMERATE,(c! @ (^[V0]: ((c==> @ (cINFINITE @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c< @ V2) @ V3)) @ ((c< @ (V1 @ V2)) @ (V1 @ V3)))))))) @ ((c= @ ((cIMAGE @ V1) @ cUNIV)) @ V0))))))))
(TINFINITE_ENUMERATE_WEAK,(c! @ (^[V0]: ((c==> @ (cINFINITE @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c< @ V2) @ V3)) @ ((c< @ (V1 @ V2)) @ (V1 @ V3)))))))) @ (c! @ (^[V2]: ((cIN @ (V1 @ V2)) @ V0))))))))))
(TBITSET_BINARYSUM,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cbitset @ (cbinarysum @ V0))) @ V0)))))
(Tnum_FINITE_AVOID,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (c? @ (^[V1]: (c~ @ ((cIN @ V1) @ V0))))))))
(Tschnirelmann,(c! @ (^[V0]: ((c= @ (cschnirelmann @ V0)) @ (cinf @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((creal_div @ (creal_of_num @ ((ccount @ V0) @ V2))) @ (creal_of_num @ V2))))))))))))
(Tsetcode,(c! @ (^[V0]: ((c= @ (csetcode @ V0)) @ ((c+ @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cbinarysum @ ((cIMAGE @ cPRE) @ V0)))))))
(Tminimal,(c! @ (^[V0]: ((c= @ (cminimal @ V0)) @ (c__at__ @ (^[V1]: ((c/__caret__ @ (V0 @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c< @ V2) @ V1)) @ (c~ @ (V0 @ V2))))))))))))
(TDIM_SPECIAL_SUBSPACE,(c! @ (^[V0]: ((c= @ (cdim @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((cIN @ V3) @ V0)))) @ ((c= @ ((c$ @ V2) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ V2))))))) @ (cCARD @ ((cDIFF @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ V0))))))
(Tbinarysum,(c! @ (^[V0]: ((c= @ (cbinarysum @ V0)) @ ((cnsum @ V0) @ (^[V1]: ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)))))))
(Tmbasis,(c! @ (^[V0]: ((c= @ (cmbasis @ V0)) @ (clambdas @ (^[V1]: (((cCOND @ ((c= @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TINFSUM_0,(c! @ (^[V0]: ((c= @ ((cinfsum @ V0) @ (^[V1]: (cvec @ (cNUMERAL @ c_0))))) @ (cvec @ (cNUMERAL @ c_0))))))
(TEVENTUALLY_SEQUENTIALLY,(c! @ (^[V0]: ((c= @ ((ceventually @ V0) @ csequentially)) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<= @ V1) @ V2)) @ (V0 @ V2))))))))))
(Tmultivector_tybij_conjunct1,(c! @ (^[V0]: ((c= @ ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdest_multivector @ (cmk_multivector @ V0))) @ V0)))))
(TALLN_conjunct0,(c! @ (^[V0]: ((c= @ ((cALLN @ V0) @ (cNUMERAL @ c_0))) @ cT))))
(TSCHNIRELMANN_EQ_1,(c! @ (^[V0]: ((c= @ ((c= @ (cschnirelmann @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V1]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((cIN @ V1) @ V0))))))))
(TMBASIS_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cmbasis @ V0)) @ (cvec @ (cNUMERAL @ c_0)))) @ (c~ @ ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))))))
(Tnum_MAX,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((c<= @ V2) @ V1)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (V0 @ V1)) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((c<= @ V2) @ V1)))))))))))
(Tnum_FINITE,(c! @ (^[V0]: ((c= @ (cFINITE @ V0)) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c<= @ V2) @ V1))))))))))
(TMINIMAL,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ ((c/__caret__ @ (V0 @ (cminimal @ V0))) @ (c! @ (^[V1]: ((c==> @ ((c< @ V1) @ (cminimal @ V0))) @ (c~ @ (V0 @ V1))))))))))
(Tnum_WOP,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: ((c/__caret__ @ (V0 @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c< @ V2) @ V1)) @ (c~ @ (V0 @ V2))))))))))))
(TFORALL_DIMINDEX_1,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (V0 @ V1))))) @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TFORALL_3,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ (V0 @ V1))))) @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (V0 @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))))))
(TFORALL_1,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V0 @ V1))))) @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TFORALL_2,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (V0 @ V1))))) @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (V0 @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))
(TFORALL_4,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (V0 @ V1))))) @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (V0 @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TFORALL_SUC,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ (V0 @ V1))))) @ (c! @ (^[V1]: (V0 @ (cSUC @ V1))))))))
(TSUMMABLE_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((csummable @ V0) @ V2)) @ ((csummable @ V0) @ (^[V3]: ((c% @ V1) @ (V2 @ V3))))))))))))
(TSCHNIRELMANN_UBOUND_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ ((creal_mul @ (cschnirelmann @ V0)) @ (creal_of_num @ V1))) @ (creal_of_num @ ((ccount @ V0) @ V1))))))))
(TMULTIVECTOR_VEC_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$$ @ (cvec @ V1)) @ V0)) @ (creal_of_num @ V1))))))))
(TSETCODE_BOUNDS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1))) @ ((cIN @ (csetcode @ V0)) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)))))))))
(TSCHNIRELMANN_UBOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((creal_le @ (cschnirelmann @ V0)) @ ((creal_div @ (creal_of_num @ ((ccount @ V0) @ V1))) @ (creal_of_num @ V1)))))))))
(TSCHNIRELMANN_SENSITIVE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ (c~ @ ((cIN @ V1) @ V0)))) @ ((creal_le @ (cschnirelmann @ V0)) @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ V1))))))))))
(TBINARYSUM_DIV_DIVISIBLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c<= @ V1) @ V2)))))) @ ((c= @ ((cnsum @ V0) @ (^[V2]: ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)))) @ ((c* @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1)) @ ((cnsum @ V0) @ (^[V2]: ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ ((c- @ V2) @ V1))))))))))))
(TINDUCT_COPRIME_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V2) @ V3))) @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3)))))) @ (V0 @ ((c* @ V2) @ V3)))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cprime @ V2)) @ (c~ @ ((c= @ V3) @ (cNUMERAL @ c_0))))) @ (V0 @ ((cEXP @ V2) @ V3))))))))) @ ((c==> @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ (V0 @ V1))))))))
(TINDUCT_COPRIME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ (cnum_coprime @ ((c__comma__ @ V2) @ V3))) @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3)))))) @ (V0 @ ((c* @ V2) @ V3)))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cprime @ V2)) @ (V0 @ ((cEXP @ V2) @ V3))))))))) @ ((c==> @ ((c< @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ (V0 @ V1))))))))
(TCAUCHY_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)))))) @ (c! @ (^[V2]: ((c==> @ (V0 @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V0 @ V2))))))) @ (V0 @ V1)))))))
(TINDUCTION_FROM_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ (V0 @ V2))) @ (V0 @ (cSUC @ V2)))))))) @ (V0 @ V1)))))))
(TPELL_INDUCTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (V0 @ ((c+ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))) @ (V0 @ V1)))))))
(TODDEVEN_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ ((c+ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))) @ (V0 @ V1)))))))
(TPRIME_FACTOR_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cprime @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cNUMERAL @ c_0)))) @ (V0 @ V3)))) @ (V0 @ ((c* @ V2) @ V3)))))))))) @ (V0 @ V1)))))))
(TBINARY_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ (cNUMERAL @ c_0))) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((c/__caret__ @ (V0 @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2))) @ (V0 @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))) @ (V0 @ V1)))))))
(Tnum_INDUCTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ (cNUMERAL @ c_0))) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cSUC @ V2))))))) @ (V0 @ V1)))))))
(TFINITE_SPECIAL_DIVISORS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cNUMERAL @ c_0)))) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ (V0 @ V3)) @ ((cnum_divides @ V3) @ V1))) @ V3))))))))))))
(TBINARYSUM_DIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cDIV @ ((cnsum @ V0) @ (^[V2]: ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))) @ ((cnsum @ V0) @ (^[V2]: (((cCOND @ ((c< @ V2) @ V1)) @ (cNUMERAL @ c_0)) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ ((c- @ V2) @ V1))))))))))))
(TBINARYSUM_BOUND_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((c< @ (cbinarysum @ V0)) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c< @ V2) @ V1)))))))))))
(TFINITE_BOUNDED_FUNCTIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ V1))) @ ((cIN @ (V3 @ V4)) @ V0))))) @ (c! @ (^[V4]: ((c==> @ (c~ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ V1)))) @ ((c= @ (V3 @ V4)) @ V4)))))) @ V3))))))))))))
(TBINARYSUM_BOUND_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c< @ V2) @ V1))))) @ ((c< @ ((cnsum @ V0) @ (^[V2]: ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))))))))
(TBINARYSUM_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c< @ V2) @ V1))))) @ ((c< @ (cbinarysum @ V0)) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))))))))
(TMINIMAL_IN_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c< @ V1) @ V2))))) @ ((c= @ (cminimal @ (^[V2]: ((cIN @ V2) @ ((cINSERT @ V1) @ V0))))) @ V1)))))))
(Tnum_WF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((c< @ V3) @ V2)) @ (V0 @ V3))))) @ (V0 @ V2))))) @ (V0 @ V1)))))))
(Tcount,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccount @ V0) @ V1)) @ (cCARD @ ((cINTER @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)))))))))
(TBINARY_DIV_POW2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDIV @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V1)) @ (^[V2]: (((cCOND @ (V0 @ V2)) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ (cNUMERAL @ c_0))))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cSUC @ V1)))) @ (cNUMERAL @ c_0)))))))
(TBINARY_PLUS_DIV_POW2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDIV @ ((c+ @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V1)) @ (^[V2]: (((cCOND @ (V0 @ V2)) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ (cNUMERAL @ c_0))))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cSUC @ V1)))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cSUC @ V1)))) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TALLN_DEF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cALLN @ V0) @ V1)) @ (((cCOND @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ V1) @ ((cNPAIR @ V2) @ V3))))))) @ ((c/__caret__ @ (V0 @ (c__at__ @ (^[V2]: (c? @ (^[V3]: ((c= @ ((cNPAIR @ V2) @ V3)) @ V1))))))) @ ((cALLN @ V0) @ (c__at__ @ (^[V2]: (c? @ (^[V3]: ((c= @ ((cNPAIR @ V3) @ V2)) @ V1)))))))) @ cT)))))))
(TCOUNT_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ ((ccount @ V0) @ V1)) @ V1))))))
(TBINARY_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c< @ ((cnsum @ ((c.. @ (cNUMERAL @ c_0)) @ V1)) @ (^[V2]: (((cCOND @ (V0 @ V2)) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V2)) @ (cNUMERAL @ c_0))))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TBOUNDED_FUNCTIONS_BIJECTIONS_1_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V8)) @ ((c<= @ V8) @ V1))) @ ((cIN @ (V7 @ V8)) @ V0))))) @ (c! @ (^[V8]: ((c==> @ (c~ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V8)) @ ((c<= @ V8) @ V1)))) @ ((c= @ (V7 @ V8)) @ V8)))))) @ V7)))))))) @ ((c__comma__ @ V4) @ V5)))))))))) @ ((c= @ ((^[V3]: ((c__comma__ @ (V3 @ (cSUC @ V1))) @ (^[V4]: (((cCOND @ ((c= @ V4) @ (cSUC @ V1))) @ V4) @ (V3 @ V4))))) @ ((cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ (^[V6]: (((cCOND @ ((c= @ V6) @ (cSUC @ V1))) @ V4) @ (V5 @ V6)))))))))) @ V2))) @ V2)))))))))
(TSUM_BINSEQUENCE_UBOUND_SHARP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((creal_le @ ((cpsum @ ((c__comma__ @ V1) @ V2)) @ (^[V3]: (((cCOND @ (V0 @ V3)) @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V3))) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((creal_sub @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V1))) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c+ @ V1) @ V2))))))))))))
(TGCD_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (V0 @ ((c+ @ V3) @ V4)))) @ (V0 @ V4))))))) @ ((c==> @ ((c/__caret__ @ (V0 @ V1)) @ (V0 @ V2))) @ (V0 @ (cnum_gcd @ ((c__comma__ @ V1) @ V2))))))))))))
(TFINITE_INTER_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (cFINITE @ ((cINTER @ V0) @ ((c.. @ V1) @ V2))))))))))
(TVSUM_DIFF_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c<= @ V1) @ V2)) @ ((c= @ ((cvector_sub @ ((cvsum @ ((cINTER @ V0) @ ((c.. @ (cNUMERAL @ c_0)) @ V2))) @ V3)) @ ((cvsum @ ((cINTER @ V0) @ ((c.. @ (cNUMERAL @ c_0)) @ V1))) @ V3))) @ ((cvsum @ ((cINTER @ V0) @ ((c.. @ ((c+ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2))) @ V3))))))))))))
(TVARIATION_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c~ @ ((c= @ (V2 @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ ((c= @ ((cvariation @ V0) @ V2)) @ ((c+ @ ((cvariation @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c<= @ V4) @ V1))) @ V4)))))) @ V2)) @ ((cvariation @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c<= @ V1) @ V4))) @ V4)))))) @ V2)))))))))))
(TBOUNDED_FUNCTIONS_BIJECTIONS_2_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cSUC @ V1)))) @ ((cIN @ (V4 @ V5)) @ V0))))) @ (c! @ (^[V5]: ((c==> @ (c~ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cSUC @ V1))))) @ ((c= @ (V4 @ V5)) @ V5)))))) @ V4))))))) @ ((c= @ ((cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ (^[V6]: (((cCOND @ ((c= @ V6) @ (cSUC @ V1))) @ V4) @ (V5 @ V6)))))))))) @ ((^[V3]: ((c__comma__ @ (V3 @ (cSUC @ V1))) @ (^[V4]: (((cCOND @ ((c= @ V4) @ (cSUC @ V1))) @ V4) @ (V3 @ V4))))) @ V2))) @ V2)))))))))
(TDET_LINEAR_ROWS_VSUM_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdet @ (clambda @ (^[V4]: (((cCOND @ ((c<= @ V4) @ V1)) @ ((cvsum @ V0) @ (V2 @ V4))) @ (V3 @ V4)))))) @ ((csum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V6)) @ ((c<= @ V6) @ V1))) @ ((cIN @ (V5 @ V6)) @ V0))))) @ (c! @ (^[V6]: ((c==> @ (c~ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V6)) @ ((c<= @ V6) @ V1)))) @ ((c= @ (V5 @ V6)) @ V6)))))) @ V5)))))) @ (^[V4]: (cdet @ (clambda @ (^[V5]: (((cCOND @ ((c<= @ V5) @ V1)) @ ((V2 @ V5) @ (V4 @ V5))) @ (V3 @ V5))))))))))))))))))
(Tmono_on,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cmono_on @ V2) @ V1) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c<= @ V3) @ V4)))) @ ((V1 @ (V2 @ V3)) @ (V2 @ V4)))))))))))))))
(Tvariation,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvariation @ V0) @ V1)) @ (cCARD @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((c< @ V3) @ V4)) @ ((c/__caret__ @ ((creal_lt @ ((creal_mul @ (V1 @ V3)) @ (V1 @ V4))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ ((c< @ V3) @ V5)) @ ((c< @ V5) @ V4)))) @ ((c= @ (V1 @ V5)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))) @ ((c__comma__ @ V3) @ V4)))))))))))))))
(TMONO_ON_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (((cmono_on @ V1) @ V2) @ V0))) @ (((cmono_on @ V1) @ V2) @ V3)))))))))))
(TPERMUTES_NUMSET_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cpermutes @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c<= @ (V1 @ V2)) @ V2)))))) @ ((c= @ V1) @ cI)))))))
(TPERMUTES_NUMSET_GE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cpermutes @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c<= @ V2) @ (V1 @ V2))))))) @ ((c= @ V1) @ cI)))))))
(TDET_LINEAR_ROWS_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cdet @ (clambda @ (^[V2]: ((cvsum @ V0) @ (V1 @ V2)))))) @ ((csum @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ (cdimindex @ cUNIV)))) @ ((cIN @ (V3 @ V4)) @ V0))))) @ (c! @ (^[V4]: ((c==> @ (c~ @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ (cdimindex @ cUNIV))))) @ ((c= @ (V3 @ V4)) @ V4)))))) @ V3)))))) @ (^[V2]: (cdet @ (clambda @ (^[V3]: ((V1 @ V3) @ (V2 @ V3))))))))))))))
(TSERIES_DROP_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((csums @ V1) @ V3) @ V0)) @ ((c/__caret__ @ (((csums @ V2) @ V4) @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((creal_le @ (cdrop @ (V1 @ V5))) @ (cdrop @ (V2 @ V5))))))))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))))))))))))))
(TSERIES_DROP_POS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((csums @ V1) @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ (V1 @ V3)))))))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ V2))))))))))
(TSERIES_LIFT_ABSCONV_IMP_CONV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csummable @ V0) @ (^[V2]: (clift @ (cvector_norm @ (V1 @ V2)))))) @ ((csummable @ V0) @ V1)))))))
(TSUMMABLE_IMP_TOZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csummable @ V0) @ V1)) @ (((c--> @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V0)) @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))) @ (cvec @ (cNUMERAL @ c_0))) @ csequentially)))))))
(TINFSUM_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinfsum @ cUNIV) @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V0)) @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((cinfsum @ V0) @ V1)))))))
(TSUMS_LIM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((csums @ V1) @ ((clim @ csequentially) @ (^[V2]: ((cvsum @ ((cINTER @ V0) @ ((c.. @ (cNUMERAL @ c_0)) @ V2))) @ V1)))) @ V0)) @ ((csummable @ V0) @ V1)))))))
(TSUMMABLE_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((csummable @ cUNIV) @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V0)) @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((csummable @ V0) @ V1)))))))
(TSUMMABLE_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V0) @ V1)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV))))) @ ((csummable @ V0) @ (^[V3]: (clift @ ((c$ @ (V1 @ V3)) @ V2))))))))))))
(TSERIES_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((csums @ V1) @ V3) @ V0)) @ ((c/__caret__ @ (((csums @ ((co @ clift) @ V2)) @ (clift @ V4)) @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((creal_le @ (cvector_norm @ (V1 @ V5))) @ (V2 @ V5)))))))) @ ((creal_le @ (cvector_norm @ V3)) @ V4)))))))))))))
(TSERIES_INJECTIVE_IMAGE_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ ((cIMAGE @ V2) @ V0)) @ (^[V3]: (clift @ (cvector_norm @ (V1 @ V3)))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4)))))))) @ (((c--> @ (^[V3]: ((cvector_sub @ ((cvsum @ ((cINTER @ ((cIMAGE @ V2) @ V0)) @ ((c.. @ (cNUMERAL @ c_0)) @ V3))) @ V1)) @ ((cvsum @ ((cINTER @ V0) @ ((c.. @ (cNUMERAL @ c_0)) @ V3))) @ ((co @ V1) @ V2))))) @ (cvec @ (cNUMERAL @ c_0))) @ csequentially)))))))))
(TORTHOGONAL_TRANSFORMATION_BETWEEN_ORTHOGONAL_SETS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpairwise @ (^[V3]: (^[V4]: ((corthogonal @ (V1 @ V3)) @ (V1 @ V4))))) @ V0)) @ ((c/__caret__ @ ((cpairwise @ (^[V3]: (^[V4]: ((corthogonal @ (V2 @ V3)) @ (V2 @ V4))))) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (cvector_norm @ (V1 @ V3))) @ (cvector_norm @ (V2 @ V3))))))))) @ (c? @ (^[V3]: ((c/__caret__ @ (corthogonal_transformation @ V3)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V3 @ (V1 @ V4))) @ (V2 @ V4))))))))))))))))
(TSERIES_FINITE_SUPPORT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ ((cINTER @ V0) @ V2))) @ (c! @ (^[V3]: ((c==> @ (c~ @ ((cIN @ V3) @ ((cINTER @ V0) @ V2)))) @ ((c= @ (V1 @ V3)) @ (cvec @ (cNUMERAL @ c_0)))))))) @ (((csums @ V1) @ ((cvsum @ ((cINTER @ V0) @ V2)) @ V1)) @ V2)))))))))
(TINFSUM_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((csums @ V1) @ V2) @ V0)) @ ((c= @ ((cinfsum @ V0) @ V1)) @ V2)))))))))
(TSUMMABLE_REARRANGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V0) @ (^[V3]: (clift @ (cvector_norm @ (V1 @ V3)))))) @ ((cpermutes @ V2) @ V0))) @ ((csummable @ V0) @ ((co @ V1) @ V2))))))))))
(TSERIES_GOESTOZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((csummable @ V0) @ V1)) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((ceventually @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_lt @ (cvector_norm @ (V1 @ V3))) @ V2)))) @ csequentially))))))))))
(TSUMMABLE_CAUCHY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((csummable @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c>= @ V4) @ V3)) @ ((creal_lt @ (cvector_norm @ ((cvsum @ ((cINTER @ V0) @ ((c.. @ V4) @ V5))) @ V1))) @ V2)))))))))))))))))
(TSERIES_CAUCHY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (((csums @ V1) @ V2) @ V0)))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c>= @ V4) @ V3)) @ ((creal_lt @ (cvector_norm @ ((cvsum @ ((cINTER @ V0) @ ((c.. @ V4) @ V5))) @ V1))) @ V2)))))))))))))))))
(TSEQUENCE_CAUCHY_WLOG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (V0 @ V4))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V1 @ V3)) @ (V1 @ V4)))) @ V2))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ ((c/__caret__ @ (V0 @ V4)) @ ((c<= @ V3) @ V4)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V1 @ V3)) @ (V1 @ V4)))) @ V2))))))))))))))
(TINFSUM_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csummable @ V0) @ V1)) @ ((c= @ ((cinfsum @ V0) @ (^[V2]: (cvector_neg @ (V1 @ V2))))) @ (cvector_neg @ ((cinfsum @ V0) @ V1)))))))))
(TSERIES_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (((csums @ (^[V4]: (((cCOND @ ((cIN @ V4) @ V3)) @ (V1 @ V4)) @ (cvec @ (cNUMERAL @ c_0))))) @ V2) @ V0))) @ (((csums @ V1) @ V2) @ V3)))))))))))
(TSUMMABLE_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csummable @ V0) @ V1)) @ ((csummable @ V0) @ (^[V2]: (cvector_neg @ (V1 @ V2))))))))))
(TSUMMABLE_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V0) @ V1)) @ ((csummable @ V0) @ V2))) @ ((csummable @ V0) @ (^[V3]: ((cvector_sub @ (V1 @ V3)) @ (V2 @ V3))))))))))))
(TSUMMABLE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V0) @ V1)) @ ((csummable @ V0) @ V2))) @ ((csummable @ V0) @ (^[V3]: ((cvector_add @ (V1 @ V3)) @ (V2 @ V3))))))))))))
(TSERIES_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ (c~ @ ((cIN @ V4) @ V0))) @ ((c= @ (V1 @ V4)) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((c= @ ((cvsum @ V0) @ V1)) @ V2))))) @ (((csums @ V1) @ V2) @ V3)))))))))))
(TSUMS_INFSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((csums @ V1) @ ((cinfsum @ V0) @ V1)) @ V0)) @ ((csummable @ V0) @ V1)))))))
(Tsums,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((csums @ V1) @ V2) @ V0)) @ (((c--> @ (^[V3]: ((cvsum @ ((cINTER @ V0) @ ((c.. @ (cNUMERAL @ c_0)) @ V3))) @ V1))) @ V2) @ csequentially)))))))))
(TLIM_CASES_COFINITE_SEQUENTIALLY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ (c~ @ (V0 @ V5))) @ V5))))))) @ ((c= @ (((c--> @ (^[V4]: (((cCOND @ (V0 @ V4)) @ (V2 @ V4)) @ (V1 @ V4)))) @ V3) @ csequentially)) @ (((c--> @ V2) @ V3) @ csequentially))))))))))))
(TLIM_CASES_FINITE_SEQUENTIALLY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ (V0 @ V5)) @ V5))))))) @ ((c= @ (((c--> @ (^[V4]: (((cCOND @ (V0 @ V4)) @ (V1 @ V4)) @ (V2 @ V4)))) @ V3) @ csequentially)) @ (((c--> @ V2) @ V3) @ csequentially))))))))))))
(TMBASIS_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$$ @ (cmbasis @ V1)) @ V0)) @ (((cCOND @ ((c= @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))
(TSCHNIRELMANN_MONO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ V1)) @ ((creal_le @ (cschnirelmann @ V0)) @ (cschnirelmann @ V1))))))))
(TSUMSET_SUPERSET_RZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ (cNUMERAL @ c_0)) @ V1)) @ ((cSUBSET @ V0) @ ((c+++ @ V0) @ V1))))))))
(TSUMSET_SUPERSET_LZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ (cNUMERAL @ c_0)) @ V0)) @ ((cSUBSET @ V1) @ ((c+++ @ V0) @ V1))))))))
(TSUMSET_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cIN @ (cNUMERAL @ c_0)) @ V0)) @ ((cIN @ (cNUMERAL @ c_0)) @ V1))) @ ((cIN @ (cNUMERAL @ c_0)) @ ((c+++ @ V0) @ V1))))))))
(TSCHNIRELMANN_INSENSITIVE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c= @ ((cIN @ V2) @ V0)) @ ((cIN @ V2) @ V1)))))) @ ((c= @ (cschnirelmann @ V0)) @ (cschnirelmann @ V1))))))))
(TSUMSET_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+++ @ V1) @ V0)) @ ((c+++ @ V0) @ V1)))))))
(Tsumset,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+++ @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((c+ @ V3) @ V4))))))))))))))
(TOUTER_MBASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((couter @ (cmbasis @ V0)) @ (cmbasis @ V1))) @ (((cCOND @ ((c/__caret__ @ ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)))) @ ((c% @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c> @ V3) @ V4)))) @ ((c__comma__ @ V3) @ V4))))))))))) @ (cmbasis @ ((cUNION @ V0) @ V1)))) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TGEOM_MBASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cgeom_mul @ (cmbasis @ V1)) @ (cmbasis @ V0))) @ (((cCOND @ ((c/__caret__ @ ((cSUBSET @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))) @ ((c% @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c> @ V3) @ V4)))) @ ((c__comma__ @ V3) @ V4))))))))))) @ (cmbasis @ ((cUNION @ ((cDIFF @ V1) @ V0)) @ ((cDIFF @ V0) @ V1))))) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TCOUNT_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V0) @ V1)) @ ((c<= @ ((ccount @ V0) @ V2)) @ ((ccount @ V1) @ V2))))))))))
(TCOUNT_INSENSITIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c= @ ((cIN @ V3) @ V0)) @ ((cIN @ V3) @ V1)))))) @ ((c= @ ((ccount @ V0) @ V2)) @ ((ccount @ V1) @ V2))))))))))
(TVARIATION_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cDIFF @ V0) @ V1))) @ ((c= @ (V2 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((cvariation @ V0) @ V2)) @ ((cvariation @ V1) @ V2))))))))))
(TSUMMABLE_SUBSET_ABSCONV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V0) @ (^[V3]: (clift @ (cvector_norm @ (V2 @ V3)))))) @ ((cSUBSET @ V1) @ V0))) @ ((csummable @ V1) @ (^[V3]: (clift @ (cvector_norm @ (V2 @ V3)))))))))))))
(TSUMMABLE_EQ_COFINITE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ ((cUNION @ ((cDIFF @ V0) @ V1)) @ ((cDIFF @ V1) @ V0)))) @ ((csummable @ V0) @ V2))) @ ((csummable @ V1) @ V2)))))))))
(TSUMMABLE_IFF_COFINITE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ ((cUNION @ ((cDIFF @ V0) @ V1)) @ ((cDIFF @ V1) @ V0)))) @ ((c= @ ((csummable @ V0) @ V2)) @ ((csummable @ V1) @ V2))))))))))
(TSUMMABLE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((csummable @ V0) @ (^[V3]: (((cCOND @ ((cIN @ V3) @ V1)) @ (V2 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((csummable @ V1) @ V2)))))))))
(TSUMSET_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c+++ @ V0) @ ((c+++ @ V1) @ V2))) @ ((c+++ @ ((c+++ @ V0) @ V1)) @ V2)))))))))
(TOUTERMORPHISM_MBASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ ((coutermorphism @ V1) @ (cmbasis @ V0))) @ (((cseqiterate @ couter) @ V0) @ ((co @ cmultivec) @ ((co @ V1) @ cbasis))))))))))
(TSUMMABLE_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V0) @ V2)) @ (clinear @ V1))) @ ((csummable @ V0) @ (^[V3]: (V1 @ (V2 @ V3))))))))))))
(TNPRODUCT_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (V0 @ V4))) @ (V0 @ ((c* @ V3) @ V4)))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (V0 @ (V2 @ V3)))))))) @ (V0 @ ((cnproduct @ V1) @ V2))))))))))
(TNSUM_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (V0 @ V4))) @ (V0 @ ((c+ @ V3) @ V4)))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (V0 @ (V2 @ V3)))))))) @ (V0 @ ((cnsum @ V1) @ V2))))))))))
(TIN_SPAN_IMAGE_BASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V1) @ (cspan @ ((cIMAGE @ cbasis) @ V0)))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ (c~ @ ((cIN @ V2) @ V0))))) @ ((c= @ ((c$ @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))
(Tnode_RECURSION,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: ((c= @ (V1 @ (cNode @ V2))) @ (V0 @ V2)))))))))
(TFCONS_UNDO,(c! @ (^[V0]: ((c= @ V0) @ ((cFCONS @ (V0 @ (cNUMERAL @ c_0))) @ ((co @ V0) @ cSUC))))))
(Tlambda,(c! @ (^[V0]: ((c= @ (clambda @ V0)) @ (c__at__ @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ V1) @ V2)) @ (V0 @ V2)))))))))))
(TLAMBDA_BETA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ (clambda @ V0)) @ V1)) @ (V0 @ V1))))))))
(TLAMBDA_BETA_PERM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpermutes @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV))))) @ ((c= @ ((c$ @ (clambda @ V0)) @ (V1 @ V2))) @ (V0 @ (V1 @ V2)))))))))))
(TLAMBDA_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ V1) @ V2)) @ (V0 @ V2)))))) @ ((c= @ (clambda @ V0)) @ V1)))))))
(TITERATE_CLAUSES_NUMSEG_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmonoidal @ V1)) @ (c! @ (^[V2]: ((c= @ (((citerate @ V1) @ ((c.. @ V2) @ (cNUMERAL @ c_0))) @ V0)) @ (((cCOND @ ((c= @ V2) @ (cNUMERAL @ c_0))) @ (V0 @ (cNUMERAL @ c_0))) @ (cneutral @ V1)))))))))))
(Tnode_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (V0 @ (cNode @ V2))))) @ (V0 @ V1)))))))
(TNADD_COMPLETE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((cnadd_le @ V2) @ V1)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((cnadd_le @ V2) @ V1))))) @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((cnadd_le @ V3) @ V2))))) @ ((cnadd_le @ V1) @ V2)))))))))))
(TFORALL_MULTIVECTOR,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ (V0 @ (cmk_multivector @ V1)))))) @ (c! @ (^[V1]: (V0 @ V1)))))))
(TMULTISET_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cmempty)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ ((cmunion @ V3) @ (cmsing @ V2)))))))))) @ (V0 @ V1)))))))
(Tproves_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ (cwelltyped @ V3)) @ ((V0 @ cNIL) @ ((c=== @ V3) @ V3)))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ ((c=== @ V5) @ V6))) @ ((c/__caret__ @ ((V0 @ V4) @ ((c=== @ V7) @ V8))) @ ((cACONV @ V6) @ V7)))) @ ((V0 @ ((cTERM_UNION @ V3) @ V4)) @ ((c=== @ V5) @ V8)))))))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ ((c=== @ V4) @ V5))) @ ((c/__caret__ @ ((V0 @ V6) @ ((c=== @ V7) @ V8))) @ (cwelltyped @ ((cComb @ V4) @ V7))))) @ ((V0 @ ((cTERM_UNION @ V3) @ V6)) @ ((c=== @ ((cComb @ V4) @ V7)) @ ((cComb @ V5) @ V8))))))))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ (c~ @ ((cEX @ (cVFREE_IN @ ((cVar @ V4) @ V5))) @ V3))) @ ((V0 @ V3) @ ((c=== @ V6) @ V7)))) @ ((V0 @ V3) @ ((c=== @ (((cAbs @ V4) @ V5) @ V6)) @ (((cAbs @ V4) @ V5) @ V7))))))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (cwelltyped @ V5)) @ ((V0 @ cNIL) @ ((c=== @ ((cComb @ (((cAbs @ V3) @ V4) @ V5)) @ ((cVar @ V3) @ V4))) @ V5)))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((chas_type @ V3) @ cBool)) @ ((V0 @ ((cCONS @ V3) @ cNIL)) @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ ((c=== @ V5) @ V6))) @ ((c/__caret__ @ ((V0 @ V4) @ V7)) @ ((cACONV @ V5) @ V7)))) @ ((V0 @ ((cTERM_UNION @ V3) @ V4)) @ V6))))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ V5)) @ ((V0 @ V4) @ V6))) @ ((V0 @ ((cTERM_UNION @ ((cFILTER @ ((co @ c~) @ (cACONV @ V6))) @ V3)) @ ((cFILTER @ ((co @ c~) @ (cACONV @ V5))) @ V4))) @ ((c=== @ V5) @ V6)))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V0 @ ((cMAP @ (cINST @ V3)) @ V4)) @ ((cINST @ V3) @ V5)))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((cMEM @ ((c__comma__ @ V7) @ V6)) @ V3)) @ (c? @ (^[V8]: (c? @ (^[V9]: ((c/__caret__ @ ((c= @ V6) @ ((cVar @ V8) @ V9))) @ ((chas_type @ V7) @ V9)))))))))))) @ ((V0 @ V4) @ V5))) @ ((V0 @ ((cMAP @ (cVSUBST @ V3)) @ V4)) @ ((cVSUBST @ V3) @ V5))))))))))))))))))) @ ((c==> @ ((c|- @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))
(TRACONV_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((cALPHAVARS @ V3) @ ((c__comma__ @ ((cVar @ V4) @ V5)) @ ((cVar @ V6) @ V7)))) @ ((V0 @ V3) @ ((c__comma__ @ ((cVar @ V4) @ V5)) @ ((cVar @ V6) @ V7))))))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((V0 @ V3) @ ((c__comma__ @ (cEqual @ V4)) @ (cEqual @ V4)))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((V0 @ V3) @ ((c__comma__ @ (cSelect @ V4)) @ (cSelect @ V4)))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ ((c__comma__ @ V4) @ V6))) @ ((V0 @ V3) @ ((c__comma__ @ V5) @ V7)))) @ ((V0 @ V3) @ ((c__comma__ @ ((cComb @ V4) @ V5)) @ ((cComb @ V6) @ V7))))))))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((c= @ V5) @ V8)) @ ((V0 @ ((cCONS @ ((c__comma__ @ ((cVar @ V4) @ V5)) @ ((cVar @ V7) @ V8))) @ V3)) @ ((c__comma__ @ V6) @ V9)))) @ ((V0 @ V3) @ ((c__comma__ @ (((cAbs @ V4) @ V5) @ V6)) @ (((cAbs @ V7) @ V8) @ V9))))))))))))))))))))))) @ ((c==> @ ((cRACONV @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))
(Tstring_RECURSION,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: ((c= @ (V1 @ (cString @ V2))) @ (V0 @ V2)))))))))
(Tterm_RECURSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ (c! @ (^[V6]: (c! @ (^[V7]: ((c= @ (V5 @ ((cVar @ V6) @ V7))) @ ((V0 @ V6) @ V7))))))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c= @ (V5 @ (cEqual @ V6))) @ (V1 @ V6))))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c= @ (V5 @ (cSelect @ V6))) @ (V2 @ V6))))) @ ((c/__caret__ @ (c! @ (^[V6]: (c! @ (^[V7]: ((c= @ (V5 @ ((cComb @ V6) @ V7))) @ ((((V3 @ V6) @ V7) @ (V5 @ V6)) @ (V5 @ V7)))))))) @ (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c= @ (V5 @ (((cAbs @ V6) @ V7) @ V8))) @ ((((V4 @ V6) @ V7) @ V8) @ (V5 @ V8))))))))))))))))))))))))))
(Ttype_RECURSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (c! @ (^[V5]: ((c= @ (V4 @ (cTyvar @ V5))) @ (V0 @ V5))))) @ ((c/__caret__ @ ((c= @ (V4 @ cBool)) @ V1)) @ ((c/__caret__ @ ((c= @ (V4 @ cInd)) @ V2)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c= @ (V4 @ ((cFun @ V5) @ V6))) @ ((((V3 @ V5) @ V6) @ (V4 @ V5)) @ (V4 @ V6)))))))))))))))))))))
(Tlist_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cNIL)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ ((cCONS @ V2) @ V3))))))))) @ (V0 @ V1)))))))
(Tlist_WF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((c< @ (cLENGTH @ V3)) @ (cLENGTH @ V2))) @ (V0 @ V3))))) @ (V0 @ V2))))) @ (V0 @ V1)))))))
(TPERMUTED_INDUCT_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((V0 @ cNIL) @ cNIL)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cPERMUTED @ V4) @ V5)) @ ((V0 @ V4) @ V5))) @ ((V0 @ ((cCONS @ V3) @ V4)) @ ((cCONS @ V3) @ V5)))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c/__caret__ @ ((cPERMUTED @ V3) @ V4)) @ ((V0 @ V3) @ V4))) @ ((c/__caret__ @ ((cPERMUTED @ V4) @ V5)) @ ((V0 @ V4) @ V5)))) @ ((V0 @ V3) @ V5))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((V0 @ ((cCONS @ V3) @ ((cCONS @ V4) @ V5))) @ ((cCONS @ V4) @ ((cCONS @ V3) @ V5))))))))))))) @ ((c==> @ ((cPERMUTED @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))
(TPERMUTED_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((V0 @ cNIL) @ cNIL)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V0 @ ((cCONS @ V3) @ V4)) @ ((cCONS @ V3) @ V5)))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V5))) @ ((V0 @ V3) @ V5))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((V0 @ ((cCONS @ V3) @ ((cCONS @ V4) @ V5))) @ ((cCONS @ V4) @ ((cCONS @ V3) @ V5))))))))))))) @ ((c==> @ ((cPERMUTED @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))
(TLIST_UNIQ_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cNIL)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (c~ @ ((cMEM @ V2) @ V3)))) @ (V0 @ ((cCONS @ V2) @ V3))))))))) @ ((c==> @ (cLIST_UNIQ @ V1)) @ (V0 @ V1))))))))
(TPOINT_CLAUSES_conjunct2,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ (cdest_point @ V1))))) @ (c? @ (^[V1]: (V0 @ V1)))))))
(TPOINT_CLAUSES_conjunct1,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ (cdest_point @ V1))))) @ (c! @ (^[V1]: (V0 @ V1)))))))
(TINT_EXISTS_POS,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ (cint_of_num @ V1))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (V0 @ V1))))))))
(TINT_EXISTS_ABS,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ (cint_of_num @ V1))))) @ (c? @ (^[V1]: (V0 @ (cint_abs @ V1))))))))
(TINT_WOP,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (V0 @ V1))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ (V0 @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (V0 @ V2))) @ ((cint_le @ V1) @ V2))))))))))))
(TEXISTS_MULTIPLE_THM_1,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ ((cint_mul @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1))))) @ (c? @ (^[V1]: (V0 @ V1)))))))
(TEXISTS_NEG,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ (cint_neg @ V1))))) @ (c? @ (^[V1]: (V0 @ V1)))))))
(TINT_EXISTS_CASES,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ ((c__caret__/ @ (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cint_lt @ V2) @ V1)) @ (V0 @ V2))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (V0 @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cint_lt @ V2) @ V1)) @ (c~ @ (V0 @ V2)))))))))))))
(TINT_FORALL_POS,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ (cint_of_num @ V1))))) @ (c! @ (^[V1]: ((c==> @ ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (V0 @ V1))))))))
(TINT_FORALL_ABS,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ (cint_of_num @ V1))))) @ (c! @ (^[V1]: (V0 @ (cint_abs @ V1))))))))
(TFORALL_NEG,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ (cint_neg @ V1))))) @ (c! @ (^[V1]: (V0 @ V1)))))))
(TINT_PRIME_FACTOR_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ (cint_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (V0 @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (V0 @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cint_prime @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ (V0 @ V3)))) @ (V0 @ ((cint_mul @ V2) @ V3))))))))))) @ (V0 @ V1)))))))
(Tcform_RECURSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c? @ (^[V9]: ((c/__caret__ @ (c! @ (^[V10]: ((c= @ (V9 @ (cLt @ V10))) @ (V0 @ V10))))) @ ((c/__caret__ @ (c! @ (^[V10]: ((c= @ (V9 @ (cGt @ V10))) @ (V1 @ V10))))) @ ((c/__caret__ @ (c! @ (^[V10]: ((c= @ (V9 @ (cEq @ V10))) @ (V2 @ V10))))) @ ((c/__caret__ @ (c! @ (^[V10]: ((c= @ (V9 @ (cNe @ V10))) @ (V3 @ V10))))) @ ((c/__caret__ @ (c! @ (^[V10]: (c! @ (^[V11]: ((c= @ (V9 @ ((cDivides @ V10) @ V11))) @ ((V4 @ V10) @ V11))))))) @ ((c/__caret__ @ (c! @ (^[V10]: (c! @ (^[V11]: ((c= @ (V9 @ ((cNdivides @ V10) @ V11))) @ ((V5 @ V10) @ V11))))))) @ ((c/__caret__ @ (c! @ (^[V10]: (c! @ (^[V11]: ((c= @ (V9 @ ((cAnd @ V10) @ V11))) @ ((((V6 @ V10) @ V11) @ (V9 @ V10)) @ (V9 @ V11)))))))) @ ((c/__caret__ @ (c! @ (^[V10]: (c! @ (^[V11]: ((c= @ (V9 @ ((cOr @ V10) @ V11))) @ ((((V7 @ V10) @ V11) @ (V9 @ V10)) @ (V9 @ V11)))))))) @ (c! @ (^[V10]: ((c= @ (V9 @ (cNox @ V10))) @ (V8 @ V10)))))))))))))))))))))))))))))))))
(TNUM_REP_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cIND_0)) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cIND_SUC @ V2))))))) @ ((c==> @ (cNUM_REP @ V1)) @ (V0 @ V1))))))))
(THREAL_COMPLETE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((chreal_le @ V2) @ V1)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((chreal_le @ V2) @ V1))))) @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((chreal_le @ V3) @ V2))))) @ ((chreal_le @ V1) @ V2)))))))))))
(TREAL_OPEN_INTERS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (creal_open @ V1)))))) @ (creal_open @ (cINTERS @ V0))))))
(TREAL_CLOSED_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (creal_closed @ V1)))))) @ (creal_closed @ (cUNIONS @ V0))))))
(TREAL_OPEN_UNIONS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (creal_open @ V1))))) @ (creal_open @ (cUNIONS @ V0))))))
(TREAL_CLOSED_INTERS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (creal_closed @ V1))))) @ (creal_closed @ (cINTERS @ V0))))))
(TEXISTS_DROP_IMAGE,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (V0 @ ((cIMAGE @ cdrop) @ V1))))))))
(TFORALL_DROP_IMAGE,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (V0 @ ((cIMAGE @ cdrop) @ V1))))))))
(TORDINAL_UNION,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ (V0 @ V1)) @ (cordinal @ V1))))) @ (cordinal @ (cUNIONS @ V0))))))
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(TUNION_FL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cfl @ (cUNIONS @ V0)) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ ((cfl @ V2) @ V1))))))))))
(TFORALL_CURRY,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (V0 @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ ((V1 @ V3) @ V4)))))))))))))))
(TEXISTS_CURRY,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (V0 @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ ((V1 @ V3) @ V4)))))))))))))))
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(TKLE_MINIMAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V0))) @ ((c__caret__/ @ (((ckle @ V1) @ V2) @ V3)) @ (((ckle @ V1) @ V3) @ V2)))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (((ckle @ V1) @ V2) @ V3)))))))))))))
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(TBILINEAR_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: (cbilinear @ ((cProduct @ V0) @ V1)))))))
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(TPRODUCT_MBASIS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((cProduct @ V0) @ V1) @ (cmbasis @ V2)) @ (cmbasis @ V3))) @ (((cCOND @ ((c/__caret__ @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((cSUBSET @ V3) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))) @ ((c% @ ((V0 @ V2) @ V3)) @ (cmbasis @ ((V1 @ V2) @ V3)))) @ (cvec @ (cNUMERAL @ c_0)))))))))))))
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(TPRODUCT_RZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((((cProduct @ V0) @ V1) @ V2) @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))))))))
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(TPRODUCT_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((cProduct @ V0) @ V1) @ V2) @ (cvector_neg @ V3))) @ (cvector_neg @ ((((cProduct @ V0) @ V1) @ V2) @ V3))))))))))))
(Teval,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ceval @ (cPropform @ V0)) @ V1)) @ (V0 @ V1)))))))
(TWF_REC_num,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((c< @ V4) @ V3)) @ ((c= @ (V1 @ V4)) @ (V2 @ V4)))))) @ ((c= @ ((V0 @ V1) @ V3)) @ ((V0 @ V2) @ V3)))))))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c= @ (V1 @ V2)) @ ((V0 @ V1) @ V2))))))))))
(Tpropform_RECURSION,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: ((c= @ (V1 @ (cPropform @ V2))) @ (V0 @ V2)))))))))
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(TFORALL_LIFT_IMAGE,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (V0 @ ((cIMAGE @ clift) @ V1))))))))
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(TSTARLIKE_IMP_CONTRACTIBLE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((creal_le @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (V0 @ (^[V4]: ((cvector_add @ ((c% @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3)) @ V4)) @ ((c% @ V3) @ V2)))))))))) @ (cstarlike @ V1))) @ (c? @ (^[V2]: ((((chomotopic_with @ V0) @ ((c__comma__ @ V1) @ V1)) @ (^[V3]: V3)) @ (^[V3]: V2))))))))))
(TOPEN_NON_GENERAL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (((V0 @ V3) @ V4) @ V5)) @ ((c/__caret__ @ ((cIN @ V4) @ V3)) @ ((cIN @ V5) @ V3)))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (((V0 @ V3) @ V4) @ V5)) @ (((V0 @ V3) @ V5) @ V4))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (((V0 @ V3) @ V4) @ V5)) @ (((V0 @ V3) @ V5) @ V6))) @ (((V0 @ V3) @ V4) @ V6))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V4)) @ (((V0 @ V3) @ V5) @ V6))) @ (((V0 @ V4) @ V5) @ V6))))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cball @ ((c__comma__ @ V4) @ V6)))) @ ((cSUBSET @ (cball @ ((c__comma__ @ V4) @ V6))) @ V3))) @ (((V0 @ (cball @ ((c__comma__ @ V4) @ V6))) @ V4) @ V5))))))))))))))) @ ((c==> @ (copen @ V1)) @ (copen @ ((cDIFF @ V1) @ ((V0 @ V1) @ V2))))))))))))
(TOPEN_GENERAL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (((V0 @ V3) @ V4) @ V5)) @ ((c/__caret__ @ ((cIN @ V4) @ V3)) @ ((cIN @ V5) @ V3)))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (((V0 @ V3) @ V4) @ V5)) @ (((V0 @ V3) @ V5) @ V4))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (((V0 @ V3) @ V4) @ V5)) @ (((V0 @ V3) @ V5) @ V6))) @ (((V0 @ V3) @ V4) @ V6))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V4)) @ (((V0 @ V3) @ V5) @ V6))) @ (((V0 @ V4) @ V5) @ V6))))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cball @ ((c__comma__ @ V4) @ V6)))) @ ((cSUBSET @ (cball @ ((c__comma__ @ V4) @ V6))) @ V3))) @ (((V0 @ (cball @ ((c__comma__ @ V4) @ V6))) @ V4) @ V5))))))))))))))) @ ((c==> @ (copen @ V1)) @ (copen @ ((V0 @ V1) @ V2)))))))))))
(TGENERAL_CONNECTED_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (((V0 @ V4) @ V5) @ V6)) @ ((c/__caret__ @ ((cIN @ V5) @ V4)) @ ((cIN @ V6) @ V4)))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (((V0 @ V4) @ V5) @ V6)) @ (((V0 @ V4) @ V6) @ V5))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ (((V0 @ V4) @ V5) @ V6)) @ (((V0 @ V4) @ V6) @ V7))) @ (((V0 @ V4) @ V5) @ V7))))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V4) @ V5)) @ (((V0 @ V4) @ V6) @ V7))) @ (((V0 @ V5) @ V6) @ V7))))))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ (cball @ ((c__comma__ @ V5) @ V7)))) @ ((cSUBSET @ (cball @ ((c__comma__ @ V5) @ V7))) @ V4))) @ (((V0 @ (cball @ ((c__comma__ @ V5) @ V7))) @ V5) @ V6))))))))))))))) @ ((c==> @ ((c/__caret__ @ (copen @ V1)) @ ((c/__caret__ @ (cconnected @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((cIN @ V3) @ V1))))) @ (((V0 @ V1) @ V2) @ V3))))))))))))
(TFRONTIER_UNIONS_SUBSET_CLOSURE,(c! @ (^[V0]: ((cSUBSET @ (cfrontier @ (cUNIONS @ V0))) @ (cclosure @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ (cfrontier @ V2))))))))))))
(THELLY_COMPACT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c==> @ (cFINITE @ V0)) @ ((c>= @ (cCARD @ V0)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (cconvex @ V1)) @ (ccompact @ V1)))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c= @ (cCARD @ V1)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY)))))))) @ (c~ @ ((c= @ (cINTERS @ V0)) @ cEMPTY))))))
(THELLY_CLOSED,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c==> @ (cFINITE @ V0)) @ ((c>= @ (cCARD @ V0)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (cconvex @ V1)) @ (cclosed @ V1)))))) @ ((c/__caret__ @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (cbounded @ V1))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c= @ (cCARD @ V1)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY))))))))) @ (c~ @ ((c= @ (cINTERS @ V0)) @ cEMPTY))))))
(THELLY,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((c>= @ (cCARD @ V0)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cconvex @ V1))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c= @ (cCARD @ V1)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY))))))))) @ (c~ @ ((c= @ (cINTERS @ V0)) @ cEMPTY))))))
(TELEMENTARY_INTERS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: ((cdivision_of @ V2) @ V1))))))))) @ (c? @ (^[V1]: ((cdivision_of @ V1) @ (cINTERS @ V0))))))))
(THELLY_ALT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cconvex @ V1))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c<= @ (cCARD @ V1)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY)))))))) @ (c~ @ ((c= @ (cINTERS @ V0)) @ cEMPTY))))))
(TENR_FINITE_UNIONS_CONVEX_CLOSED,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ (cconvex @ V1))))))) @ (cENR @ (cUNIONS @ V0))))))
(TANR_FINITE_UNIONS_CONVEX_CLOSED,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ (cconvex @ V1))))))) @ (cANR @ (cUNIONS @ V0))))))
(TPOLYHEDRON_INTERS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cpolyhedron @ V1)))))) @ (cpolyhedron @ (cINTERS @ V0))))))
(TMEASURE_UNIONS_LE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cmeasurable @ V1)))))) @ ((creal_le @ (cmeasure @ (cUNIONS @ V0))) @ ((csum @ V0) @ (^[V1]: (cmeasure @ V1))))))))
(TMEASURABLE_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cmeasurable @ V1)))))) @ (cmeasurable @ (cUNIONS @ V0))))))
(TLEBESGUE_MEASURABLE_INTERS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (clebesgue_measurable @ V1)))))) @ (clebesgue_measurable @ (cINTERS @ V0))))))
(TAUSTIN_LEMMA,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV)))) @ ((c= @ ((creal_sub @ ((c$ @ V4) @ V5)) @ ((c$ @ V3) @ V5))) @ V2)))))))))))))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ ((cpairwise @ cDISJOINT) @ V1)) @ ((creal_ge @ (cmeasure @ (cUNIONS @ V1))) @ ((creal_div @ (cmeasure @ (cUNIONS @ V0))) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cdimindex @ cUNIV))))))))))))
(TELEMENTARY_UNIONS_INTERVALS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))) @ (c? @ (^[V1]: ((cdivision_of @ V1) @ (cUNIONS @ V0))))))))
(TMEASURABLE_COUNTABLE_INTERS_GEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cmeasurable @ V1))))))) @ (cmeasurable @ (cINTERS @ V0))))))
(TNEGLIGIBLE_COUNTABLE_UNIONS_GEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cnegligible @ V1)))))) @ (cnegligible @ (cUNIONS @ V0))))))
(TLEBESGUE_MEASURABLE_COUNTABLE_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (clebesgue_measurable @ V1)))))) @ (clebesgue_measurable @ (cUNIONS @ V0))))))
(TLEBESGUE_MEASURABLE_COUNTABLE_INTERS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (clebesgue_measurable @ V1)))))) @ (clebesgue_measurable @ (cINTERS @ V0))))))
(TCOUNTABLE_ELEMENTARY_DIVISION,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c= @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((c= @ ((cINTER @ (cinterior @ V2)) @ (cinterior @ V3))) @ cEMPTY))))))) @ ((c= @ (cUNIONS @ V1)) @ (cUNIONS @ V0)))))))))))
(THELLY_COMPACT_ALT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (cconvex @ V1)) @ (ccompact @ V1)))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c<= @ (cCARD @ V1)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY))))))) @ (c~ @ ((c= @ (cINTERS @ V0)) @ cEMPTY))))))
(THELLY_CLOSED_ALT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (cconvex @ V1)) @ (cclosed @ V1)))))) @ ((c/__caret__ @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (cbounded @ V1))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c<= @ (cCARD @ V1)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY)))))))) @ (c~ @ ((c= @ (cINTERS @ V0)) @ cEMPTY))))))
(TCOMPACT_CHAIN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (ccompact @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((c__caret__/ @ ((cSUBSET @ V1) @ V2)) @ ((cSUBSET @ V2) @ V1))))))))) @ (c~ @ ((c= @ (cINTERS @ V0)) @ cEMPTY))))))
(TCONNECTED_CHAIN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (ccompact @ V1)) @ (cconnected @ V1)))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((c__caret__/ @ ((cSUBSET @ V1) @ V2)) @ ((cSUBSET @ V2) @ V1))))))))) @ (cconnected @ (cINTERS @ V0))))))
(TCONNECTED_CHAIN_GEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ (cconnected @ V1)))))) @ ((c/__caret__ @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (ccompact @ V1))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((c__caret__/ @ ((cSUBSET @ V1) @ V2)) @ ((cSUBSET @ V2) @ V1)))))))))) @ (cconnected @ (cINTERS @ V0))))))
(TCOUNTABLE_DISJOINT_OPEN_SUBSETS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (copen @ V1))))) @ ((cpairwise @ cDISJOINT) @ V0))) @ (cCOUNTABLE @ V0)))))
(TCLOSURE_INTERS_CONVEX,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cconvex @ V1))))) @ (c~ @ ((c= @ (cINTERS @ ((cIMAGE @ crelative_interior) @ V0))) @ cEMPTY)))) @ ((c= @ (cclosure @ (cINTERS @ V0))) @ (cINTERS @ ((cIMAGE @ cclosure) @ V0)))))))
(TCONNECTED_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cconnected @ V1))))) @ (c~ @ ((c= @ (cINTERS @ V0)) @ cEMPTY)))) @ (cconnected @ (cUNIONS @ V0))))))
(TCOMPACT_INTERS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (ccompact @ V1))))) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (ccompact @ (cINTERS @ V0))))))
(TCOMPACT_FIP,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (ccompact @ V1))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cSUBSET @ V1) @ V0))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY))))))) @ (c~ @ ((c= @ (cINTERS @ V0)) @ cEMPTY))))))
(TCLOSED_FIP,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cclosed @ V1))))) @ ((c/__caret__ @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (cbounded @ V1))))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cSUBSET @ V1) @ V0))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY)))))))) @ (c~ @ ((c= @ (cINTERS @ V0)) @ cEMPTY))))))
(TCONVEX_HULL_INTERS,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ (cUNIONS @ V0)))) @ ((c= @ ((chull @ cconvex) @ (cINTERS @ V0))) @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ ((chull @ cconvex) @ V2))))))))))))
(TAFFINE_HULL_INTERS,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ (cUNIONS @ V0)))) @ ((c= @ ((chull @ caffine) @ (cINTERS @ V0))) @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ ((chull @ caffine) @ V2))))))))))))
(TTRIANGULATION_SIMPLICIAL_COMPLEX,(c! @ (^[V0]: ((c==> @ (ctriangulation @ V0)) @ (csimplicial_complex @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cface_of @ V2) @ V3))))) @ V2))))))))))
(TFRONTIER_UNIONS_SUBSET,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((cSUBSET @ (cfrontier @ (cUNIONS @ V0))) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ (cfrontier @ V2))))))))))))
(TINTERIOR_FINITE_INTERS,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cinterior @ (cINTERS @ V0))) @ (cINTERS @ ((cIMAGE @ cinterior) @ V0)))))))
(TBOUNDED_INTERS,(c! @ (^[V0]: ((c==> @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (cbounded @ V1))))) @ (cbounded @ (cINTERS @ V0))))))
(TCLOSURE_INTERS_CONVEX_OPEN,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (cconvex @ V1)) @ (copen @ V1)))))) @ ((c= @ (cclosure @ (cINTERS @ V0))) @ (((cCOND @ ((c= @ (cINTERS @ V0)) @ cEMPTY)) @ cEMPTY) @ (cINTERS @ ((cIMAGE @ cclosure) @ V0))))))))
(TLINDELOF,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (copen @ V1))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c= @ (cUNIONS @ V1)) @ (cUNIONS @ V0))))))))))
(TCONVEX_CONE_INTERS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cconvex_cone @ V1))))) @ (cconvex_cone @ (cINTERS @ V0))))))
(TCLOSED_INTERS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cclosed @ V1))))) @ (cclosed @ (cINTERS @ V0))))))
(TPROPERTY_EMPTY_INTERVAL,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (V0 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))) @ (V0 @ cEMPTY)))))
(Ttriangulation,(c! @ (^[V0]: ((c= @ (ctriangulation @ V0)) @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: ((csimplex @ V2) @ V1))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((c/__caret__ @ ((cface_of @ ((cINTER @ V1) @ V2)) @ V1)) @ ((cface_of @ ((cINTER @ V1) @ V2)) @ V2)))))))))))))
(TTRANSLATION_EQ_IMP,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (V0 @ ((cIMAGE @ (^[V3]: ((cvector_add @ V1) @ V3))) @ V2))) @ (V0 @ V2))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ ((cIMAGE @ (^[V3]: ((cvector_add @ V1) @ V3))) @ V2)))))))))))
(TMEASURE_COUNTABLE_UNIONS_LE_GEN_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cmeasurable @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ (cFINITE @ V2))) @ ((creal_le @ ((csum @ V2) @ (^[V3]: (cmeasure @ V3)))) @ V1))))))) @ ((creal_le @ (cmeasure @ (cUNIONS @ V0))) @ V1)))))))
(TMEASURE_COUNTABLE_UNIONS_LE_STRONG_GEN_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cmeasurable @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ (cFINITE @ V2))) @ ((creal_le @ (cmeasure @ (cUNIONS @ V2))) @ V1))))))) @ ((creal_le @ (cmeasure @ (cUNIONS @ V0))) @ V1)))))))
(THAS_MEASURE_DISJOINT_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((chas_measure @ V2) @ (V1 @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((cDISJOINT @ V2) @ V3))))))))) @ ((chas_measure @ (cUNIONS @ V0)) @ ((csum @ V0) @ V1))))))))
(TMEASURE_DISJOINT_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((chas_measure @ V2) @ (V1 @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((cDISJOINT @ V2) @ V3))))))))) @ ((c= @ (cmeasure @ (cUNIONS @ V0))) @ ((csum @ V0) @ V1))))))))
(THAS_MEASURE_NEGLIGIBLE_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((chas_measure @ V2) @ (V1 @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ (cnegligible @ ((cINTER @ V2) @ V3)))))))))) @ ((chas_measure @ (cUNIONS @ V0)) @ ((csum @ V0) @ V1))))))))
(TMEASURE_NEGLIGIBLE_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((chas_measure @ V2) @ (V1 @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ (cnegligible @ ((cINTER @ V2) @ V3)))))))))) @ ((c= @ (cmeasure @ (cUNIONS @ V0))) @ ((csum @ V0) @ V1))))))))
(TCONNECTED_DISJOINT_UNIONS_OPEN_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cpairwise @ cDISJOINT) @ V0)) @ ((c/__caret__ @ ((cpairwise @ cDISJOINT) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ (cconnected @ V2)) @ (c~ @ ((c= @ V2) @ cEMPTY)))))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ (cconnected @ V2)) @ (c~ @ ((c= @ V2) @ cEMPTY)))))))) @ ((c= @ (cUNIONS @ V0)) @ (cUNIONS @ V1))))))) @ ((c= @ V0) @ V1)))))))
(TDIVISION_OF_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ (cUNIONS @ V0))) @ ((cSUBSET @ V1) @ V0))) @ ((cdivision_of @ V1) @ (cUNIONS @ V1))))))))
(TTRIANGULATION_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ctriangulation @ V0)) @ ((cSUBSET @ V1) @ V0))) @ (ctriangulation @ V1)))))))
(TDIVISION_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ V2)) @ ((cdivision_of @ V1) @ V3))) @ ((cdivision_of @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ (c~ @ ((c= @ ((cINTER @ V5) @ V6)) @ cEMPTY))))) @ ((cINTER @ V5) @ V6))))))))) @ ((cINTER @ V2) @ V3))))))))))))
(TDIVISION_DISJOINT_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ V2)) @ ((c/__caret__ @ ((cdivision_of @ V1) @ V3)) @ ((c= @ ((cINTER @ (cinterior @ V2)) @ (cinterior @ V3))) @ cEMPTY)))) @ ((cdivision_of @ ((cUNION @ V0) @ V1)) @ ((cUNION @ V2) @ V3))))))))))))
(TEXPOSED_FACE_OF_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cexposed_face_of @ V2) @ V1)))))) @ ((cexposed_face_of @ (cINTERS @ V0)) @ V1)))))))
(TCONVEX_HULL_UNION_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ (cUNIONS @ V0))) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((chull @ cconvex) @ ((cUNION @ V1) @ (cUNIONS @ V0)))) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((chull @ cconvex) @ ((cUNION @ V1) @ V3)))))))))))))))
(TBAIRE_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c= @ (cUNIONS @ V0)) @ V1))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cSUBSET @ V3) @ (cclosure @ V2))))))))))))))
(TPARACOMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (copen @ V2))))) @ ((cSUBSET @ V1) @ (cUNIONS @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V1) @ (cUNIONS @ V2))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ (copen @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cSUBSET @ V3) @ V4))))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (c? @ (^[V4]: ((c/__caret__ @ (copen @ V4)) @ ((c/__caret__ @ ((cIN @ V3) @ V4)) @ (cFINITE @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ (c~ @ ((c= @ ((cINTER @ V6) @ V4)) @ cEMPTY)))) @ V6)))))))))))))))))))))))
(TCOMPACT_IMP_HEINE_BOREL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (ccompact @ V1)) @ ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (copen @ V2))))) @ ((cSUBSET @ V1) @ (cUNIONS @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ (cFINITE @ V2)) @ ((cSUBSET @ V1) @ (cUNIONS @ V2)))))))))))))
(TDIVISION_OF_REFLECT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdivision_of @ ((cIMAGE @ (cIMAGE @ cvector_neg)) @ V0)) @ ((cIMAGE @ cvector_neg) @ V1))) @ ((cdivision_of @ V0) @ V1)))))))
(TCOMPONENTS_UNIQUE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (ccomponents @ V1)) @ V0)) @ ((c/__caret__ @ ((c= @ (cUNIONS @ V0)) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ (cconnected @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconnected @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V3)) @ ((cSUBSET @ V3) @ V1)))) @ ((c= @ V3) @ V2))))))))))))))))
(TFACETS_OF_POLYHEDRON_EXPLICIT_DISTINCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((c= @ V1) @ ((cINTER @ ((chull @ caffine) @ V1)) @ (cINTERS @ V0)))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ (V2 @ V6)) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_le @ ((cdot @ (V2 @ V6)) @ V8)) @ (V3 @ V6))) @ V8))))))))))) @ (c! @ (^[V6]: ((c==> @ ((cPSUBSET @ V6) @ V0)) @ ((cPSUBSET @ V1) @ ((cINTER @ ((chull @ caffine) @ V1)) @ (cINTERS @ V6)))))))))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c= @ ((cINTER @ V1) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c= @ ((cdot @ (V2 @ V4)) @ V7)) @ (V3 @ V4))) @ V7))))))) @ ((cINTER @ V1) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c= @ ((cdot @ (V2 @ V5)) @ V7)) @ (V3 @ V5))) @ V7)))))))))) @ ((c= @ V4) @ V5))))))))))))))))
(TPARTIAL_DIVISION_EXTEND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V2) @ V1)) @ ((c/__caret__ @ ((cdivision_of @ V0) @ V3)) @ ((cSUBSET @ V1) @ V3)))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cSUBSET @ V2) @ V4)) @ ((cdivision_of @ V4) @ V3))))))))))))))
(THOMEOMORPHIC_LOCALLY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((chomeomorphic @ V4) @ V5)) @ ((c= @ (V0 @ V4)) @ (V2 @ V5)))))))) @ ((c==> @ ((chomeomorphic @ V1) @ V3)) @ ((c= @ ((clocally @ V0) @ V1)) @ ((clocally @ V2) @ V3)))))))))))))
(TLOCALLY_DIFF_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((clocally @ V0) @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2))) @ ((clocally @ V0) @ ((cDIFF @ V1) @ V2))))))))))
(TTRIANGULATION_INTER_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ctriangulation @ V0)) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0)))) @ ((c= @ ((cINTER @ V1) @ V2)) @ ((chull @ cconvex) @ ((cINTER @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cextreme_point_of @ V4) @ V1)) @ V4)))))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cextreme_point_of @ V4) @ V2)) @ V4))))))))))))))))
(TLOCALLY_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (V0 @ V4))) @ (V0 @ ((cINTER @ V3) @ V4)))))))) @ ((c==> @ ((c/__caret__ @ ((clocally @ V0) @ V1)) @ ((clocally @ V0) @ V2))) @ ((clocally @ V0) @ ((cINTER @ V1) @ V2)))))))))))
(TFACE_OF_POLYHEDRON_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((c= @ V2) @ ((cINTER @ ((chull @ caffine) @ V2)) @ (cINTERS @ V0)))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ (V3 @ V5)) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V5) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_le @ ((cdot @ (V3 @ V5)) @ V7)) @ (V4 @ V5))) @ V7))))))))))) @ (c! @ (^[V5]: ((c==> @ ((cPSUBSET @ V5) @ V0)) @ ((cPSUBSET @ V2) @ ((cINTER @ ((chull @ caffine) @ V2)) @ (cINTERS @ V5)))))))))) @ ((c==> @ ((c/__caret__ @ ((cface_of @ V1) @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c~ @ ((c= @ V1) @ V2))))) @ ((c= @ V1) @ (cINTERS @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((cSUBSET @ V1) @ ((cINTER @ V2) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c= @ ((cdot @ (V3 @ V6)) @ V8)) @ (V4 @ V6))) @ V8))))))))) @ ((cINTER @ V2) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c= @ ((cdot @ (V3 @ V6)) @ V8)) @ (V4 @ V6))) @ V8))))))))))))))))))))))))))
(TFACE_OF_POLYHEDRON_SUBSET_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((c= @ V2) @ ((cINTER @ ((chull @ caffine) @ V2)) @ (cINTERS @ V0)))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ (V3 @ V5)) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V5) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_le @ ((cdot @ (V3 @ V5)) @ V7)) @ (V4 @ V5))) @ V7))))))))))) @ (c! @ (^[V5]: ((c==> @ ((cPSUBSET @ V5) @ V0)) @ ((cPSUBSET @ V2) @ ((cINTER @ ((chull @ caffine) @ V2)) @ (cINTERS @ V5)))))))))) @ ((c==> @ ((c/__caret__ @ ((cface_of @ V1) @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c~ @ ((c= @ V1) @ V2))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cSUBSET @ V1) @ ((cINTER @ V2) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c= @ ((cdot @ (V3 @ V5)) @ V7)) @ (V4 @ V5))) @ V7)))))))))))))))))))))))
(TFACET_OF_POLYHEDRON_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((c= @ V2) @ ((cINTER @ ((chull @ caffine) @ V2)) @ (cINTERS @ V0)))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ (V3 @ V5)) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V5) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_le @ ((cdot @ (V3 @ V5)) @ V7)) @ (V4 @ V5))) @ V7))))))))))) @ (c! @ (^[V5]: ((c==> @ ((cPSUBSET @ V5) @ V0)) @ ((cPSUBSET @ V2) @ ((cINTER @ ((chull @ caffine) @ V2)) @ (cINTERS @ V5)))))))))) @ ((c= @ ((cfacet_of @ V1) @ V2)) @ (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c= @ V1) @ ((cINTER @ V2) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c= @ ((cdot @ (V3 @ V5)) @ V7)) @ (V4 @ V5))) @ V7)))))))))))))))))))))))
(TWLOG_LINEAR_INJECTIVE_IMAGE_2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V2 @ V4)) @ (clinear @ V3))) @ (V0 @ ((cIMAGE @ V3) @ V4)))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V4)) @ (clinear @ V3))) @ (V2 @ ((cIMAGE @ V3) @ V4))))))))) @ ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V1 @ V3)) @ (V1 @ V4))) @ ((c= @ V3) @ V4)))))))) @ (c! @ (^[V3]: ((c= @ (V0 @ ((cIMAGE @ V1) @ V3))) @ (V2 @ V3)))))))))))))
(TLOCALLY_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (clinear @ V4)) @ (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c= @ (V4 @ V6)) @ (V4 @ V7))) @ ((c= @ V6) @ V7)))))))) @ ((c= @ (V0 @ ((cIMAGE @ V4) @ V5))) @ (V2 @ V5)))))))) @ ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c= @ (V1 @ V4)) @ (V1 @ V5))) @ ((c= @ V4) @ V5)))))))) @ ((c= @ ((clocally @ V0) @ ((cIMAGE @ V1) @ V3))) @ ((clocally @ V2) @ V3)))))))))))))
(TADDITIVE_CONTENT_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c= @ ((csum @ V0) @ ccontent)) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))
(TDIVISION_OF_NONTRIVIAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (c~ @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((cdivision_of @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (c~ @ ((c= @ (ccontent @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ V4)))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TPARTIAL_DIVISION_EXTEND_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ (cUNIONS @ V0))) @ ((cSUBSET @ (cUNIONS @ V0)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V0) @ V3)) @ ((cdivision_of @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))))
(TINTERVAL_BISECTION_STEP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ cEMPTY)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ ((c/__caret__ @ (V0 @ V4)) @ ((c= @ ((cINTER @ (cinterior @ V3)) @ (cinterior @ V4))) @ cEMPTY)))) @ (V0 @ ((cUNION @ V3) @ V4))))))))) @ ((c==> @ (c~ @ (V0 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V1)) @ cNIL))))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (c~ @ (V0 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V2) @ V5)) @ ((c$ @ V3) @ V5))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V3) @ V5)) @ ((c$ @ V4) @ V5))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V4) @ V5)) @ ((c$ @ V1) @ V5))) @ ((creal_le @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V4) @ V5)) @ ((c$ @ V3) @ V5)))) @ ((creal_sub @ ((c$ @ V1) @ V5)) @ ((c$ @ V2) @ V5)))))))))))))))))))))))
(TDIVISION_SPLIT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV))))) @ ((cdivision_of @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ (c~ @ ((c= @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_le @ ((c$ @ V8) @ V3)) @ V4)) @ V8))))))) @ cEMPTY)))) @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_le @ ((c$ @ V8) @ V3)) @ V4)) @ V8)))))))))))) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((c$ @ V6) @ V3)) @ V4)) @ V6)))))))))))))))))))
(TDIVISION_SPLIT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV))))) @ ((cdivision_of @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ (c~ @ ((c= @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_ge @ ((c$ @ V8) @ V3)) @ V4)) @ V8))))))) @ cEMPTY)))) @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((creal_ge @ ((c$ @ V8) @ V3)) @ V4)) @ V8)))))))))))) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_ge @ ((c$ @ V6) @ V3)) @ V4)) @ V6)))))))))))))))))))
(TDIVISION_DOUBLESPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV))))) @ ((cdivision_of @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V0)) @ (c~ @ ((c= @ ((cINTER @ V7) @ (cGSPEC @ (^[V8]: (c? @ (^[V9]: (((cSETSPEC @ V8) @ ((creal_le @ (creal_abs @ ((creal_sub @ ((c$ @ V9) @ V3)) @ V4))) @ V5)) @ V9))))))) @ cEMPTY)))) @ ((cINTER @ V7) @ (cGSPEC @ (^[V8]: (c? @ (^[V9]: (((cSETSPEC @ V8) @ ((creal_le @ (creal_abs @ ((creal_sub @ ((c$ @ V9) @ V3)) @ V4))) @ V5)) @ V9)))))))))))) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_le @ (creal_abs @ ((creal_sub @ ((c$ @ V7) @ V3)) @ V4))) @ V5)) @ V7)))))))))))))))))))))
(TOPERATIVE_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((coperative @ V1) @ V0)) @ ((c= @ (V0 @ cEMPTY)) @ (cneutral @ V1))))))))
(THOMOTOPIC_WITH_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: ((c==> @ ((c/__caret__ @ ((((chomotopic_with @ V0) @ ((c__comma__ @ V3) @ V5)) @ V7) @ V9)) @ ((c/__caret__ @ ((((chomotopic_with @ V1) @ ((c__comma__ @ V4) @ V6)) @ V8) @ V10)) @ (c! @ (^[V11]: (c! @ (^[V12]: ((c==> @ ((c/__caret__ @ (V0 @ V11)) @ (V1 @ V12))) @ (V2 @ (^[V13]: ((cpastecart @ (V11 @ (cfstcart @ V13))) @ (V12 @ (csndcart @ V13))))))))))))) @ ((((chomotopic_with @ V2) @ ((c__comma__ @ ((cPCROSS @ V3) @ V4)) @ ((cPCROSS @ V5) @ V6))) @ (^[V11]: ((cpastecart @ (V7 @ (cfstcart @ V11))) @ (V8 @ (csndcart @ V11))))) @ (^[V11]: ((cpastecart @ (V9 @ (cfstcart @ V11))) @ (V10 @ (csndcart @ V11)))))))))))))))))))))))))))))
(TEQUIINTEGRABLE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cequiintegrable_on @ V0) @ V2)) @ ((cequiintegrable_on @ V1) @ V2))) @ ((cequiintegrable_on @ ((cUNION @ V0) @ V1)) @ V2)))))))))
(TEQUIINTEGRABLE_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cequiintegrable_on @ V0) @ V2)) @ ((cequiintegrable_on @ V1) @ V2))) @ ((cequiintegrable_on @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ V1))) @ (^[V6]: ((cvector_sub @ (V4 @ V6)) @ (V5 @ V6))))))))))) @ V2)))))))))
(TEQUIINTEGRABLE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cequiintegrable_on @ V0) @ V2)) @ ((cequiintegrable_on @ V1) @ V2))) @ ((cequiintegrable_on @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ V1))) @ (^[V6]: ((cvector_add @ (V4 @ V6)) @ (V5 @ V6))))))))))) @ V2)))))))))
(TEQUIINTEGRABLE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cequiintegrable_on @ V0) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c= @ (V4 @ V5)) @ (V3 @ V5))))))))))))) @ ((cequiintegrable_on @ V1) @ V2)))))))))
(THOMOTOPIC_WITH_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((((chomotopic_with @ V0) @ ((c__comma__ @ V2) @ V3)) @ V4) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V6) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V6) @ V2)) @ V3)) @ (V0 @ V6)))) @ (V1 @ V6)))))) @ ((((chomotopic_with @ V1) @ ((c__comma__ @ V2) @ V3)) @ V4) @ V5)))))))))))))))
(THOMOTOPIC_WITH_IMP_CONTINUOUS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((chomotopic_with @ V0) @ ((c__comma__ @ V4) @ V1)) @ V3) @ V2)) @ ((ccontinuous_on @ V3) @ V4)))))))))))))
(THOMOTOPIC_WITH_IMP_CONTINUOUS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((chomotopic_with @ V0) @ ((c__comma__ @ V4) @ V1)) @ V2) @ V3)) @ ((ccontinuous_on @ V3) @ V4)))))))))))))
(THOMOTOPIC_WITH_IMP_SUBSET_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((chomotopic_with @ V0) @ ((c__comma__ @ V3) @ V4)) @ V2) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V3)) @ V4)))))))))))))
(THOMOTOPIC_WITH_IMP_SUBSET_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((chomotopic_with @ V0) @ ((c__comma__ @ V3) @ V4)) @ V1) @ V2)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V3)) @ V4)))))))))))))
(TEQUIINTEGRABLE_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cequiintegrable_on @ V0) @ V1)) @ ((cequiintegrable_on @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ (^[V4]: (cvector_neg @ (V3 @ V4))))))))) @ V1)))))))
(Tequiintegrable_on,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cequiintegrable_on @ V0) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cintegrable_on @ V2) @ V1))))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (cgauge @ V3)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((ctagged_division_of @ V5) @ V1)) @ ((cfine @ V3) @ V5)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cvsum @ V5) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ ((c% @ (ccontent @ V8)) @ (V4 @ V7))))))))))) @ ((cintegral @ V1) @ V4)))) @ V2)))))))))))))))))))
(TCOMPACT_UNIFORMLY_EQUICONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4))) @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V7) @ V3))) @ V5)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V6 @ V7)) @ (V6 @ V3)))) @ V4))))))))))))))) @ (ccompact @ V1))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V6) @ V5))) @ V3))))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V4 @ V6)) @ (V4 @ V5)))) @ V2))))))))))))))))))))
(THOMOTOPIC_WITH_EQUAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ ((c/__caret__ @ (V0 @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V2)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((c= @ (V4 @ V5)) @ (V3 @ V5)))))))))) @ ((((chomotopic_with @ V0) @ ((c__comma__ @ V1) @ V2)) @ V3) @ V4)))))))))))))
(THOMOTOPIC_WITH_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((((chomotopic_with @ V0) @ ((c__comma__ @ V1) @ V2)) @ V4) @ V3)) @ ((((chomotopic_with @ V0) @ ((c__comma__ @ V1) @ V2)) @ V3) @ V4)))))))))))))
(TEQUIINTEGRABLE_REFLECT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cequiintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V1)) @ cNIL)))) @ ((cequiintegrable_on @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ V0)) @ (^[V5]: (V4 @ (cvector_neg @ V5))))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvector_neg @ V1)) @ (cvector_neg @ V2))) @ cNIL)))))))))))
(TEQUIINTEGRABLE_UNIFORM_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cequiintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cequiintegrable_on @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ (c! @ (^[V5]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ V0)) @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ (V4 @ V7)) @ (V6 @ V7)))) @ V5))))))))))) @ V4)))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TEQUIINTEGRABLE_SUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cequiintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cequiintegrable_on @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V3) @ ((c/__caret__ @ (cFINITE @ V4)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V4)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V5 @ V7))) @ ((cIN @ (V6 @ V7)) @ V0)))))) @ ((c= @ ((csum @ V4) @ V5)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (^[V7]: ((cvsum @ V4) @ (^[V8]: ((c% @ (V5 @ V8)) @ ((V6 @ V8) @ V7))))))))))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TEQUIINTEGRABLE_ON_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((cequiintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TTAGGED_DIVISION_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((ctagged_division_of @ (V0 @ V2)) @ V2))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((c= @ ((cINTER @ (cinterior @ V2)) @ (cinterior @ V3))) @ cEMPTY))))))))) @ ((ctagged_division_of @ (cUNIONS @ ((cIMAGE @ V0) @ V1))) @ (cUNIONS @ V1))))))))
(TSETVARIATION_EQUAL_LEMMA_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c/__caret__ @ ((c= @ (V0 @ (V2 @ V3))) @ V3)) @ ((c= @ (V2 @ (V0 @ V3))) @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))) @ cEMPTY))) @ ((c/__caret__ @ ((c= @ ((V1 @ V3) @ (V2 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))) @ (V3 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))) @ (c? @ (^[V6]: (c? @ (^[V7]: ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V7)) @ cNIL))) @ cEMPTY))) @ ((c= @ (V0 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V7)) @ cNIL))))))))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cSUBSET @ V3) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ (V2 @ V3)) @ (V2 @ V4))) @ ((cSUBSET @ (V0 @ V3)) @ (V0 @ V4))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cdivision_of @ V3) @ V4)) @ ((c/__caret__ @ ((cdivision_of @ ((cIMAGE @ V2) @ V3)) @ (V2 @ V4))) @ ((cdivision_of @ ((cIMAGE @ V0) @ V3)) @ (V0 @ V4)))))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((chas_bounded_setvariation_on @ (V1 @ V3)) @ (V2 @ V4))) @ ((chas_bounded_setvariation_on @ V3) @ V4))))))))))))))
(TSETVARIATION_EQUAL_LEMMA_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c/__caret__ @ ((c= @ (V0 @ (V1 @ V3))) @ V3)) @ ((c= @ (V1 @ (V0 @ V3))) @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))) @ cEMPTY))) @ ((c/__caret__ @ ((c= @ ((V2 @ V3) @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))) @ (V3 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))) @ (c? @ (^[V6]: (c? @ (^[V7]: ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V7)) @ cNIL))) @ cEMPTY))) @ ((c= @ (V0 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V7)) @ cNIL))))))))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cSUBSET @ V3) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ (V1 @ V3)) @ (V1 @ V4))) @ ((cSUBSET @ (V0 @ V3)) @ (V0 @ V4))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cdivision_of @ V3) @ V4)) @ ((c/__caret__ @ ((cdivision_of @ ((cIMAGE @ V1) @ V3)) @ (V1 @ V4))) @ ((cdivision_of @ ((cIMAGE @ V0) @ V3)) @ (V0 @ V4)))))))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((cset_variation @ (V1 @ V4)) @ (V2 @ V3))) @ ((cset_variation @ V4) @ V3))))))))))))))
(TOPERATIVE_LIFTED_SETVARIATION,(c! @ (^[V0]: ((c==> @ ((coperative @ cvector_add) @ V0)) @ ((coperative @ (clifted @ creal_add)) @ (^[V1]: (((cCOND @ ((chas_bounded_setvariation_on @ V0) @ V1)) @ (cSOME @ ((cset_variation @ V1) @ V0))) @ cNONE)))))))
(THAS_BOUNDED_SETVARIATION_ON_UNIV,(c! @ (^[V0]: ((c= @ ((chas_bounded_setvariation_on @ V0) @ cUNIV)) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cdivision_of @ V2) @ (cUNIONS @ V2))) @ ((creal_le @ ((csum @ V2) @ (^[V3]: (cvector_norm @ (V0 @ V3))))) @ V1))))))))))
(THAS_BOUNDED_SETVARIATION_ON_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V0) @ V2)) @ ((chas_bounded_setvariation_on @ V1) @ V2))) @ ((chas_bounded_setvariation_on @ (^[V3]: ((cvector_sub @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(THAS_BOUNDED_SETVARIATION_ON_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V0) @ V2)) @ ((chas_bounded_setvariation_on @ V1) @ V2))) @ ((chas_bounded_setvariation_on @ (^[V3]: ((cvector_add @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(THAS_BOUNDED_SETVARIATION_ON_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ cEMPTY))) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ V2))) @ ((c= @ (V0 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))) @ ((chas_bounded_setvariation_on @ V0) @ V2))) @ ((chas_bounded_setvariation_on @ V1) @ V2)))))))))
(THAS_BOUNDED_SETVARIATION_ON_NORM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_setvariation_on @ V0) @ V1)) @ ((chas_bounded_setvariation_on @ (^[V2]: (clift @ (cvector_norm @ (V0 @ V2))))) @ V1)))))))
(THAS_BOUNDED_SETVARIATION_ON_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_setvariation_on @ V0) @ V1)) @ ((chas_bounded_setvariation_on @ (^[V2]: (cvector_neg @ (V0 @ V2)))) @ V1)))))))
(THAS_BOUNDED_SETVARIATION_ON_NULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ (V0 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (cvec @ (cNUMERAL @ c_0))))))))) @ ((c/__caret__ @ ((c= @ (ccontent @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (cbounded @ V1)))) @ ((chas_bounded_setvariation_on @ V0) @ V1)))))))
(THAS_BOUNDED_SETVARIATION_REFLECT2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_bounded_setvariation_on @ (^[V2]: (V0 @ ((cIMAGE @ cvector_neg) @ V2)))) @ ((cIMAGE @ cvector_neg) @ V1))) @ ((chas_bounded_setvariation_on @ V0) @ V1)))))))
(THAS_BOUNDED_SETVARIATION_ON_COMPONENTWISE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_bounded_setvariation_on @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((chas_bounded_setvariation_on @ (^[V3]: (clift @ ((c$ @ (V0 @ V3)) @ V2)))) @ V1))))))))))
(TSET_VARIATION_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V0) @ V1)) @ ((chas_bounded_setvariation_on @ V2) @ V1))) @ ((creal_le @ ((cset_variation @ V1) @ (^[V3]: ((cvector_add @ (V0 @ V3)) @ (V2 @ V3))))) @ ((creal_add @ ((cset_variation @ V1) @ V0)) @ ((cset_variation @ V1) @ V2)))))))))))
(TSET_VARIATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ cEMPTY))) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ V1))) @ ((c= @ (V0 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (V2 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))) @ ((c= @ ((cset_variation @ V1) @ V0)) @ ((cset_variation @ V1) @ V2))))))))))
(THAS_BOUNDED_SETVARIATION_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chas_bounded_setvariation_on @ V0) @ V2)) @ ((chas_bounded_setvariation_on @ (^[V3]: (V0 @ ((cIMAGE @ (^[V4]: ((cvector_add @ V1) @ V4))) @ V3)))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ (cvector_neg @ V1)) @ V3))) @ V2))))))))))
(TLOCALLY_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (V0 @ V5)) @ (V1 @ V6))) @ (V2 @ ((cPCROSS @ V5) @ V6)))))))) @ ((c==> @ ((c/__caret__ @ ((clocally @ V0) @ V3)) @ ((clocally @ V1) @ V4))) @ ((clocally @ V2) @ ((cPCROSS @ V3) @ V4)))))))))))))))
(TLOCALLY_OPEN_MAP_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V3)) @ V4)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V2) @ V3))) @ ((cIMAGE @ V2) @ V4)))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V4) @ V3)) @ (V0 @ V4))) @ (V1 @ ((cIMAGE @ V2) @ V4)))))) @ ((clocally @ V0) @ V3))))) @ ((clocally @ V1) @ ((cIMAGE @ V2) @ V3))))))))))))
(THAS_BOUNDED_SETVARIATION_ON_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((coperative @ cvector_add) @ V1)) @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ ((c= @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((chas_bounded_setvariation_on @ V1) @ V4))))) @ ((chas_bounded_setvariation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))
(TINESSENTIAL_ON_CLOPEN_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath_connected @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ (cUNIONS @ V0))) @ V3)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ (cUNIONS @ V0))) @ V3)) @ (c? @ (^[V4]: ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V3) @ V1)) @ V2) @ (^[V5]: V4))))))))))) @ (c? @ (^[V3]: ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ (cUNIONS @ V0)) @ V1)) @ V2) @ (^[V4]: V3))))))))))))
(THOMOTOPIC_ON_CLOPEN_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ (cUNIONS @ V0))) @ V4)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ (cUNIONS @ V0))) @ V4)) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V4) @ V1)) @ V2) @ V3))))))) @ ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ (cUNIONS @ V0)) @ V1)) @ V2) @ V3)))))))))))
(TAPPROXIMABLE_ON_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c/__caret__ @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ (c? @ (^[V6]: ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V5)) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ (V1 @ V7)) @ (V6 @ V7)))) @ V2))))) @ ((cintegrable_on @ V6) @ V5)))))))))) @ (c? @ (^[V5]: ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ (V1 @ V6)) @ (V5 @ V6)))) @ V2))))) @ ((cintegrable_on @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))))))))))
(TTAGGED_DIVISION_UNIONS_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ ((ctagged_division_of @ V4) @ V3)) @ ((cfine @ V2) @ V4)))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (c~ @ ((c= @ V3) @ V4))))) @ ((c= @ ((cINTER @ (cinterior @ V3)) @ (cinterior @ V4))) @ cEMPTY))))))) @ ((c= @ (cUNIONS @ V0)) @ V1))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((ctagged_division_of @ V3) @ V1)) @ ((cfine @ V2) @ V3))))))))))))
(TINTEGRABLE_ON_SUBDIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ V3)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ ((cSUBSET @ V3) @ V1)))) @ ((cintegrable_on @ V2) @ V3)))))))))))
(TDSUM_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ ((creal_le @ (cvector_norm @ V1)) @ V2))) @ ((creal_le @ (cvector_norm @ ((cvsum @ V0) @ (^[V5]: ((c% @ (ccontent @ V5)) @ V1))))) @ ((creal_mul @ V2) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))))
(TSET_VARIATION_ON_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((coperative @ cvector_add) @ V3)) @ ((c/__caret__ @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((chas_bounded_setvariation_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))) @ ((c= @ ((csum @ V0) @ (^[V4]: ((cset_variation @ V4) @ V3)))) @ ((cset_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V3))))))))))))
(TSET_VARIATION_WORKS_ON_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))) @ ((creal_le @ ((csum @ V0) @ (^[V4]: (cvector_norm @ (V3 @ V4))))) @ ((cset_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V3))))))))))))
(TLEBESGUE_MEASURABLE_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (clebesgue_measurable @ V1)))))) @ (clebesgue_measurable @ (cUNIONS @ V0))))))
(TMEASURABLE_ELEMENTARY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdivision_of @ V0) @ V1)) @ (cmeasurable @ V1)))))))
(TEQUIINTEGRABLE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cequiintegrable_on @ V0) @ V2)) @ ((cSUBSET @ V1) @ V0))) @ ((cequiintegrable_on @ V1) @ V2)))))))))
(TINTEGRABLE_COMBINE_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V0) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cintegrable_on @ V1) @ V3)))))) @ ((cintegrable_on @ V1) @ V2)))))))))
(TOPERATIVE_DIVISION_AND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((coperative @ c/__caret__) @ V1)) @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ ((c= @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ (V1 @ V4))))) @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))
(TNEGLIGIBLE_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cnegligible @ V1)))))) @ (cnegligible @ (cUNIONS @ V0))))))
(TOPERATIVE_TRIVIAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((coperative @ V3) @ V0)) @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (V0 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (cneutral @ V3))))))))))))
(TDIVISION_OF_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdivision_of @ V0) @ V1)) @ (cclosed @ V1)))))))
(TDIVISION_OF_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdivision_of @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V1)) @ cNIL)))) @ ((c= @ V0) @ ((cINSERT @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V1)) @ cNIL))) @ cEMPTY))))))))
(TDIVISION_OF_TRIVIAL,(c! @ (^[V0]: ((c= @ ((cdivision_of @ V0) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TDIVISION_OF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdivision_of @ V0) @ V1)) @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((c= @ ((cINTER @ (cinterior @ V2)) @ (cinterior @ V3))) @ cEMPTY))))))) @ ((c= @ (cUNIONS @ V0)) @ V1))))))))))
(Tdivision_of,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdivision_of @ V0) @ V1)) @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((c= @ ((cINTER @ (cinterior @ V2)) @ (cinterior @ V3))) @ cEMPTY))))))) @ ((c= @ (cUNIONS @ V0)) @ V1))))))))))
(TENR_SIMPLICIAL_COMPLEX,(c! @ (^[V0]: ((c==> @ (csimplicial_complex @ V0)) @ (cENR @ (cUNIONS @ V0))))))
(TENR_TRIANGULATION,(c! @ (^[V0]: ((c==> @ (ctriangulation @ V0)) @ (cENR @ (cUNIONS @ V0))))))
(TANR_SIMPLICIAL_COMPLEX,(c! @ (^[V0]: ((c==> @ (csimplicial_complex @ V0)) @ (cANR @ (cUNIONS @ V0))))))
(TANR_TRIANGULATION,(c! @ (^[V0]: ((c==> @ (ctriangulation @ V0)) @ (cANR @ (cUNIONS @ V0))))))
(TTRIANGULATION_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctriangulation @ ((cUNION @ V0) @ V1))) @ ((c/__caret__ @ (ctriangulation @ V0)) @ ((c/__caret__ @ (ctriangulation @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V1))) @ ((c/__caret__ @ ((cface_of @ ((cINTER @ V2) @ V3)) @ V2)) @ ((cface_of @ ((cINTER @ V2) @ V3)) @ V3)))))))))))))))
(TSIMPLICIAL_COMPLEX_IMP_TRIANGULATION,(c! @ (^[V0]: ((c==> @ (csimplicial_complex @ V0)) @ (ctriangulation @ V0)))))
(Tsimplicial_complex,(c! @ (^[V0]: ((c= @ (csimplicial_complex @ V0)) @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: ((csimplex @ V2) @ V1))))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cface_of @ V1) @ V2))) @ ((cIN @ V1) @ V0))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((c/__caret__ @ ((cface_of @ ((cINTER @ V1) @ V2)) @ V1)) @ ((cface_of @ ((cINTER @ V1) @ V2)) @ V2))))))))))))))
(TFACE_OF_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cface_of @ V2) @ V1)))))) @ ((cface_of @ (cINTERS @ V0)) @ V1)))))))
(TLOCALLY_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((clocally @ V0) @ ((cINSERT @ V1) @ cEMPTY))) @ (V0 @ ((cINSERT @ V1) @ cEMPTY))))))))
(TLOCALLY_EMPTY,(c! @ (^[V0]: ((clocally @ V0) @ cEMPTY))))
(TLOCALLY_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V1 @ V3))))) @ ((clocally @ V0) @ V2))) @ ((clocally @ V1) @ V2)))))))))
(TCONIC_INTERS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cconic @ V1))))) @ (cconic @ (cINTERS @ V0))))))
(TCONVEX_INTERS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cconvex @ V1))))) @ (cconvex @ (cINTERS @ V0))))))
(TAFFINE_INTERS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (caffine @ V1))))) @ (caffine @ (cINTERS @ V0))))))
(TCOMPACT_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (ccompact @ V1)))))) @ (ccompact @ (cUNIONS @ V0))))))
(TBOUNDED_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cbounded @ V1)))))) @ (cbounded @ (cUNIONS @ V0))))))
(TCLOSURE_UNIONS,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cclosure @ (cUNIONS @ V0))) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ (cclosure @ V2))))))))))))
(TCLOSURE_INTERS_SUBSET,(c! @ (^[V0]: ((cSUBSET @ (cclosure @ (cINTERS @ V0))) @ (cINTERS @ ((cIMAGE @ cclosure) @ V0))))))
(TINTERIOR_INTERS_SUBSET,(c! @ (^[V0]: ((cSUBSET @ (cinterior @ (cINTERS @ V0))) @ (cINTERS @ ((cIMAGE @ cinterior) @ V0))))))
(TCLOSED_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cclosed @ V1)))))) @ (cclosed @ (cUNIONS @ V0))))))
(TOPEN_INTERS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (copen @ V1)))))) @ (copen @ (cINTERS @ V0))))))
(TOPEN_UNIONS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (copen @ V1))))) @ (copen @ (cUNIONS @ V0))))))
(TWLOG_LINEAR_INJECTIVE_IMAGE_2_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (V2 @ V5)) @ (clinear @ V4))) @ (V0 @ ((cIMAGE @ V4) @ V5)))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (V0 @ V5)) @ (clinear @ V4))) @ (V2 @ ((cIMAGE @ V4) @ V5)))))))) @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c= @ (V1 @ V4)) @ (V1 @ V5))) @ ((c= @ V4) @ V5)))))))))) @ ((c= @ (V0 @ ((cIMAGE @ V1) @ V3))) @ (V2 @ V3))))))))))))
(TSUBSPACE_INTERS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (csubspace @ V1))))) @ (csubspace @ (cINTERS @ V0))))))
(TPCROSS_UNIONS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cPCROSS @ (cUNIONS @ V0)) @ V1)) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cPCROSS @ V3) @ V1)))))))))))))
(TPCROSS_UNIONS_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cPCROSS @ (cUNIONS @ V0)) @ (cUNIONS @ V1))) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cPCROSS @ V3) @ V4)))))))))))))))
(TIN_ELIM_THM_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cGSPEC @ (^[V2]: (V0 @ (cSETSPEC @ V2)))) @ V1)) @ (V0 @ (^[V2]: (^[V3]: ((c/__caret__ @ V2) @ ((c= @ V1) @ V3)))))))))))
(TIN_ELIM_THM_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V1) @ (cGSPEC @ (^[V2]: (V0 @ (cSETSPEC @ V2)))))) @ (V0 @ (^[V2]: (^[V3]: ((c/__caret__ @ V2) @ ((c= @ V1) @ V3)))))))))))
(TORS,(c! @ (^[V0]: ((c= @ (cORS @ V0)) @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ (V2 @ V1)))))))))
(TANDS,(c! @ (^[V0]: ((c= @ (cANDS @ V0)) @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V2 @ V1)))))))))
(Tcommand_RECURSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (c! @ (^[V5]: ((c= @ (V4 @ (cAssign @ V5))) @ (V0 @ V5))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c= @ (V4 @ ((cSeq @ V5) @ V6))) @ ((((V1 @ V5) @ V6) @ (V4 @ V5)) @ (V4 @ V6)))))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c= @ (V4 @ (((cIte @ V5) @ V6) @ V7))) @ (((((V2 @ V5) @ V6) @ V7) @ (V4 @ V6)) @ (V4 @ V7)))))))))) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c= @ (V4 @ ((cWhile @ V5) @ V6))) @ (((V3 @ V5) @ V6) @ (V4 @ V6)))))))))))))))))))))
(TEXISTS_SWAP,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (V0 @ (^[V2]: (^[V3]: ((V1 @ V3) @ V2))))))))))
(TEXISTS_DROP_FUN,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (V0 @ ((co @ cdrop) @ V1))))))))
(TFORALL_DROP_FUN,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (V0 @ ((co @ cdrop) @ V1))))))))
(TFORALL_OF_DROP,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ ((co @ cdrop) @ V1))))) @ (c! @ (^[V1]: (V0 @ V1)))))))
(TEXISTS_UNCURRY,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (V0 @ (^[V2]: (^[V3]: (V1 @ ((c__comma__ @ V2) @ V3)))))))))))
(TFORALL_UNCURRY,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (V0 @ (^[V2]: (^[V3]: (V1 @ ((c__comma__ @ V2) @ V3)))))))))))
(TEXISTS_LIFT_FUN,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (V0 @ ((co @ clift) @ V1))))))))
(TFORALL_LIFT_FUN,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (V0 @ ((co @ clift) @ V1))))))))
(TFORALL_OF_PASTECART,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((V0 @ ((co @ cfstcart) @ V1)) @ ((co @ csndcart) @ V1))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((V0 @ V1) @ V2)))))))))
(TKUHN_COMPLETE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c= @ ((V0 @ V5) @ V6)) @ (c? @ (^[V7]: ((c/__caret__ @ ((cIN @ V7) @ V6)) @ ((c= @ V5) @ ((cDELETE @ V6) @ V7))))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((cHAS_SIZE @ V5) @ ((c+ @ V4) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((cSUBSET @ ((cIMAGE @ V3) @ V5)) @ ((c.. @ (cNUMERAL @ c_0)) @ ((c+ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ (c? @ (^[V8]: ((c/__caret__ @ ((cIN @ V8) @ V2)) @ ((V0 @ V7) @ V8))))) @ V7))))))) @ (V1 @ V5))) @ ((c= @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V2)) @ ((V0 @ V5) @ V7))) @ V7))))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ (c? @ (^[V8]: ((c/__caret__ @ ((cIN @ V8) @ V2)) @ ((V0 @ V7) @ V8))))) @ V7))))))) @ (c~ @ (V1 @ V5)))) @ ((c= @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V2)) @ ((V0 @ V5) @ V7))) @ V7))))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))) @ ((c==> @ (cODD @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ (c? @ (^[V9]: ((c/__caret__ @ ((cIN @ V9) @ V2)) @ ((V0 @ V8) @ V9))))) @ V8))))))) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V3) @ V6)) @ ((c.. @ (cNUMERAL @ c_0)) @ V4))) @ (V1 @ V6)))) @ V6)))))))) @ (cODD @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ ((c= @ ((cIMAGE @ V3) @ V6)) @ ((c.. @ (cNUMERAL @ c_0)) @ ((c+ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ V6))))))))))))))))))))
(TTARSKI_SET,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V1) @ V2)) @ ((cSUBSET @ (V0 @ V1)) @ (V0 @ V2)))))))) @ (c? @ (^[V1]: ((c= @ (V0 @ V1)) @ V1)))))))
(TCARD_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cFINITE @ V1))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c~ @ ((c= @ V1) @ V2))))) @ ((c= @ ((cINTER @ V1) @ V2)) @ cEMPTY))))))))) @ ((c= @ (cCARD @ (cUNIONS @ V0))) @ ((cnsum @ V0) @ cCARD))))))
(TCOUNTABLE_UNIONS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cCOUNTABLE @ V1)))))) @ (cCOUNTABLE @ (cUNIONS @ V0))))))
(TZL_SUBSETS_UNIONS_NONEMPTY,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c? @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c? @ (^[V2]: ((cIN @ V2) @ V1)))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (V0 @ V2))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((cIN @ V3) @ V1))) @ ((c__caret__/ @ ((cSUBSET @ V2) @ V3)) @ ((cSUBSET @ V3) @ V2)))))))))) @ (V0 @ (cUNIONS @ V1))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (V0 @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((cSUBSET @ V1) @ V2))) @ ((c= @ V1) @ V2)))))))))))
(TUNIONS_MAXIMAL_SETS,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c~ @ ((cPSUBSET @ V2) @ V3))))))) @ V2))))))) @ (cUNIONS @ V0))))))
(TZL_SUBSETS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (V0 @ V2))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((cIN @ V3) @ V1))) @ ((c__caret__/ @ ((cSUBSET @ V2) @ V3)) @ ((cSUBSET @ V3) @ V2))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cSUBSET @ V3) @ V2))))))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (V0 @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((cSUBSET @ V1) @ V2))) @ ((c= @ V1) @ V2)))))))))))
(TZL_SUBSETS_UNIONS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (V0 @ V2))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((cIN @ V3) @ V1))) @ ((c__caret__/ @ ((cSUBSET @ V2) @ V3)) @ ((cSUBSET @ V3) @ V2))))))))) @ (V0 @ (cUNIONS @ V1)))))) @ (c? @ (^[V1]: ((c/__caret__ @ (V0 @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((cSUBSET @ V1) @ V2))) @ ((c= @ V1) @ V2)))))))))))
(Tre_Union,(c! @ (^[V0]: ((c= @ (cre_Union @ V0)) @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ (V2 @ V1)))))))))
(TUNIONS,(c! @ (^[V0]: ((c= @ (cUNIONS @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V2) @ V3))))) @ V2)))))))))
(TINTERS,(c! @ (^[V0]: ((c= @ (cINTERS @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cIN @ V2) @ V3))))) @ V2)))))))))
(Ttopology_tybij_conjunct1,(c! @ (^[V0]: ((c= @ (cistopology @ V0)) @ ((c= @ (copen_in @ (ctopology @ V0))) @ V0)))))
(TFINITE_UNIONS,(c! @ (^[V0]: ((c= @ (cFINITE @ (cUNIONS @ V0))) @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cFINITE @ V1)))))))))
(TEXISTS_DIFF,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ ((cDIFF @ cUNIV) @ V1))))) @ (c? @ (^[V1]: (V0 @ V1)))))))
(TSUM_UNIONS_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cFINITE @ V2))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V3))) @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((cIN @ V4) @ V3)))))) @ ((c= @ (V1 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))) @ ((c= @ ((csum @ (cUNIONS @ V0)) @ V1)) @ ((csum @ V0) @ (^[V2]: ((csum @ V2) @ V1))))))))))
(TNSUM_UNIONS_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cFINITE @ V2))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V3))) @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((cIN @ V4) @ V3)))))) @ ((c= @ (V1 @ V4)) @ (cNUMERAL @ c_0)))))))))))) @ ((c= @ ((cnsum @ (cUNIONS @ V0)) @ V1)) @ ((cnsum @ V0) @ (^[V2]: ((cnsum @ V2) @ V1))))))))))
(TVSUM_UNIONS_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cFINITE @ V2))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V3))) @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((cIN @ V4) @ V3)))))) @ ((c= @ (V1 @ V4)) @ (cvec @ (cNUMERAL @ c_0))))))))))))) @ ((c= @ ((cvsum @ (cUNIONS @ V0)) @ V1)) @ ((cvsum @ V0) @ (^[V2]: ((cvsum @ V2) @ V1))))))))))
(TFINITE_INDUCT_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cEMPTY)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ (c~ @ ((c= @ V2) @ cEMPTY)))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V2)) @ ((c==> @ (V0 @ ((cDELETE @ V2) @ V3))) @ (V0 @ V2)))))))))) @ ((c==> @ (cFINITE @ V1)) @ (V0 @ V1))))))))
(TFINITE_INDUCT_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cEMPTY)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ ((c/__caret__ @ (c~ @ ((cIN @ V2) @ V3))) @ (cFINITE @ V3)))) @ (V0 @ ((cINSERT @ V2) @ V3))))))))) @ ((c==> @ (cFINITE @ V1)) @ (V0 @ V1))))))))
(TSET_PROVE_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cEMPTY)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c~ @ ((cIN @ V2) @ V3))) @ (V0 @ ((cINSERT @ V2) @ V3))))))))) @ (V0 @ V1)))))))
(TFINITE_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cEMPTY)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ ((cINSERT @ V2) @ V3))))))))) @ ((c==> @ (cFINITE @ V1)) @ (V0 @ V1))))))))
(THULL_UNION_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chull @ V0) @ ((cUNION @ V1) @ V2))) @ ((chull @ V0) @ ((cUNION @ ((chull @ V0) @ V1)) @ V2))))))))))
(THULL_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ (V2 @ V4))))) @ (V0 @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ (V2 @ V5)) @ V5)))))))) @ ((c==> @ ((cIN @ V3) @ ((chull @ V0) @ V1))) @ (V2 @ V3))))))))))))
(TIN_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V1) @ (cUNIONS @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V1) @ V2))))))))))
(TIN_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V1) @ (cINTERS @ V0))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cIN @ V1) @ V2))))))))))
(TCANTOR_TAYLOR,(c! @ (^[V0]: (c~ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))))
(TUNIONS_PRED,(c! @ (^[V0]: ((c= @ (cUNIONS @ V0)) @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ (V2 @ V1)))))))))
(Tadmissible,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((cadmissible @ V1) @ V0) @ V2) @ V3)) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V0 @ V4) @ V6)) @ ((c/__caret__ @ ((V0 @ V5) @ V6)) @ (c! @ (^[V7]: ((c==> @ ((V1 @ V7) @ (V2 @ V6))) @ ((c= @ (V4 @ V7)) @ (V5 @ V7)))))))) @ ((c= @ ((V3 @ V4) @ V6)) @ ((V3 @ V5) @ V6)))))))))))))))))))
(TFORALL_COUNTABLE_AS_IMAGE,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c==> @ (cCOUNTABLE @ V1)) @ (V0 @ V1))))) @ ((c/__caret__ @ (V0 @ cEMPTY)) @ (c! @ (^[V1]: (V0 @ ((cIMAGE @ V1) @ cUNIV)))))))))
(TFL_RESTRICTED_SUBSET,(c! @ (^[V0]: ((c= @ (cfl @ (cGABS @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((cGEQ @ (V1 @ ((c__comma__ @ V2) @ V3))) @ ((c/__caret__ @ (V0 @ V2)) @ ((c/__caret__ @ (V0 @ V3)) @ ((cSUBSET @ V2) @ V3)))))))))))) @ V0))))
(TPOSET_RESTRICTED_SUBSET,(c! @ (^[V0]: (cposet @ (cGABS @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((cGEQ @ (V1 @ ((c__comma__ @ V2) @ V3))) @ ((c/__caret__ @ (V0 @ V2)) @ ((c/__caret__ @ (V0 @ V3)) @ ((cSUBSET @ V2) @ V3))))))))))))))
(TORDERED_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ V3) @ cNIL)))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ V5)) @ ((cALL @ (V3 @ V4)) @ V5))) @ ((V0 @ V3) @ ((cCONS @ V4) @ V5))))))))))) @ ((c==> @ ((cORDERED @ V1) @ V2)) @ ((V0 @ V1) @ V2))))))))))
(TFINITE_FINITE_UNIONS,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cFINITE @ (cUNIONS @ V0))) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (cFINITE @ V1)))))))))
(TDIFF_UNIONS_NONEMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c= @ ((cDIFF @ V1) @ (cUNIONS @ V0))) @ (cINTERS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cDIFF @ V1) @ V3))))))))))))))
(TDIFF_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDIFF @ V1) @ (cUNIONS @ V0))) @ ((cINTER @ V1) @ (cINTERS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cDIFF @ V1) @ V3))))))))))))))
(TUNIONS_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDIFF @ (cUNIONS @ V0)) @ V1)) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cDIFF @ V3) @ V1)))))))))))))
(TUNIONS_INTERS,(c! @ (^[V0]: ((c= @ (cUNIONS @ V0)) @ ((cDIFF @ cUNIV) @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ ((cDIFF @ cUNIV) @ V2))))))))))))
(TINTERS_UNIONS,(c! @ (^[V0]: ((c= @ (cINTERS @ V0)) @ ((cDIFF @ cUNIV) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ ((cDIFF @ cUNIV) @ V2))))))))))))
(TDIFF_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDIFF @ V1) @ (cINTERS @ V0))) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cDIFF @ V1) @ V3)))))))))))))
(TSUBSET_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cSUBSET @ V1) @ (cINTERS @ V0))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cSUBSET @ V1) @ V2))))))))))
(TUNIONS_MONO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((cSUBSET @ V2) @ V3)))))))) @ ((cSUBSET @ (cUNIONS @ V0)) @ (cUNIONS @ V1))))))))
(TINTERS_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cINTERS @ ((cUNION @ V0) @ V1))) @ ((cINTER @ (cINTERS @ V0)) @ (cINTERS @ V1))))))))
(TUNIONS_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cUNIONS @ ((cUNION @ V0) @ V1))) @ ((cUNION @ (cUNIONS @ V0)) @ (cUNIONS @ V1))))))))
(TSUBSET_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ V1)) @ ((cSUBSET @ (cUNIONS @ V0)) @ (cUNIONS @ V1))))))))
(TUNIONS_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cSUBSET @ (cUNIONS @ V0)) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cSUBSET @ V2) @ V1))))))))))
(TINTER_UNIONS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINTER @ V1) @ (cUNIONS @ V0))) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cINTER @ V1) @ V3)))))))))))))
(TINTER_UNIONS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINTER @ (cUNIONS @ V0)) @ V1)) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cINTER @ V3) @ V1)))))))))))))
(TEMPTY_UNIONS,(c! @ (^[V0]: ((c= @ ((c= @ (cUNIONS @ V0)) @ cEMPTY)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c= @ V1) @ cEMPTY))))))))
(TEXISTS_IN_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ (cUNIONS @ V0))) @ (V1 @ V2))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V2)) @ (V1 @ V3)))))))))))))
(TFORALL_IN_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (cUNIONS @ V0))) @ (V1 @ V2))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V2))) @ (V1 @ V3))))))))))))
(Tistopology,(c! @ (^[V0]: ((c= @ (cistopology @ V0)) @ ((c/__caret__ @ ((cIN @ cEMPTY) @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((cIN @ ((cINTER @ V1) @ V2)) @ V0))))))) @ (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V1) @ V0)) @ ((cIN @ (cUNIONS @ V1)) @ V0))))))))))
(THULL_P_AND_Q,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ (V0 @ V4))))) @ (V0 @ (cINTERS @ V3)))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ (V1 @ V4))))) @ (V1 @ (cINTERS @ V3)))))) @ (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ (V1 @ ((chull @ V0) @ V3)))))))) @ ((c= @ ((chull @ (^[V3]: ((c/__caret__ @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((chull @ V0) @ ((chull @ V1) @ V2)))))))))))
(THULL_UNION_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((cSUBSET @ ((cUNION @ ((chull @ V0) @ V1)) @ ((chull @ V0) @ V2))) @ ((chull @ V0) @ ((cUNION @ V1) @ V2))))))))))
(THULL_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ ((c/__caret__ @ (V0 @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V3)) @ (V0 @ V3))) @ ((cSUBSET @ V2) @ V3))))))) @ ((c= @ ((chull @ V0) @ V1)) @ V2)))))))))
(TSUBSET_HULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((c= @ ((cSUBSET @ ((chull @ V0) @ V1)) @ V2)) @ ((cSUBSET @ V1) @ V2))))))))))
(THULL_MINIMAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ (V0 @ V2))) @ ((cSUBSET @ ((chull @ V0) @ V1)) @ V2)))))))))
(THULL_ANTIMONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V1) @ V0)) @ ((cSUBSET @ ((chull @ V0) @ V2)) @ ((chull @ V1) @ V2))))))))))
(THULL_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ V1) @ ((chull @ V0) @ V1)))))))
(THULL_HULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ V0) @ ((chull @ V0) @ V1))) @ ((chull @ V0) @ V1)))))))
(THULL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (V0 @ V3))))) @ (V0 @ (cINTERS @ V2)))))) @ ((c= @ ((c= @ ((chull @ V0) @ V1)) @ V1)) @ (V0 @ V1))))))))
(TP_HULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (V0 @ V3))))) @ (V0 @ (cINTERS @ V2)))))) @ (V0 @ ((chull @ V0) @ V1))))))))
(THULL_P,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (V0 @ V1)) @ ((c= @ ((chull @ V0) @ V1)) @ V1)))))))
(Thull,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ V0) @ V1)) @ (cINTERS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ (V0 @ V3)) @ ((cSUBSET @ V1) @ V3))) @ V3))))))))))))
(TFORALL_FINITE_INDEX,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (V0 @ (cfinite_index @ V1)))))))))
(Tcart_tybij_conjunct1,(c! @ (^[V0]: ((c= @ cT) @ ((c= @ (cdest_cart @ (cmk_cart @ V0))) @ V0)))))
(TDIMINDEX_FINITE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdimindex @ V0)) @ (cdimindex @ V1)))))))
(Texpression_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cConstant @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cNegation @ V2)))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cInverse @ V2)))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cAddition @ V2) @ V3)))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cMultiplication @ V2) @ V3)))))))) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V0 @ (cSqrt @ V2))))))))))) @ (V0 @ V1)))))))
(Tcommand_INDUCTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cAssign @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cSeq @ V2) @ V3)))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (V0 @ V4))) @ (V0 @ (((cIte @ V2) @ V3) @ V4)))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ ((cWhile @ V2) @ V3))))))))))) @ (V0 @ V1)))))))
(Tsem_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (((V0 @ (cAssign @ V4)) @ V5) @ (V4 @ V5))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ (((V0 @ V4) @ V6) @ V7)) @ (((V0 @ V5) @ V7) @ V8))) @ (((V0 @ ((cSeq @ V4) @ V5)) @ V6) @ V8))))))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ (V4 @ V7)) @ (((V0 @ V5) @ V7) @ V8))) @ (((V0 @ (((cIte @ V4) @ V5) @ V6)) @ V7) @ V8))))))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ (c~ @ (V4 @ V7))) @ (((V0 @ V6) @ V7) @ V8))) @ (((V0 @ (((cIte @ V4) @ V5) @ V6)) @ V7) @ V8))))))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (c~ @ (V4 @ V6))) @ (((V0 @ ((cWhile @ V4) @ V5)) @ V6) @ V6))))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ (V4 @ V6)) @ ((c/__caret__ @ (((V0 @ V5) @ V6) @ V7)) @ (((V0 @ ((cWhile @ V4) @ V5)) @ V7) @ V8)))) @ (((V0 @ ((cWhile @ V4) @ V5)) @ V6) @ V8)))))))))))))))))) @ ((c==> @ (((csem @ V1) @ V2) @ V3)) @ (((V0 @ V1) @ V2) @ V3))))))))))))
(Tchar_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: (V0 @ ((((((((cASCII @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9))))))))))))))))))) @ (V0 @ V1)))))))
(Tcform_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cLt @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cGt @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cEq @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ (cNe @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (V0 @ ((cDivides @ V2) @ V3))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (V0 @ ((cNdivides @ V2) @ V3))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cAnd @ V2) @ V3)))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cOr @ V2) @ V3)))))))) @ (c! @ (^[V2]: (V0 @ (cNox @ V2))))))))))))) @ (V0 @ V1)))))))
(TMBASIS_EXTENSION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ (V0 @ (cmbasis @ V2)))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ ((c% @ V2) @ V3)))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cvector_add @ V2) @ V3)))))))))) @ (V0 @ V1)))))))
(TBILINEAR_EQ_MBASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbilinear @ V0)) @ ((c/__caret__ @ (cbilinear @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((cSUBSET @ V3) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))) @ ((c= @ ((V0 @ (cmbasis @ V2)) @ (cmbasis @ V3))) @ ((V1 @ (cmbasis @ V2)) @ (cmbasis @ V3))))))))))) @ ((c= @ V0) @ V1)))))))
(TLINEAR_EQ_MBASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ (V0 @ (cmbasis @ V2))) @ (V1 @ (cmbasis @ V2))))))))) @ ((c= @ V0) @ V1)))))))
(TDIRECTION_CLAUSES_conjunct1,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ (cdest_dir @ V1))))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ (V0 @ V1))))))))
(TDIRECTION_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ (cdest_dir @ V1))))) @ (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ (V0 @ V1))))))))
(TCOMPUTE_FACES_2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((c/__caret__ @ ((cface_of @ V0) @ ((chull @ cconvex) @ V1))) @ ((c= @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cLET @ (^[V5]: (cLET_END @ ((c/__caret__ @ (c~ @ ((c= @ V5) @ (cvec @ (cNUMERAL @ c_0))))) @ ((cLET @ (^[V6]: (cLET_END @ ((c/__caret__ @ ((c__caret__/ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V1)) @ ((creal_le @ ((cdot @ V5) @ V7)) @ V6))))) @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V1)) @ ((creal_ge @ ((cdot @ V5) @ V7)) @ V6)))))) @ ((c= @ V0) @ ((chull @ cconvex) @ ((cINTER @ V1) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c= @ ((cdot @ V5) @ V8)) @ V6)) @ V8)))))))))))) @ ((cdot @ V5) @ V2)))))) @ ((ccross @ ((cvector_sub @ V4) @ V2)) @ ((cvector_sub @ V3) @ V2)))))))))))))))))))
(THAS_PATH_INTEGRAL_INTEGRAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpath_integrable_on @ V0) @ V1)) @ (((chas_path_integral @ V0) @ ((cpath_integral @ V1) @ V0)) @ V1)))))))
(TVALID_PATH_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cvalid_path @ V1)) @ ((cdifferentiable_on @ V0) @ (cpath_image @ V1)))) @ (cvalid_path @ ((co @ V0) @ V1))))))))
(Tpath_integral,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpath_integral @ V1) @ V0)) @ (c__at__ @ (^[V2]: (((chas_path_integral @ V0) @ V2) @ V1)))))))))
(TPATH_INTEGRABLE_ON,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpath_integrable_on @ V0) @ V1)) @ ((cintegrable_on @ (^[V2]: ((ccomplex_mul @ (V0 @ (V1 @ V2))) @ ((cvector_derivative @ V1) @ (cat @ V2))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))))))))
(Tpath_integrable_on,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpath_integrable_on @ V0) @ V1)) @ (c? @ (^[V2]: (((chas_path_integral @ V0) @ V2) @ V1)))))))))
(Thas_path_integral,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_path_integral @ V0) @ V2) @ V1)) @ (((chas_integral @ (^[V3]: ((ccomplex_mul @ (V0 @ (V1 @ V3))) @ ((cvector_derivative @ V1) @ ((cwithin @ (cat @ V3)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))))) @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))))))))))
(THAS_PATH_INTEGRAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_path_integral @ V0) @ V2) @ V1)) @ (((chas_integral @ (^[V3]: ((ccomplex_mul @ (V0 @ (V1 @ V3))) @ ((cvector_derivative @ V1) @ (cat @ V3))))) @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))))))))))
(THAS_PATH_INTEGRAL_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chas_path_integral @ V0) @ V2) @ V1)) @ (((chas_path_integral @ V0) @ V3) @ V1))) @ ((c= @ V2) @ V3)))))))))))
(THAS_INTEGRAL_LOCALIZED_VECTOR_DERIVATIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((chas_integral @ (^[V5]: ((ccomplex_mul @ (V0 @ (V1 @ V5))) @ ((cvector_derivative @ V1) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))) @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (((chas_integral @ (^[V5]: ((ccomplex_mul @ (V0 @ (V1 @ V5))) @ ((cvector_derivative @ V1) @ (cat @ V5))))) @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))
(TCOLLINEAR_IMP_NEGLIGIBLE,(c! @ (^[V0]: ((c==> @ (ccollinear @ V0)) @ (cnegligible @ V0)))))
(TEXISTS_COMPLEX,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c? @ (^[V2]: (V0 @ (ccomplex @ ((c__comma__ @ V1) @ V2)))))))))))
(TFORALL_COMPLEX,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (c! @ (^[V2]: (V0 @ (ccomplex @ ((c__comma__ @ V1) @ V2)))))))))))
(TTARSKI_AXIOM_11_EUCLIDEAN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cbetween @ V3) @ ((c__comma__ @ V2) @ V4)))))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cbetween @ V2) @ ((c__comma__ @ V3) @ V4)))))))))))))))
(Tconstructible_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (crational @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (crational @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (V0 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((c/__caret__ @ (V0 @ V3)) @ ((c/__caret__ @ (V0 @ V4)) @ ((c/__caret__ @ (V0 @ V5)) @ ((c/__caret__ @ (c~ @ ((cparallel @ ((c__comma__ @ V2) @ V3)) @ ((c__comma__ @ V4) @ V5)))) @ (((cis_intersection @ V6) @ ((c__comma__ @ V2) @ V3)) @ ((c__comma__ @ V4) @ V5)))))))) @ (V0 @ V6))))))))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((c/__caret__ @ (V0 @ V3)) @ ((c/__caret__ @ (V0 @ V4)) @ ((c/__caret__ @ (V0 @ V5)) @ ((c/__caret__ @ (V0 @ V6)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V3))) @ ((c/__caret__ @ (((ccollinear3 @ V2) @ V7) @ V3)) @ ((c= @ (clength @ ((c__comma__ @ V4) @ V7))) @ (clength @ ((c__comma__ @ V5) @ V6))))))))))) @ (V0 @ V7))))))))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((c/__caret__ @ (V0 @ V3)) @ ((c/__caret__ @ (V0 @ V4)) @ ((c/__caret__ @ (V0 @ V5)) @ ((c/__caret__ @ (V0 @ V6)) @ ((c/__caret__ @ (V0 @ V7)) @ ((c/__caret__ @ (c~ @ ((c/__caret__ @ ((c= @ V2) @ V5)) @ ((c= @ (clength @ ((c__comma__ @ V3) @ V4))) @ (clength @ ((c__comma__ @ V6) @ V7)))))) @ ((c/__caret__ @ ((c= @ (clength @ ((c__comma__ @ V2) @ V8))) @ (clength @ ((c__comma__ @ V3) @ V4)))) @ ((c= @ (clength @ ((c__comma__ @ V5) @ V8))) @ (clength @ ((c__comma__ @ V6) @ V7)))))))))))) @ (V0 @ V8)))))))))))))))))))) @ ((c==> @ (cconstructible @ V1)) @ (V0 @ V1))))))))
(TOPERATIVE_REAL_FUNCTION_ENDPOINT_DIFF,(c! @ (^[V0]: ((coperative @ creal_add) @ (^[V1]: ((creal_sub @ (V0 @ (cinterval_upperbound @ V1))) @ (V0 @ (cinterval_lowerbound @ V1))))))))
(TSECOND_MEAN_VALUE_THEOREM_GEN_FULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))) @ cEMPTY))) @ ((c/__caret__ @ ((cintegrable_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ (copen_interval @ ((c__comma__ @ V4) @ V5)))) @ ((c/__caret__ @ ((creal_le @ V1) @ (V0 @ V6))) @ ((creal_le @ (V0 @ V6)) @ V2)))))) @ (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ ((creal_le @ (cdrop @ V6)) @ (cdrop @ V7))))) @ ((creal_le @ (V0 @ V6)) @ (V0 @ V7))))))))))) @ (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ (((chas_integral @ (^[V7]: ((c% @ (V0 @ V7)) @ (V3 @ V7)))) @ ((cvector_add @ ((c% @ V1) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V6)) @ cNIL))) @ V3))) @ ((c% @ V2) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V5)) @ cNIL))) @ V3)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))))))))))))))))))
(TSECOND_MEAN_VALUE_THEOREM_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL))) @ cEMPTY))) @ ((c/__caret__ @ ((cintegrable_on @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL)))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ (copen_interval @ ((c__comma__ @ V2) @ V4)))) @ ((c/__caret__ @ ((creal_le @ V1) @ (V0 @ V6))) @ ((creal_le @ (V0 @ V6)) @ V3)))))) @ (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL)))) @ ((creal_le @ (cdrop @ V6)) @ (cdrop @ V7))))) @ ((creal_le @ (V0 @ V6)) @ (V0 @ V7))))))))))) @ (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL)))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL))) @ (^[V7]: ((c% @ (V0 @ V7)) @ (V5 @ V7))))) @ ((cvector_add @ ((c% @ V1) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V6)) @ cNIL))) @ V5))) @ ((c% @ V3) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V4)) @ cNIL))) @ V5)))))))))))))))))))))
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(THAS_BOUNDED_VARIATION_ON_MAX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V0) @ V2)) @ ((chas_bounded_variation_on @ V1) @ V2))) @ ((chas_bounded_variation_on @ (^[V3]: (clift @ ((creal_max @ (cdrop @ (V0 @ V3))) @ (cdrop @ (V1 @ V3)))))) @ V2)))))))))
(THAS_BOUNDED_VARIATION_ON_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((chas_bounded_variation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ ((chas_bounded_variation_on @ (^[V4]: ((c% @ (cdrop @ (V0 @ V4))) @ (V1 @ V4)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(THAS_BOUNDED_VARIATION_DARBOUX_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chas_bounded_variation_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (c! @ (^[V5]: ((c= @ (V0 @ V5)) @ ((cvector_sub @ (V3 @ V5)) @ (V4 @ V5)))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_le @ (cdrop @ V5)) @ (cdrop @ V6))))) @ ((creal_le @ (cdrop @ (V3 @ V5))) @ (cdrop @ (V3 @ V6))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_le @ (cdrop @ V5)) @ (cdrop @ V6))))) @ ((creal_le @ (cdrop @ (V4 @ V5))) @ (cdrop @ (V4 @ V6))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_lt @ (cdrop @ V5)) @ (cdrop @ V6))))) @ ((creal_lt @ (cdrop @ (V3 @ V5))) @ (cdrop @ (V3 @ V6))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_lt @ (cdrop @ V5)) @ (cdrop @ V6))))) @ ((creal_lt @ (cdrop @ (V4 @ V5))) @ (cdrop @ (V4 @ V6))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((ccontinuous @ V0) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V5)) @ cNIL)))))) @ ((c/__caret__ @ ((ccontinuous @ V3) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V5)) @ cNIL))))) @ ((ccontinuous @ V4) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V5)) @ cNIL))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((ccontinuous @ V0) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V2)) @ cNIL)))))) @ ((c/__caret__ @ ((ccontinuous @ V3) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V2)) @ cNIL))))) @ ((ccontinuous @ V4) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V2)) @ cNIL))))))))) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((ccontinuous @ V0) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))) @ ((c/__caret__ @ ((ccontinuous @ V3) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))) @ ((ccontinuous @ V4) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))))))))))))))))))
(TINTEGRABLE_DECREASING_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))))) @ ((creal_le @ (cdrop @ (V0 @ V4))) @ (cdrop @ (V0 @ V3))))))))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TDECREASING_BOUNDED_VARIATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))))) @ ((creal_le @ (cdrop @ (V0 @ V4))) @ (cdrop @ (V0 @ V3))))))))) @ ((chas_bounded_variation_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TINTEGRABLE_INCREASING_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))))) @ ((creal_le @ (cdrop @ (V0 @ V3))) @ (cdrop @ (V0 @ V4))))))))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TINCREASING_BOUNDED_VARIATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))))) @ ((creal_le @ (cdrop @ (V0 @ V3))) @ (cdrop @ (V0 @ V4))))))))) @ ((chas_bounded_variation_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TROLLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (cdrop @ V1)) @ (cdrop @ V2))) @ ((c/__caret__ @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (copen_interval @ ((c__comma__ @ V1) @ V2)))) @ (((chas_derivative @ V0) @ (V3 @ V4)) @ (cat @ V4))))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ (copen_interval @ ((c__comma__ @ V1) @ V2)))) @ ((c= @ (V3 @ V4)) @ (^[V5]: (cvec @ (cNUMERAL @ c_0)))))))))))))))))
(TVECTOR_VARIATION_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ ((c= @ ((ccontinuous @ (^[V4]: (clift @ ((cvector_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL))) @ V0)))) @ ((cwithin @ (cat @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ ((ccontinuous @ V0) @ ((cwithin @ (cat @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))))
(TOPERATIVE_LIFTED_VECTOR_VARIATION,(c! @ (^[V0]: ((coperative @ (clifted @ creal_add)) @ (^[V1]: (((cCOND @ ((chas_bounded_variation_on @ V0) @ V1)) @ (cSOME @ ((cvector_variation @ V1) @ V0))) @ cNONE))))))
(TOPERATIVE_FUNCTION_ENDPOINT_DIFF,(c! @ (^[V0]: ((coperative @ cvector_add) @ (^[V1]: ((cvector_sub @ (V0 @ (cinterval_upperbound @ V1))) @ (V0 @ (cinterval_lowerbound @ V1))))))))
(THAS_BOUNDED_VARIATION_ON_EMPTY,(c! @ (^[V0]: ((chas_bounded_variation_on @ V0) @ cEMPTY))))
(THOMEOMORPHIC_MONOTONE_IMAGE_INTERVAL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c/__caret__ @ (c! @ (^[V1]: (cconnected @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V0 @ V3)) @ V1))) @ V3))))))))) @ (c~ @ ((c= @ (V0 @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V0 @ (cvec @ (cNUMERAL @ c_0)))))))) @ ((chomeomorphic @ ((cIMAGE @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))))))
(TNEGLIGIBLE_RECTIFIABLE_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (crectifiable_path @ V0))) @ (cnegligible @ (cpath_image @ V0))))))
(TPATH_CONNECTED_ARC_COMPLEMENT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (carc @ V0))) @ (cpath_connected @ ((cDIFF @ cUNIV) @ (cpath_image @ V0)))))))
(TCONNECTED_ARC_COMPLEMENT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (carc @ V0))) @ (cconnected @ ((cDIFF @ cUNIV) @ (cpath_image @ V0)))))))
(TSIMPLE_PATH_IMP_ARC,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (csimple_path @ V0)) @ (c~ @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V0))))) @ (carc @ V0)))))
(TSIMPLE_PATH_CASES,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ ((c__caret__/ @ (carc @ V0)) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V0)))))))
(TSIMPLE_PATH_ENDLESS,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ ((c= @ ((cDIFF @ (cpath_image @ V0)) @ ((cINSERT @ (cpathstart @ V0)) @ ((cINSERT @ (cpathfinish @ V0)) @ cEMPTY)))) @ ((cIMAGE @ V0) @ (copen_interval @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TNONEMPTY_SIMPLE_PATH_ENDLESS,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ (c~ @ ((c= @ ((cDIFF @ (cpath_image @ V0)) @ ((cINSERT @ (cpathstart @ V0)) @ ((cINSERT @ (cpathfinish @ V0)) @ cEMPTY)))) @ cEMPTY))))))
(TCONNECTED_SIMPLE_PATH_ENDLESS,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ (cconnected @ ((cDIFF @ (cpath_image @ V0)) @ ((cINSERT @ (cpathstart @ V0)) @ ((cINSERT @ (cpathfinish @ V0)) @ cEMPTY))))))))
(TRECTIFIABLE_PATH_IMP_PATH,(c! @ (^[V0]: ((c==> @ (crectifiable_path @ V0)) @ (cpath @ V0)))))
(TBOUNDED_RECTIFIABLE_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (crectifiable_path @ V0)) @ (cbounded @ (cpath_image @ V0))))))
(TLOCALLY_PATH_CONNECTED_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (cpath @ V0)) @ ((clocally @ cpath_connected) @ (cpath_image @ V0))))))
(TLOCALLY_CONNECTED_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (cpath @ V0)) @ ((clocally @ cconnected) @ (cpath_image @ V0))))))
(TPATH_CONNECTED_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (cpath @ V0)) @ (cpath_connected @ (cpath_image @ V0))))))
(TLINEAR_FROM_REALS,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ V0) @ (^[V1]: ((c% @ (cdrop @ V1)) @ ((ccolumn @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cmatrix @ V0)))))))))
(TINSIDE_ARC_EMPTY,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ ((c= @ (cinside @ (cpath_image @ V0))) @ cEMPTY)))))
(TARC_DISTINCT_ENDS,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (c~ @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V0)))))))
(THOMEOMORPHISM_ARC,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (c? @ (^[V1]: ((chomeomorphism @ ((c__comma__ @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ (cpath_image @ V0))) @ ((c__comma__ @ V0) @ V1))))))))
(TRETRACTION_ARC,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((ccontinuous_on @ V1) @ cUNIV)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ cUNIV)) @ (cpath_image @ V0))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (cpath_image @ V0))) @ ((c= @ (V1 @ V2)) @ V2))))))))))))
(TPATH_LENGTH_REVERSEPATH,(c! @ (^[V0]: ((c= @ (cpath_length @ (creversepath @ V0))) @ (cpath_length @ V0)))))
(Tpath_length,(c! @ (^[V0]: ((c= @ (cpath_length @ V0)) @ ((cvector_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V0)))))
(TJOIN_SUBPATHS_MIDDLE,(c! @ (^[V0]: ((c= @ ((c++ @ (((csubpath @ (cvec @ (cNUMERAL @ c_0))) @ (clift @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ V0)) @ (((csubpath @ (clift @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))) @ V0))))
(TREVERSEPATH_REVERSEPATH,(c! @ (^[V0]: ((c= @ (creversepath @ (creversepath @ V0))) @ V0))))
(Treversepath,(c! @ (^[V0]: ((c= @ (creversepath @ V0)) @ (^[V1]: (V0 @ ((cvector_sub @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)))))))
(TPATH_IMAGE_REVERSEPATH,(c! @ (^[V0]: ((c= @ (cpath_image @ (creversepath @ V0))) @ (cpath_image @ V0)))))
(Tpath_image,(c! @ (^[V0]: ((c= @ (cpath_image @ V0)) @ ((cIMAGE @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))))))
(Tpathstart,(c! @ (^[V0]: ((c= @ (cpathstart @ V0)) @ (V0 @ (cvec @ (cNUMERAL @ c_0)))))))
(Tpathfinish,(c! @ (^[V0]: ((c= @ (cpathfinish @ V0)) @ (V0 @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(Tsimple_path,(c! @ (^[V0]: ((c= @ (csimple_path @ V0)) @ ((c/__caret__ @ (cpath @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V0 @ V1)) @ (V0 @ V2))))) @ ((c__caret__/ @ ((c= @ V1) @ V2)) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c= @ V2) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))))))))))))))
(TRECTIFIABLE_PATH_REVERSEPATH,(c! @ (^[V0]: ((c= @ (crectifiable_path @ (creversepath @ V0))) @ (crectifiable_path @ V0)))))
(Trectifiable_path,(c! @ (^[V0]: ((c= @ (crectifiable_path @ V0)) @ ((c/__caret__ @ (cpath @ V0)) @ ((chas_bounded_variation_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))))))
(TPATH_REVERSEPATH,(c! @ (^[V0]: ((c= @ (cpath @ (creversepath @ V0))) @ (cpath @ V0)))))
(Tpath,(c! @ (^[V0]: ((c= @ (cpath @ V0)) @ ((ccontinuous_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))))))
(TARC_SIMPLE_PATH,(c! @ (^[V0]: ((c= @ (carc @ V0)) @ ((c/__caret__ @ (csimple_path @ V0)) @ (c~ @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V0))))))))
(Tarc,(c! @ (^[V0]: ((c= @ (carc @ V0)) @ ((c/__caret__ @ (cpath @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V0 @ V1)) @ (V0 @ V2))))) @ ((c= @ V1) @ V2)))))))))))
(THAS_BOUNDED_VARIATION_AFFINITY_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((chas_bounded_variation_on @ (^[V4]: (V0 @ ((cvector_add @ ((c% @ V1) @ V4)) @ V2)))) @ V3)) @ ((c__caret__/ @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((chas_bounded_variation_on @ V0) @ ((cIMAGE @ (^[V4]: ((cvector_add @ ((c% @ V1) @ V4)) @ V2))) @ V3)))))))))))))
(Tvector_derivative,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_derivative @ V0) @ V1)) @ (c__at__ @ (^[V2]: (((chas_vector_derivative @ V0) @ V2) @ V1)))))))))
(TVECTOR_DERIVATIVE_WORKS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdifferentiable @ V0) @ V1)) @ (((chas_vector_derivative @ V0) @ ((cvector_derivative @ V0) @ V1)) @ V1)))))))
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(TPATH_JOIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))) @ ((c= @ (cpath @ ((c++ @ V0) @ V1))) @ ((c/__caret__ @ (cpath @ V0)) @ (cpath @ V1)))))))))
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(TPATH_LENGTH_JOIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (crectifiable_path @ V0)) @ ((c/__caret__ @ (crectifiable_path @ V1)) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))))) @ ((c= @ (cpath_length @ ((c++ @ V0) @ V1))) @ ((creal_add @ (cpath_length @ V0)) @ (cpath_length @ V1)))))))))
(TRECTIFIABLE_PATH_JOIN_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (crectifiable_path @ V0)) @ ((c/__caret__ @ (crectifiable_path @ V1)) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))))) @ (crectifiable_path @ ((c++ @ V0) @ V1))))))))
(TRECTIFIABLE_PATH_JOIN_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (crectifiable_path @ V0)) @ (crectifiable_path @ V1))) @ ((c= @ (crectifiable_path @ ((c++ @ V0) @ V1))) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1)))))))))
(TPATH_JOIN_PATH_ENDS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ (cpath @ ((c++ @ V0) @ V1)))) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))))))))
(TPATH_JOIN_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V0)) @ ((c/__caret__ @ (cpath @ V1)) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))))) @ (cpath @ ((c++ @ V0) @ V1))))))))
(TPATH_JOIN_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V0)) @ (cpath @ V1))) @ ((c= @ (cpath @ ((c++ @ V0) @ V1))) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1)))))))))
(TARC_JOIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (carc @ V0)) @ ((c/__caret__ @ (carc @ V1)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))) @ ((cSUBSET @ ((cINTER @ (cpath_image @ V0)) @ (cpath_image @ V1))) @ ((cINSERT @ (cpathstart @ V1)) @ cEMPTY)))))) @ (carc @ ((c++ @ V0) @ V1))))))))
(TSIMPLE_PATH_JOIN_LOOP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (carc @ V0)) @ ((c/__caret__ @ (carc @ V1)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V0))) @ ((cSUBSET @ ((cINTER @ (cpath_image @ V0)) @ (cpath_image @ V1))) @ ((cINSERT @ (cpathstart @ V0)) @ ((cINSERT @ (cpathstart @ V1)) @ cEMPTY)))))))) @ (csimple_path @ ((c++ @ V0) @ V1))))))))
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(TSIMPLE_PATH_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))) @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V2)))) @ ((c= @ (csimple_path @ ((c++ @ V0) @ ((c++ @ V1) @ V2)))) @ (csimple_path @ ((c++ @ ((c++ @ V0) @ V1)) @ V2)))))))))))
(TPATH_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))) @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V2)))) @ ((c= @ (cpath @ ((c++ @ V0) @ ((c++ @ V1) @ V2)))) @ (cpath @ ((c++ @ ((c++ @ V0) @ V1)) @ V2)))))))))))
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(TSUBSET_PATH_IMAGE_JOIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V0)) @ V2)) @ ((cSUBSET @ (cpath_image @ V1)) @ V2))) @ ((cSUBSET @ (cpath_image @ ((c++ @ V0) @ V1))) @ V2)))))))))
(TFUNDAMENTAL_THEOREM_OF_CALCULUS_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_le @ (cdrop @ V2)) @ (cdrop @ V3))) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (copen_interval @ ((c__comma__ @ V2) @ V3)))) @ (((chas_vector_derivative @ V1) @ (V0 @ V4)) @ (cat @ V4)))))))) @ (((chas_integral @ V0) @ ((cvector_sub @ (V1 @ V3)) @ (V1 @ V2))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(TFUNDAMENTAL_THEOREM_OF_CALCULUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_le @ (cdrop @ V2)) @ (cdrop @ V3))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (((chas_vector_derivative @ V1) @ (V0 @ V4)) @ ((cwithin @ (cat @ V4)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))) @ (((chas_integral @ V0) @ ((cvector_sub @ (V1 @ V3)) @ (V1 @ V2))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(THAS_BOUNDED_VARIATION_ON_REFLECT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_variation_on @ V0) @ ((cIMAGE @ cvector_neg) @ V1))) @ ((chas_bounded_variation_on @ (^[V2]: (V0 @ (cvector_neg @ V2)))) @ V1)))))))
(THAS_BOUNDED_VARIATION_ON_NORM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_variation_on @ V0) @ V1)) @ ((chas_bounded_variation_on @ (^[V2]: (clift @ (cvector_norm @ (V0 @ V2))))) @ V1)))))))
(THAS_BOUNDED_VARIATION_ON_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_variation_on @ V0) @ V1)) @ ((chas_bounded_variation_on @ (^[V2]: (cvector_neg @ (V0 @ V2)))) @ V1)))))))
(THAS_BOUNDED_VARIATION_ON_NULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (ccontent @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (cbounded @ V1))) @ ((chas_bounded_variation_on @ V0) @ V1)))))))
(THAS_BOUNDED_VARIATION_REFLECT2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_bounded_variation_on @ (^[V2]: (V0 @ (cvector_neg @ V2)))) @ ((cIMAGE @ cvector_neg) @ V1))) @ ((chas_bounded_variation_on @ V0) @ V1)))))))
(THAS_BOUNDED_VARIATION_REFLECT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_bounded_variation_on @ (^[V2]: (V0 @ (cvector_neg @ V2)))) @ V1)) @ ((chas_bounded_variation_on @ V0) @ ((cIMAGE @ cvector_neg) @ V1))))))))
(Thas_bounded_variation_on,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_bounded_variation_on @ V0) @ V1)) @ ((chas_bounded_setvariation_on @ (^[V2]: ((cvector_sub @ (V0 @ (cinterval_upperbound @ V2))) @ (V0 @ (cinterval_lowerbound @ V2))))) @ V1)))))))
(THAS_BOUNDED_VARIATION_ON_COMPONENTWISE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_bounded_variation_on @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((chas_bounded_variation_on @ (^[V3]: (clift @ ((c$ @ (V0 @ V3)) @ V2)))) @ V1))))))))))
(TVECTOR_VARIATION_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V0) @ V1)) @ ((chas_bounded_variation_on @ V2) @ V1))) @ ((creal_le @ ((cvector_variation @ V1) @ (^[V3]: ((cvector_add @ (V0 @ V3)) @ (V2 @ V3))))) @ ((creal_add @ ((cvector_variation @ V1) @ V0)) @ ((cvector_variation @ V1) @ V2)))))))))))
(TVECTOR_VARIATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3)))))) @ ((c= @ ((cvector_variation @ V1) @ V0)) @ ((cvector_variation @ V1) @ V2))))))))))
(TEXISTS_PATH_SUBPATH_TO_FRONTIER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V0)) @ ((c/__caret__ @ ((cIN @ (cpathstart @ V0)) @ V1)) @ (c~ @ ((cIN @ (cpathfinish @ V0)) @ V1))))) @ (c? @ (^[V2]: ((c/__caret__ @ (cpath @ V2)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V2)) @ (cpathstart @ V0))) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V2)) @ (cpath_image @ V0))) @ ((c/__caret__ @ ((cSUBSET @ ((cDELETE @ (cpath_image @ V2)) @ (cpathfinish @ V2))) @ (cinterior @ V1))) @ ((cIN @ (cpathfinish @ V2)) @ (cfrontier @ V1))))))))))))))
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(THAS_BOUNDED_VARIATION_ON_IMP_BOUNDED_ON_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chas_bounded_variation_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (cbounded @ ((cIMAGE @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))
(TDIFFERENTIABLE_ON_IMP_PIECEWISE_DIFFERENTIABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cdifferentiable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cpiecewise_differentiable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
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(TNEGLIGIBLE_IMAGE_BOUNDED_VARIATION_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((chas_bounded_variation_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))) @ (cnegligible @ ((cIMAGE @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))
(THOMEOMORPHIC_ARC_IMAGE_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (carc @ V0)) @ ((creal_lt @ (cdrop @ V1)) @ (cdrop @ V2)))) @ ((chomeomorphic @ (cpath_image @ V0)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
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(TINTEGRABLE_INCREASING,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV))))))) @ ((creal_le @ ((c$ @ (V0 @ V3)) @ V5)) @ ((c$ @ (V0 @ V4)) @ V5)))))))))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TPATH_IMAGE_SUBPATH_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cpath_image @ (((csubpath @ V1) @ V2) @ V0))) @ ((cIMAGE @ V0) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(THAS_BOUNDED_VARIATION_REFLECT_EQ_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chas_bounded_variation_on @ (^[V3]: (V0 @ (cvector_neg @ V3)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V1)) @ cNIL)))) @ ((chas_bounded_variation_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvector_neg @ V1)) @ (cvector_neg @ V2))) @ cNIL)))))))))))
(TINTEGRAL_HAS_VECTOR_DERIVATIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((ccontinuous_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((c==> @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (((chas_vector_derivative @ (^[V4]: ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL))) @ V0))) @ (V0 @ V1)) @ ((cwithin @ (cat @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))))
(THAS_BOUNDED_VARIATION_TRANSLATION_EQ_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((chas_bounded_variation_on @ (^[V4]: (V0 @ ((cvector_add @ V2) @ V4)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V3)) @ cNIL)))) @ ((chas_bounded_variation_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cvector_add @ V2) @ V1)) @ ((cvector_add @ V2) @ V3))) @ cNIL)))))))))))))
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(TVECTOR_DERIVATIVE_UNIQUE_WITHIN_CLOSED_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (cdrop @ V2)) @ (cdrop @ V3))) @ ((c/__caret__ @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((c/__caret__ @ (((chas_vector_derivative @ V0) @ V4) @ ((cwithin @ (cat @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ (((chas_vector_derivative @ V0) @ V5) @ ((cwithin @ (cat @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))) @ ((c= @ V4) @ V5)))))))))))))))
(THAS_VECTOR_DERIVATIVE_UNIQUE_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_vector_derivative @ V0) @ V2) @ (cat @ V1))) @ ((c= @ ((cvector_derivative @ V0) @ (cat @ V1))) @ V2)))))))))
(TVECTOR_DERIVATIVE_UNIQUE_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chas_vector_derivative @ V0) @ V2) @ (cat @ V1))) @ (((chas_vector_derivative @ V0) @ V3) @ (cat @ V1)))) @ ((c= @ V2) @ V3)))))))))))
(TPATH_COMPONENT_PATH_IMAGE_PATHSTART,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V0)) @ ((cIN @ V1) @ (cpath_image @ V0)))) @ (((cpath_component @ (cpath_image @ V0)) @ (cpathstart @ V0)) @ V1)))))))
(TPATH_CONTAINS_ARC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V0)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V0)) @ V1)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V0)) @ V2)) @ (c~ @ ((c= @ V1) @ V2)))))) @ (c? @ (^[V3]: ((c/__caret__ @ (carc @ V3)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V3)) @ (cpath_image @ V0))) @ ((c/__caret__ @ ((c= @ (cpathstart @ V3)) @ V1)) @ ((c= @ (cpathfinish @ V3)) @ V2))))))))))))))
(THOMEOMORPHIC_ARC_IMAGE_SEGMENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (carc @ V0)) @ (c~ @ ((c= @ V1) @ V2)))) @ ((chomeomorphic @ (cpath_image @ V0)) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(THOMEOMORPHIC_ARC_IMAGES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (carc @ V0)) @ (carc @ V1))) @ ((chomeomorphic @ (cpath_image @ V0)) @ (cpath_image @ V1))))))))
(THAS_VECTOR_DERIVATIVE_BILINEAR_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((chas_vector_derivative @ V0) @ V3) @ (cat @ V5))) @ ((c/__caret__ @ (((chas_vector_derivative @ V4) @ V1) @ (cat @ V5))) @ (cbilinear @ V2)))) @ (((chas_vector_derivative @ (^[V6]: ((V2 @ (V0 @ V6)) @ (V4 @ V6)))) @ ((cvector_add @ ((V2 @ (V0 @ V5)) @ V1)) @ ((V2 @ V3) @ (V4 @ V5)))) @ (cat @ V5))))))))))))))))
(THAS_VECTOR_DERIVATIVE_BILINEAR_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (((chas_vector_derivative @ V0) @ V3) @ ((cwithin @ (cat @ V5)) @ V6))) @ ((c/__caret__ @ (((chas_vector_derivative @ V4) @ V1) @ ((cwithin @ (cat @ V5)) @ V6))) @ (cbilinear @ V2)))) @ (((chas_vector_derivative @ (^[V7]: ((V2 @ (V0 @ V7)) @ (V4 @ V7)))) @ ((cvector_add @ ((V2 @ (V0 @ V5)) @ V1)) @ ((V2 @ V3) @ (V4 @ V5)))) @ ((cwithin @ (cat @ V5)) @ V6))))))))))))))))))
(Tclosed_path,(c! @ (^[V0]: ((c= @ (cclosed_path @ V0)) @ ((c= @ (cpathstart @ V0)) @ (cpathfinish @ V0))))))
(TVECTOR_DIFF_CHAIN_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((chas_vector_derivative @ V1) @ V2) @ ((cwithin @ (cat @ V4)) @ V5))) @ (((chas_vector_derivative @ V0) @ V3) @ ((cwithin @ (cat @ (V1 @ V4))) @ ((cIMAGE @ V1) @ V5))))) @ (((chas_vector_derivative @ ((co @ V0) @ V1)) @ ((c% @ (cdrop @ V2)) @ V3)) @ ((cwithin @ (cat @ V4)) @ V5))))))))))))))))
(TVECTOR_DIFF_CHAIN_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_vector_derivative @ V1) @ V2) @ (cat @ V4))) @ (((chas_vector_derivative @ V0) @ V3) @ (cat @ (V1 @ V4))))) @ (((chas_vector_derivative @ ((co @ V0) @ V1)) @ ((c% @ (cdrop @ V2)) @ V3)) @ (cat @ V4))))))))))))))
(THAS_VECTOR_DERIVATIVE_AT_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((chas_vector_derivative @ V0) @ V1) @ (cat @ V2))) @ (((chas_vector_derivative @ V0) @ V1) @ ((cwithin @ (cat @ V2)) @ V3))))))))))))
(THAS_VECTOR_DERIVATIVE_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_vector_derivative @ V0) @ V2) @ V4)) @ (((chas_vector_derivative @ V1) @ V3) @ V4))) @ (((chas_vector_derivative @ (^[V5]: ((cvector_sub @ (V0 @ V5)) @ (V1 @ V5)))) @ ((cvector_sub @ V2) @ V3)) @ V4)))))))))))))
(THAS_VECTOR_DERIVATIVE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_vector_derivative @ V0) @ V2) @ V4)) @ (((chas_vector_derivative @ V1) @ V3) @ V4))) @ (((chas_vector_derivative @ (^[V5]: ((cvector_add @ (V0 @ V5)) @ (V1 @ V5)))) @ ((cvector_add @ V2) @ V3)) @ V4)))))))))))))
(THAS_VECTOR_DERIVATIVE_NEG_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_vector_derivative @ (^[V3]: (cvector_neg @ (V0 @ V3)))) @ (cvector_neg @ V1)) @ V2)) @ (((chas_vector_derivative @ V0) @ V1) @ V2)))))))))
(THAS_VECTOR_DERIVATIVE_NEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_vector_derivative @ V0) @ V1) @ V2)) @ (((chas_vector_derivative @ (^[V3]: (cvector_neg @ (V0 @ V3)))) @ (cvector_neg @ V1)) @ V2)))))))))
(THAS_VECTOR_DERIVATIVE_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((chas_vector_derivative @ V0) @ V2) @ V3)) @ (((chas_vector_derivative @ (^[V4]: ((c% @ V1) @ (V0 @ V4)))) @ ((c% @ V1) @ V2)) @ V3)))))))))))
(TVECTOR_DERIVATIVE_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_vector_derivative @ V0) @ V2) @ (cat @ V1))) @ ((c= @ ((cvector_derivative @ V0) @ (cat @ V1))) @ V2)))))))))
(Thas_vector_derivative,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_vector_derivative @ V0) @ V1) @ V2)) @ (((chas_derivative @ V0) @ (^[V3]: ((c% @ (cdrop @ V3)) @ V1))) @ V2)))))))))
(THOMOTOPIC_LOOPS_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chomotopic_loops @ V1) @ V2) @ V0)) @ (((chomotopic_loops @ V1) @ V0) @ V3))) @ (((chomotopic_loops @ V1) @ V2) @ V3)))))))))))
(THOMOTOPIC_LOOPS_IMP_SUBSET_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chomotopic_loops @ V2) @ V1) @ V0)) @ ((cSUBSET @ (cpath_image @ V1)) @ V2)))))))))
(THOMOTOPIC_LOOPS_IMP_SUBSET_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chomotopic_loops @ V2) @ V0) @ V1)) @ ((cSUBSET @ (cpath_image @ V1)) @ V2)))))))))
(THOMOTOPIC_PATHS_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chomotopic_paths @ V1) @ V2) @ V0)) @ (((chomotopic_paths @ V1) @ V0) @ V3))) @ (((chomotopic_paths @ V1) @ V2) @ V3)))))))))))
(THOMOTOPIC_PATHS_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((chomotopic_paths @ V1) @ V0) @ V0)) @ ((c/__caret__ @ (cpath @ V0)) @ ((cSUBSET @ (cpath_image @ V0)) @ V1))))))))
(THOMOTOPIC_PATHS_IMP_SUBSET_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chomotopic_paths @ V2) @ V1) @ V0)) @ ((cSUBSET @ (cpath_image @ V1)) @ V2)))))))))
(THOMOTOPIC_PATHS_IMP_SUBSET_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chomotopic_paths @ V2) @ V0) @ V1)) @ ((cSUBSET @ (cpath_image @ V1)) @ V2)))))))))
(TSUBPATH_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((csubpath @ V1) @ V1) @ V0)) @ (clinepath @ ((c__comma__ @ (V0 @ V1)) @ (V0 @ V1)))))))))
(TSIMPLE_PATH_SUBPATH_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (csimple_path @ (((csubpath @ V2) @ V1) @ V0))) @ ((c/__caret__ @ (cpath @ (((csubpath @ V2) @ V1) @ V0))) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V1))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V2) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V2) @ V1)) @ cNIL)))) @ ((c= @ (V0 @ V3)) @ (V0 @ V4))))) @ ((c__caret__/ @ ((c= @ V3) @ V4)) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V3) @ V2)) @ ((c= @ V4) @ V1))) @ ((c/__caret__ @ ((c= @ V3) @ V1)) @ ((c= @ V4) @ V2)))))))))))))))))))
(TSUBPATH_REVERSEPATH,(c! @ (^[V0]: ((c= @ (((csubpath @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ (creversepath @ V0)))))
(TENDPOINTS_SHIFTPATH_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V0))) @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((c= @ (cpathstart @ ((cshiftpath @ V1) @ V0))) @ (V0 @ V1))))))))
(TENDPOINTS_SHIFTPATH_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V0))) @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((c= @ (cpathfinish @ ((cshiftpath @ V1) @ V0))) @ (V0 @ V1))))))))
(TPATHFINISH_SHIFTPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ V1))) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V0)))) @ ((c= @ (cpathfinish @ ((cshiftpath @ V1) @ V0))) @ (V0 @ V1))))))))
(TPATHSTART_SHIFTPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_le @ (cdrop @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cpathstart @ ((cshiftpath @ V1) @ V0))) @ (V0 @ V1))))))))
(TPATH_IMAGE_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V0))) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1)))) @ ((c= @ (cpath_image @ ((c++ @ V1) @ V0))) @ (cpath_image @ ((c++ @ V0) @ V1)))))))))
(TSIMPLE_PATH_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V0))) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1)))) @ ((c= @ (csimple_path @ ((c++ @ V1) @ V0))) @ (csimple_path @ ((c++ @ V0) @ V1)))))))))
(TPATH_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V0))) @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1)))) @ ((c= @ (cpath @ ((c++ @ V1) @ V0))) @ (cpath @ ((c++ @ V0) @ V1)))))))))
(TREVERSEPATH_JOINPATHS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V0))) @ ((c= @ (creversepath @ ((c++ @ V1) @ V0))) @ ((c++ @ (creversepath @ V0)) @ (creversepath @ V1)))))))))
(TSIMPLE_PATH_REVERSEPATH,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ (csimple_path @ (creversepath @ V0))))))
(TARC_REVERSEPATH,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (carc @ (creversepath @ V0))))))
(TPATH_IMAGE_JOIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))) @ ((c= @ (cpath_image @ ((c++ @ V0) @ V1))) @ ((cUNION @ (cpath_image @ V0)) @ (cpath_image @ V1)))))))))
(TPATHFINISH_JOIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpathfinish @ ((c++ @ V0) @ V1))) @ (cpathfinish @ V1)))))))
(TPATHSTART_JOIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpathstart @ ((c++ @ V1) @ V0))) @ (cpathstart @ V1)))))))
(TPATHFINISH_REVERSEPATH,(c! @ (^[V0]: ((c= @ (cpathfinish @ (creversepath @ V0))) @ (cpathstart @ V0)))))
(TPATHSTART_REVERSEPATH,(c! @ (^[V0]: ((c= @ (cpathstart @ (creversepath @ V0))) @ (cpathfinish @ V0)))))
(TJOINPATHS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (cpathfinish @ V0)) @ (cpathstart @ V1))) @ ((c= @ ((c++ @ V0) @ V1)) @ (^[V2]: (((cCOND @ ((creal_lt @ (cdrop @ V2)) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (V0 @ ((c% @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2))) @ (V1 @ ((cvector_sub @ ((c% @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2)) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))
(TINFINITE_ARC_IMAGE,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (cINFINITE @ (cpath_image @ V0))))))
(TCARD_EQ_ARC_IMAGE,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ ((c=_c @ (cpath_image @ V0)) @ cUNIV)))))
(TINFINITE_SIMPLE_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ (cINFINITE @ (cpath_image @ V0))))))
(TCARD_EQ_SIMPLE_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ ((c=_c @ (cpath_image @ V0)) @ cUNIV)))))
(TCLOSED_ARC_IMAGE,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (cclosed @ (cpath_image @ V0))))))
(TBOUNDED_ARC_IMAGE,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (cbounded @ (cpath_image @ V0))))))
(TCOMPACT_ARC_IMAGE,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (ccompact @ (cpath_image @ V0))))))
(TCONNECTED_ARC_IMAGE,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (cconnected @ (cpath_image @ V0))))))
(TCLOSED_SIMPLE_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ (cclosed @ (cpath_image @ V0))))))
(TBOUNDED_SIMPLE_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ (cbounded @ (cpath_image @ V0))))))
(TCOMPACT_SIMPLE_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ (ccompact @ (cpath_image @ V0))))))
(TCONNECTED_SIMPLE_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ (cconnected @ (cpath_image @ V0))))))
(TCLOSED_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (cpath @ V0)) @ (cclosed @ (cpath_image @ V0))))))
(TBOUNDED_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (cpath @ V0)) @ (cbounded @ (cpath_image @ V0))))))
(TCOMPACT_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (cpath @ V0)) @ (ccompact @ (cpath_image @ V0))))))
(TCONNECTED_PATH_IMAGE,(c! @ (^[V0]: ((c==> @ (cpath @ V0)) @ (cconnected @ (cpath_image @ V0))))))
(TPATHFINISH_IN_PATH_IMAGE,(c! @ (^[V0]: ((cIN @ (cpathfinish @ V0)) @ (cpath_image @ V0)))))
(TPATHSTART_IN_PATH_IMAGE,(c! @ (^[V0]: ((cIN @ (cpathstart @ V0)) @ (cpath_image @ V0)))))
(TPATH_IMAGE_NONEMPTY,(c! @ (^[V0]: (c~ @ ((c= @ (cpath_image @ V0)) @ cEMPTY)))))
(TSIMPLE_PATH_EQ_ARC,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cpathstart @ V0)) @ (cpathfinish @ V0)))) @ ((c= @ (csimple_path @ V0)) @ (carc @ V0))))))
(TSIMPLE_PATH_IMP_PATH,(c! @ (^[V0]: ((c==> @ (csimple_path @ V0)) @ (cpath @ V0)))))
(TARC_IMP_PATH,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (cpath @ V0)))))
(TARC_IMP_SIMPLE_PATH,(c! @ (^[V0]: ((c==> @ (carc @ V0)) @ (csimple_path @ V0)))))
(TPATH_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V0 @ V2)) @ (V1 @ V2)))))) @ (cpath @ V0))) @ (cpath @ V1)))))))
(TCONTINUOUS_ON_LIFT_SQRT,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ V1)))))) @ ((ccontinuous_on @ ((co @ clift) @ ((co @ csqrt) @ cdrop))) @ V0)))))
(TSUP_CLOSURE,(c! @ (^[V0]: ((c= @ (csup @ ((cIMAGE @ cdrop) @ (cclosure @ V0)))) @ (csup @ ((cIMAGE @ cdrop) @ V0))))))
(TINF_CLOSURE,(c! @ (^[V0]: ((c= @ (cinf @ ((cIMAGE @ cdrop) @ (cclosure @ V0)))) @ (cinf @ ((cIMAGE @ cdrop) @ V0))))))
(TIMAGE_LIFT_DROP_conjunct0,(c! @ (^[V0]: ((c= @ ((cIMAGE @ ((co @ clift) @ cdrop)) @ V0)) @ V0))))
(TCONNECTED_COMPACT_INTERVAL_1,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ (cconnected @ V0)) @ (ccompact @ V0))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TIS_INTERVAL_1_CASES,(c! @ (^[V0]: ((c= @ (cis_interval @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V0) @ cUNIV)) @ ((c__caret__/ @ (c? @ (^[V1]: ((c= @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_lt @ V1) @ (cdrop @ V3))) @ V3))))))))) @ ((c__caret__/ @ (c? @ (^[V1]: ((c= @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_le @ V1) @ (cdrop @ V3))) @ V3))))))))) @ ((c__caret__/ @ (c? @ (^[V1]: ((c= @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_le @ (cdrop @ V3)) @ V1)) @ V3))))))))) @ ((c__caret__/ @ (c? @ (^[V1]: ((c= @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_lt @ (cdrop @ V3)) @ V1)) @ V3))))))))) @ ((c__caret__/ @ (c? @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((creal_lt @ V1) @ (cdrop @ V4))) @ ((creal_lt @ (cdrop @ V4)) @ V2))) @ V4))))))))))) @ ((c__caret__/ @ (c? @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((creal_lt @ V1) @ (cdrop @ V4))) @ ((creal_le @ (cdrop @ V4)) @ V2))) @ V4))))))))))) @ ((c__caret__/ @ (c? @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((creal_le @ V1) @ (cdrop @ V4))) @ ((creal_lt @ (cdrop @ V4)) @ V2))) @ V4))))))))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((creal_le @ V1) @ (cdrop @ V4))) @ ((creal_le @ (cdrop @ V4)) @ V2))) @ V4)))))))))))))))))))))))
(TIS_INTERVAL_SIMPLY_CONNECTED_1,(c! @ (^[V0]: ((c= @ (cis_interval @ V0)) @ (csimply_connected @ V0)))))
(TIS_INTERVAL_PATH_CONNECTED_1,(c! @ (^[V0]: ((c= @ (cis_interval @ V0)) @ (cpath_connected @ V0)))))
(TIS_INTERVAL_CONVEX_1,(c! @ (^[V0]: ((c= @ (cis_interval @ V0)) @ (cconvex @ V0)))))
(TIS_INTERVAL_CONTRACTIBLE_1,(c! @ (^[V0]: ((c= @ (cis_interval @ V0)) @ (ccontractible @ V0)))))
(TIS_INTERVAL_CONNECTED_1,(c! @ (^[V0]: ((c= @ (cis_interval @ V0)) @ (cconnected @ V0)))))
(TIS_INTERVAL_1,(c! @ (^[V0]: ((c= @ (cis_interval @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((creal_le @ (cdrop @ V1)) @ (cdrop @ V3))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V2)))))) @ ((cIN @ V3) @ V0))))))))))))
(TCONVEX_CONNECTED_1,(c! @ (^[V0]: ((c= @ (cconvex @ V0)) @ (cconnected @ V0)))))
(TCONNECTED_CONVEX_1,(c! @ (^[V0]: ((c= @ (cconnected @ V0)) @ (cconvex @ V0)))))
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(TFORALL_LIFT,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (V0 @ (clift @ V1))))))))
(TFORALL_REAL_ONE,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (V0 @ (clambda @ (^[V2]: V1)))))))))
(TCOLLINEAR_1,(c! @ (^[V0]: (ccollinear @ V0))))
(TCONTINUOUS_INJECTIVE_IFF_MONOTONIC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (cis_interval @ V0))) @ ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))) @ ((c__caret__/ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((creal_lt @ (cdrop @ V2)) @ (cdrop @ V3))))) @ ((creal_lt @ (cdrop @ (V1 @ V2))) @ (cdrop @ (V1 @ V3))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((creal_lt @ (cdrop @ V2)) @ (cdrop @ V3))))) @ ((creal_lt @ (cdrop @ (V1 @ V3))) @ (cdrop @ (V1 @ V2))))))))))))))))
(TINJECTIVE_EQ_1D_OPEN_MAP_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (cis_interval @ V0))) @ ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (copen @ V2)) @ ((cSUBSET @ V2) @ V0))) @ (copen @ ((cIMAGE @ V1) @ V2))))))))))))
(TVECTOR_VARIATION_POS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_variation_on @ V1) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cvector_variation @ V0) @ V1))))))))
(THAS_BOUNDED_VARIATION_ON_IMP_BOUNDED_ON_SUBINTERVALS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_variation_on @ V1) @ V0)) @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V3)) @ cNIL))) @ V0)) @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V3)) @ cNIL))) @ cEMPTY)))) @ ((cvector_sub @ (V1 @ V3)) @ (V1 @ V4))))))))))))))))
(TVECTOR_VARIATION_CONST_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cis_interval @ V0)) @ ((chas_bounded_variation_on @ V1) @ V0))) @ ((c= @ ((c= @ ((cvector_variation @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2)))))))))))))
(TPATH_LENGTH_DIFFERENTIABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ (crectifiable_path @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ ((cDIFF @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V0))) @ ((cdifferentiable @ V1) @ (cat @ V2)))))))) @ ((c= @ (cpath_length @ V1)) @ (cdrop @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ (^[V2]: (clift @ (cvector_norm @ ((cvector_derivative @ V1) @ (cat @ V2))))))))))))))
(TRECTIFIABLE_PATH_DIFFERENTIABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ (cpath @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ ((cDIFF @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V0))) @ ((cdifferentiable @ V1) @ (cat @ V2)))))))) @ ((c= @ (crectifiable_path @ V1)) @ ((cabsolutely_integrable_on @ (^[V2]: ((cvector_derivative @ V1) @ (cat @ V2)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))))))))
(TVECTOR_VARIATION_REFLECT2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_variation @ ((cIMAGE @ cvector_neg) @ V0)) @ (^[V2]: (V1 @ (cvector_neg @ V2))))) @ ((cvector_variation @ V0) @ V1)))))))
(TVECTOR_VARIATION_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_variation @ V0) @ (^[V2]: (cvector_neg @ (V1 @ V2))))) @ ((cvector_variation @ V0) @ V1)))))))
(TVECTOR_VARIATION_REFLECT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_variation @ V0) @ (^[V2]: (V1 @ (cvector_neg @ V2))))) @ ((cvector_variation @ ((cIMAGE @ cvector_neg) @ V0)) @ V1)))))))
(Tvector_variation,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_variation @ V0) @ V1)) @ ((cset_variation @ V0) @ (^[V2]: ((cvector_sub @ (V1 @ (cinterval_upperbound @ V2))) @ (V1 @ (cinterval_lowerbound @ V2)))))))))))
(TMEASURABLE_ON_VECTOR_DERIVATIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnegligible @ V0)) @ ((c/__caret__ @ (cnegligible @ (cfrontier @ V3))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ V3) @ V0))) @ (((chas_vector_derivative @ V1) @ (V2 @ V4)) @ (cat @ V4)))))))) @ ((cmeasurable_on @ V2) @ V3)))))))))))
(TFUNDAMENTAL_THEOREM_OF_CALCULUS_INTERIOR_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ ((cDIFF @ (copen_interval @ ((c__comma__ @ V3) @ V4))) @ V0))) @ (((chas_vector_derivative @ V2) @ (V1 @ V5)) @ (cat @ V5))))))))) @ (((chas_integral @ V1) @ ((cvector_sub @ (V2 @ V4)) @ (V2 @ V3))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))
(TFUNDAMENTAL_THEOREM_OF_CALCULUS_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ ((cDIFF @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ V0))) @ (((chas_vector_derivative @ V2) @ (V1 @ V5)) @ ((cwithin @ (cat @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))) @ (((chas_integral @ V1) @ ((cvector_sub @ (V2 @ V4)) @ (V2 @ V3))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))
(THAS_BOUNDED_VARIATION_ON_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V1) @ V0)) @ ((cSUBSET @ V2) @ V0))) @ ((chas_bounded_variation_on @ V1) @ V2)))))))))
(THAS_BOUNDED_VARIATION_INTEGRABLE_NORM_DERIVATIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V0))) @ ((cdifferentiable @ V1) @ (cat @ V4)))))))) @ ((c= @ ((chas_bounded_variation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((cintegrable_on @ (^[V4]: (clift @ (cvector_norm @ ((cvector_derivative @ V1) @ (cat @ V4)))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))
(THAS_BOUNDED_VARIATION_ABSOLUTELY_INTEGRABLE_DERIVATIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V0))) @ ((cdifferentiable @ V1) @ (cat @ V4)))))))) @ ((c= @ ((chas_bounded_variation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((cabsolutely_integrable_on @ (^[V4]: ((cvector_derivative @ V1) @ (cat @ V4)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))
(TVECTOR_VARIATION_ON_NULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (ccontent @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (cbounded @ V0))) @ ((c= @ ((cvector_variation @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(THAS_VECTOR_DERIVATIVE_TRANSFORM_WITHIN_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))) @ (((chas_vector_derivative @ V1) @ V3) @ (cat @ V4)))))) @ (((chas_vector_derivative @ V2) @ V3) @ (cat @ V4))))))))))))))
(THAS_VECTOR_DERIVATIVE_WITHIN_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_vector_derivative @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ V0))) @ ((cSUBSET @ V4) @ V0))) @ (((chas_vector_derivative @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ V4))))))))))))))
(TSUBSET_DROP_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cSUBSET @ ((cIMAGE @ cdrop) @ V0)) @ ((cIMAGE @ cdrop) @ V1))) @ ((cSUBSET @ V0) @ V1)))))))
(TVECTOR_VARIATION_MONOTONE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V2) @ V1)) @ ((cSUBSET @ V0) @ V1))) @ ((creal_le @ ((cvector_variation @ V0) @ V2)) @ ((cvector_variation @ V1) @ V2))))))))))
(TVECTOR_VARIATION_INTEGRAL_NORM_DERIVATIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V0))) @ ((cdifferentiable @ V3) @ (cat @ V4)))))) @ ((chas_bounded_variation_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))) @ ((c= @ ((cvector_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V3)) @ (cdrop @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ (^[V4]: (clift @ (cvector_norm @ ((cvector_derivative @ V3) @ (cat @ V4))))))))))))))))))
(THAS_DERIVATIVE_ZERO_UNIQUE_STRONG_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((c= @ (V3 @ V1)) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ ((cDIFF @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V0))) @ (((chas_derivative @ V3) @ (^[V7]: (cvec @ (cNUMERAL @ c_0)))) @ ((cwithin @ (cat @ V6)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))) @ ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c= @ (V3 @ V4)) @ V5))))))))))))))))
(TVECTOR_VARIATION_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_variation @ V0) @ (^[V2]: V1))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TSUBPATH_TRIVIAL,(c! @ (^[V0]: ((c= @ (((csubpath @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ V0))))
(Tsubpath,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((csubpath @ V2) @ V1) @ V0)) @ (^[V3]: (V0 @ ((cvector_add @ V2) @ ((c% @ (cdrop @ ((cvector_sub @ V1) @ V2))) @ V3))))))))))))
(TPATH_COMPOSE_JOIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((co @ V1) @ ((c++ @ V0) @ V2))) @ ((c++ @ ((co @ V1) @ V0)) @ ((co @ V1) @ V2))))))))))
(Tjoinpaths,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c++ @ V0) @ V1)) @ (^[V2]: (((cCOND @ ((creal_le @ (cdrop @ V2)) @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (V0 @ ((c% @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2))) @ (V1 @ ((cvector_sub @ ((c% @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2)) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(THAS_DERIVATIVE_BILINEAR_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((chas_derivative @ V0) @ V3) @ (cat @ V5))) @ ((c/__caret__ @ (((chas_derivative @ V4) @ V1) @ (cat @ V5))) @ (cbilinear @ V2)))) @ (((chas_derivative @ (^[V6]: ((V2 @ (V0 @ V6)) @ (V4 @ V6)))) @ (^[V6]: ((cvector_add @ ((V2 @ (V0 @ V5)) @ (V1 @ V6))) @ ((V2 @ (V3 @ V6)) @ (V4 @ V5))))) @ (cat @ V5))))))))))))))))
(THAS_DERIVATIVE_BILINEAR_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (((chas_derivative @ V0) @ V3) @ ((cwithin @ (cat @ V5)) @ V6))) @ ((c/__caret__ @ (((chas_derivative @ V4) @ V1) @ ((cwithin @ (cat @ V5)) @ V6))) @ (cbilinear @ V2)))) @ (((chas_derivative @ (^[V7]: ((V2 @ (V0 @ V7)) @ (V4 @ V7)))) @ (^[V7]: ((cvector_add @ ((V2 @ (V0 @ V5)) @ (V1 @ V7))) @ ((V2 @ (V3 @ V7)) @ (V4 @ V5))))) @ ((cwithin @ (cat @ V5)) @ V6))))))))))))))))))
(TCOVERING_SPACE_LIFT_HOMOTOPIC_FUNCTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V3) @ V5)) @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V0) @ V4)) @ V3)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V4)) @ ((c= @ (V5 @ (V0 @ V7))) @ (V2 @ V7)))))) @ ((((chomotopic_with @ (^[V7]: cT)) @ ((c__comma__ @ V4) @ V1)) @ V2) @ V6)))))) @ (c? @ (^[V7]: ((c/__caret__ @ ((ccontinuous_on @ V7) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V7) @ V4)) @ V3)) @ (c! @ (^[V8]: ((c==> @ ((cIN @ V8) @ V4)) @ ((c= @ (V5 @ (V7 @ V8))) @ (V6 @ V8)))))))))))))))))))))))))
(TPROPER_MAP_FROM_COMPOSITION_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V3)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V2)) @ V0)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V6) @ V0)) @ (ccompact @ V6))) @ (ccompact @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V3)) @ ((cIN @ (((co @ V1) @ V4) @ V8)) @ V6))) @ V8)))))))))))))) @ ((c==> @ ((c/__caret__ @ ((cSUBSET @ V5) @ V2)) @ (ccompact @ V5))) @ (ccompact @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V3)) @ ((cIN @ (V4 @ V7)) @ V5))) @ V7)))))))))))))))))))))
(THOMEOMORPHISM_FROM_COMPOSITION_INJECTIVE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V2)) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V3)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V3)) @ ((c/__caret__ @ ((cIN @ V6) @ V3)) @ ((c= @ (V1 @ V5)) @ (V1 @ V6))))) @ ((c= @ V5) @ V6))))))) @ (c? @ (^[V5]: ((chomeomorphism @ ((c__comma__ @ V2) @ V0)) @ ((c__comma__ @ ((co @ V1) @ V4)) @ V5)))))))))) @ (c? @ (^[V5]: ((chomeomorphism @ ((c__comma__ @ V2) @ V3)) @ ((c__comma__ @ V4) @ V5))))))))))))))))
(THOMEOMORPHISM_FROM_COMPOSITION_SURJECTIVE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V2)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V4) @ V2)) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V3)) @ V0)) @ (c? @ (^[V5]: ((chomeomorphism @ ((c__comma__ @ V2) @ V0)) @ ((c__comma__ @ ((co @ V1) @ V4)) @ V5))))))))) @ (c? @ (^[V5]: ((chomeomorphism @ ((c__comma__ @ V2) @ V3)) @ ((c__comma__ @ V4) @ V5))))))))))))))))
(TOPEN_MAP_FROM_COMPOSITION_INJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V2)) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V3)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V3)) @ ((c/__caret__ @ (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V3)) @ ((c/__caret__ @ ((cIN @ V7) @ V3)) @ ((c= @ (V1 @ V6)) @ (V1 @ V7))))) @ ((c= @ V6) @ V7))))))) @ (c! @ (^[V6]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V6)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ ((co @ V1) @ V4)) @ V6)))))))))) @ ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V5)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V3)) @ ((cIMAGE @ V4) @ V5)))))))))))))))))
(TCLOSED_MAP_FROM_COMPOSITION_INJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V2)) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V3)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V3)) @ ((c/__caret__ @ (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V3)) @ ((c/__caret__ @ ((cIN @ V7) @ V3)) @ ((c= @ (V1 @ V6)) @ (V1 @ V7))))) @ ((c= @ V6) @ V7))))))) @ (c! @ (^[V6]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V6)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ ((co @ V1) @ V4)) @ V6)))))))))) @ ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V5)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V3)) @ ((cIMAGE @ V4) @ V5)))))))))))))))))
(TCONTINUOUS_ON_COMPOSE_QUOTIENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V2)) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V4)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cSUBSET @ V5) @ V4)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V2)) @ ((cIN @ (V1 @ V7)) @ V5))) @ V7))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V4)) @ V5)))))) @ ((ccontinuous_on @ ((co @ V3) @ V1)) @ V2))))) @ ((ccontinuous_on @ V3) @ V4)))))))))))))
(TINTEGRABLE_MIN_CONST_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V0 @ V3)))))) @ ((cintegrable_on @ (^[V3]: (clift @ (V0 @ V3)))) @ V2)))) @ ((cintegrable_on @ (^[V3]: (clift @ ((creal_min @ (V0 @ V3)) @ V1)))) @ V2)))))))))
(TCONTINUOUS_ON_LIFT_POW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous_on @ (^[V3]: (clift @ (V0 @ V3)))) @ V2)) @ ((ccontinuous_on @ (^[V3]: (clift @ ((creal_pow @ (V0 @ V3)) @ V1)))) @ V2)))))))))
(TCONTINUOUS_MIDPOINT_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ ((co @ clift) @ V0)) @ V1)) @ ((c/__caret__ @ (cconvex @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((cIN @ V3) @ V1))) @ ((creal_le @ (V0 @ (cmidpoint @ ((c__comma__ @ V2) @ V3)))) @ ((creal_div @ ((creal_add @ (V0 @ V2)) @ (V0 @ V3))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))) @ ((cconvex_on @ V0) @ V1)))))))
(TCONTINUOUS_ON_LIFT_SQRT_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ ((co @ clift) @ V0)) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V0 @ V2))))))) @ ((ccontinuous_on @ (^[V2]: (clift @ (csqrt @ (V0 @ V2))))) @ V1)))))))
(TCONVEX_ON_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V1)) @ ((cconvex_on @ V0) @ V1))) @ ((ccontinuous_on @ ((co @ clift) @ V0)) @ V1)))))))
(TSPAN_IMAGE_SCALE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c~ @ ((c= @ (V0 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ ((c= @ (cspan @ ((cIMAGE @ (^[V2]: ((c% @ (V0 @ V2)) @ V2))) @ V1))) @ (cspan @ V1))))))))
(TCONVEX_ON_DERIVATIVES_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V0) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V5) @ V4)) @ cNIL))) @ V1)) @ ((c/__caret__ @ (((chas_derivative @ ((co @ clift) @ V0)) @ ((co @ clift) @ V2)) @ ((cwithin @ (cat @ V5)) @ V1))) @ (((chas_derivative @ ((co @ clift) @ V0)) @ ((co @ clift) @ V3)) @ ((cwithin @ (cat @ V4)) @ V1)))))) @ ((creal_le @ (V2 @ ((cvector_sub @ V4) @ V5))) @ (V3 @ ((cvector_sub @ V4) @ V5)))))))))))))))))
(TCONVEX_ON_DERIVATIVES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (((chas_derivative @ ((co @ clift) @ V0)) @ ((co @ clift) @ (V2 @ V3))) @ ((cwithin @ (cat @ V3)) @ V1))))))) @ ((c= @ ((cconvex_on @ V0) @ V1)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((cIN @ V4) @ V1))) @ ((creal_le @ ((V2 @ V3) @ ((cvector_sub @ V4) @ V3))) @ ((V2 @ V4) @ ((cvector_sub @ V4) @ V3)))))))))))))))))
(TCONVEX_ON_COMPOSE_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V0) @ ((cIMAGE @ V1) @ V2))) @ (clinear @ V1))) @ ((cconvex_on @ ((co @ V0) @ V1)) @ V2)))))))))
(TCONTINUOUS_AT_SQRT_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ (^[V2]: (clift @ (V0 @ V2)))) @ (cat @ V1))) @ ((c__caret__/ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V0 @ V1))) @ (c! @ (^[V2]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V0 @ V2))))))) @ ((ccontinuous @ (^[V2]: (clift @ (csqrt @ (V0 @ V2))))) @ (cat @ V1))))))))
(TCONTINUOUS_WITHIN_SQRT_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ (^[V3]: (clift @ (V0 @ V3)))) @ ((cwithin @ (cat @ V1)) @ V2))) @ ((c__caret__/ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V0 @ V1))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V0 @ V3)))))))) @ ((ccontinuous @ (^[V3]: (clift @ (csqrt @ (V0 @ V3))))) @ ((cwithin @ (cat @ V1)) @ V2))))))))))
(TCONTINUOUS_AT_WITHIN_INV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ ((co @ clift) @ V0)) @ ((cwithin @ (cat @ V1)) @ V2))) @ (c~ @ ((c= @ (V0 @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((ccontinuous @ ((co @ clift) @ ((co @ creal_inv) @ V0))) @ ((cwithin @ (cat @ V1)) @ V2))))))))))
(TCONVEX_ON_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cconvex_on @ V0) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V1) @ V3))) @ V2))) @ ((cconvex_on @ (^[V3]: (V0 @ ((cvector_add @ V1) @ V3)))) @ V2)))))))))
(TAFFINE_HULL_FINITE_STEP_GEN_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((V0 @ V4) @ V5))) @ ((V0 @ V4) @ ((creal_div @ V5) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((c/__caret__ @ ((V0 @ V4) @ V5)) @ ((V0 @ V4) @ V6)))) @ ((V0 @ V4) @ ((creal_add @ V5) @ V6)))))))))) @ ((c= @ (c? @ (^[V5]: ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ ((cINSERT @ V4) @ V2))) @ ((V0 @ V6) @ (V5 @ V6)))))) @ ((c/__caret__ @ ((c= @ ((csum @ ((cINSERT @ V4) @ V2)) @ V5)) @ V1)) @ ((c= @ ((cvsum @ ((cINSERT @ V4) @ V2)) @ (^[V6]: ((c% @ (V5 @ V6)) @ V6)))) @ V3)))))) @ (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((V0 @ V4) @ V5)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V2)) @ ((V0 @ V7) @ (V6 @ V7)))))) @ ((c/__caret__ @ ((c= @ ((csum @ V2) @ V6)) @ ((creal_sub @ V1) @ V5))) @ ((c= @ ((cvsum @ V2) @ (^[V7]: ((c% @ (V6 @ V7)) @ V7)))) @ ((cvector_sub @ V3) @ ((c% @ V5) @ V4)))))))))))))))))))))))
(TAFFINE_HULL_FINITE_STEP_GEN_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ cEMPTY)) @ ((V0 @ V4) @ (V3 @ V4)))))) @ ((c/__caret__ @ ((c= @ ((csum @ cEMPTY) @ V3)) @ V1)) @ ((c= @ ((cvsum @ cEMPTY) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))))) @ ((c/__caret__ @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))))))))))
(TBILINEAR_UNIFORMLY_CONTINUOUS_ON_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cuniformly_continuous_on @ V1) @ V3)) @ ((c/__caret__ @ ((cuniformly_continuous_on @ V2) @ V3)) @ ((c/__caret__ @ (cbilinear @ V0)) @ ((c/__caret__ @ (cbounded @ ((cIMAGE @ V1) @ V3))) @ (cbounded @ ((cIMAGE @ V2) @ V3))))))) @ ((cuniformly_continuous_on @ (^[V4]: ((V0 @ (V1 @ V4)) @ (V2 @ V4)))) @ V3)))))))))))
(TMEASURABLE_ON_COMBINE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V3)) @ ((c/__caret__ @ ((cmeasurable_on @ V2) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ (^[V4]: ((V0 @ (cfstcart @ V4)) @ (csndcart @ V4)))) @ cUNIV)) @ ((c= @ ((V0 @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((cmeasurable_on @ (^[V4]: ((V0 @ (V1 @ V4)) @ (V2 @ V4)))) @ V3)))))))))))
(TBILINEAR_DIFFERENTIABLE_ON_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdifferentiable_on @ V1) @ V3)) @ ((c/__caret__ @ ((cdifferentiable_on @ V2) @ V3)) @ (cbilinear @ V0)))) @ ((cdifferentiable_on @ (^[V4]: ((V0 @ (V1 @ V4)) @ (V2 @ V4)))) @ V3)))))))))))
(TBILINEAR_DIFFERENTIABLE_AT_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ V1) @ (cat @ V3))) @ ((c/__caret__ @ ((cdifferentiable @ V2) @ (cat @ V3))) @ (cbilinear @ V0)))) @ ((cdifferentiable @ (^[V4]: ((V0 @ (V1 @ V4)) @ (V2 @ V4)))) @ (cat @ V3))))))))))))
(TBILINEAR_DIFFERENTIABLE_WITHIN_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ V1) @ ((cwithin @ (cat @ V3)) @ V4))) @ ((c/__caret__ @ ((cdifferentiable @ V2) @ ((cwithin @ (cat @ V3)) @ V4))) @ (cbilinear @ V0)))) @ ((cdifferentiable @ (^[V5]: ((V0 @ (V1 @ V5)) @ (V2 @ V5)))) @ ((cwithin @ (cat @ V3)) @ V4))))))))))))))
(THAS_DERIVATIVE_INVERSE_ON,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (copen @ V1)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V1)) @ ((c/__caret__ @ (((chas_derivative @ V4) @ (V0 @ V6)) @ (cat @ V6))) @ ((c/__caret__ @ ((c= @ (V2 @ (V4 @ V6))) @ V6)) @ ((c= @ ((co @ (V0 @ V6)) @ (V3 @ V6))) @ cI)))))))) @ ((c==> @ ((cIN @ V5) @ V1)) @ (((chas_derivative @ V2) @ (V3 @ V5)) @ (cat @ (V4 @ V5))))))))))))))))))
(TGAUGE_MODIFY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (copen @ V2)) @ (copen @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ (V1 @ V4)) @ V2)) @ V4)))))))))) @ ((c==> @ (cgauge @ V0)) @ (cgauge @ (^[V2]: (^[V3]: ((V0 @ (V1 @ V2)) @ (V1 @ V3))))))))))))
(TCOVERING_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V1)) @ cNIL)))) @ ((c/__caret__ @ (c~ @ ((c= @ (copen_interval @ ((c__comma__ @ V2) @ V1))) @ cEMPTY))) @ (cgauge @ V0)))) @ (c? @ (^[V4]: ((c/__caret__ @ (cCOUNTABLE @ V4)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V1)) @ cNIL)))) @ ((c/__caret__ @ (c~ @ ((c= @ (cinterior @ V5)) @ cEMPTY))) @ (c? @ (^[V6]: (c? @ (^[V7]: ((c= @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V7)) @ cNIL))))))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V4)) @ ((c/__caret__ @ ((cIN @ V6) @ V4)) @ (c~ @ ((c= @ V5) @ V6))))) @ ((c= @ ((cINTER @ (cinterior @ V5)) @ (cinterior @ V6))) @ cEMPTY))))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V4)) @ (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ ((cINTER @ V3) @ V5))) @ ((cSUBSET @ V5) @ (V0 @ V6))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((cIN @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL))) @ V4)) @ (c? @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V8)) @ ((c<= @ V8) @ (cdimindex @ cUNIV)))) @ ((c= @ ((creal_sub @ ((c$ @ V6) @ V8)) @ ((c$ @ V5) @ V8))) @ ((creal_div @ ((creal_sub @ ((c$ @ V1) @ V8)) @ ((c$ @ V2) @ V8))) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V7)))))))))))))) @ ((cSUBSET @ V3) @ (cUNIONS @ V4)))))))))))))))))))
(TABSOLUTELY_INTEGRABLE_SUP_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cabsolutely_integrable_on @ (^[V4]: (clift @ ((V0 @ V4) @ V3)))) @ V2))))))) @ ((cabsolutely_integrable_on @ (^[V3]: (clift @ (csup @ ((cIMAGE @ (V0 @ V3)) @ V1))))) @ V2)))))))))
(TABSOLUTELY_INTEGRABLE_INF_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cabsolutely_integrable_on @ (^[V4]: (clift @ ((V0 @ V4) @ V3)))) @ V2))))))) @ ((cabsolutely_integrable_on @ (^[V3]: (clift @ (cinf @ ((cIMAGE @ (V0 @ V3)) @ V1))))) @ V2)))))))))
(TLINEAR_TO_REALS,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ V0) @ (^[V1]: (clift @ ((cdot @ ((crow @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cmatrix @ V0))) @ V1))))))))
(THAS_INTEGRAL_STRADDLE_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ (V1 @ V3)))) @ ((creal_le @ (cdrop @ (V1 @ V3))) @ (cdrop @ (V0 @ V3)))))))) @ (((chas_integral @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ V2))) @ (((chas_integral @ V1) @ (cvec @ (cNUMERAL @ c_0))) @ V2)))))))))
(TINTEGRABLE_STRADDLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ (((chas_integral @ V3) @ V5) @ V1)) @ ((c/__caret__ @ (((chas_integral @ V4) @ V6) @ V1)) @ ((c/__caret__ @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V5) @ V6))) @ V2)) @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V1)) @ ((c/__caret__ @ ((creal_le @ (cdrop @ (V3 @ V7))) @ (cdrop @ (V0 @ V7)))) @ ((creal_le @ (cdrop @ (V0 @ V7))) @ (cdrop @ (V4 @ V7)))))))))))))))))))))) @ ((cintegrable_on @ V0) @ V1)))))))
(TINTEGRAL_DROP_LE_MEASURABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V0) @ V1)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ (V0 @ V3)))) @ ((creal_le @ (cdrop @ (V0 @ V3))) @ (cdrop @ (V2 @ V3)))))))))) @ ((creal_le @ (cdrop @ ((cintegral @ V1) @ V0))) @ (cdrop @ ((cintegral @ V1) @ V2)))))))))))
(TSUBSET_CONTINUOUS_IMAGE_SEGMENT_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous_on @ V0) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ (V0 @ V1)) @ (V0 @ V2))) @ cNIL))) @ ((cIMAGE @ V0) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))
(TINTEGRABLE_STRADDLE_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (c? @ (^[V7]: ((c/__caret__ @ (((chas_integral @ V4) @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ (((chas_integral @ V5) @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V6) @ V7))) @ V3)) @ (c! @ (^[V8]: ((c==> @ ((cIN @ V8) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((creal_le @ (cdrop @ (V4 @ V8))) @ (cdrop @ (V0 @ V8)))) @ ((creal_le @ (cdrop @ (V0 @ V8))) @ (cdrop @ (V5 @ V8)))))))))))))))))))))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(THAS_BOUNDED_SETVARIATION_ON_COMPOSE_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V1) @ V2)) @ (clinear @ V0))) @ ((chas_bounded_setvariation_on @ ((co @ V0) @ V1)) @ V2)))))))))
(TMEASURABLE_ON_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V1 @ V3)) @ (V1 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((cmeasurable_on @ ((co @ V0) @ V1)) @ V2)) @ ((cmeasurable_on @ V0) @ ((cIMAGE @ V1) @ V2)))))))))))
(TMEASURABLE_ON_COMPOSE_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ cUNIV)) @ ((ccontinuous_on @ V0) @ cUNIV))) @ ((cmeasurable_on @ ((co @ V0) @ V1)) @ cUNIV)))))))
(THAS_INTEGRAL_TWIDDLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c= @ (V4 @ (V1 @ V7))) @ V7)))) @ ((c/__caret__ @ (c! @ (^[V7]: ((c= @ (V1 @ (V4 @ V7))) @ V7)))) @ ((c/__caret__ @ (c! @ (^[V7]: ((ccontinuous @ V1) @ (cat @ V7))))) @ ((c/__caret__ @ (c! @ (^[V7]: (c! @ (^[V8]: (c? @ (^[V9]: (c? @ (^[V10]: ((c= @ ((cIMAGE @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V7) @ V8)) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V9) @ V10)) @ cNIL)))))))))))) @ ((c/__caret__ @ (c! @ (^[V7]: (c! @ (^[V8]: (c? @ (^[V9]: (c? @ (^[V10]: ((c= @ ((cIMAGE @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V7) @ V8)) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V9) @ V10)) @ cNIL)))))))))))) @ ((c/__caret__ @ (c! @ (^[V7]: (c! @ (^[V8]: ((c= @ (ccontent @ ((cIMAGE @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V7) @ V8)) @ cNIL))))) @ ((creal_mul @ V2) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V7) @ V8)) @ cNIL)))))))))) @ (((chas_integral @ V0) @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL))))))))))) @ (((chas_integral @ (^[V7]: (V0 @ (V1 @ V7)))) @ ((c% @ (creal_inv @ V2)) @ V3)) @ ((cIMAGE @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL))))))))))))))))))))
(TDIFF_CHAIN_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_derivative @ V1) @ V3) @ (cat @ V4))) @ (((chas_derivative @ V0) @ V2) @ (cat @ (V1 @ V4))))) @ (((chas_derivative @ ((co @ V0) @ V1)) @ ((co @ V2) @ V3)) @ (cat @ V4))))))))))))))
(TDIFF_CHAIN_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((chas_derivative @ V1) @ V3) @ ((cwithin @ (cat @ V4)) @ V5))) @ (((chas_derivative @ V0) @ V2) @ ((cwithin @ (cat @ (V1 @ V4))) @ ((cIMAGE @ V1) @ V5))))) @ (((chas_derivative @ ((co @ V0) @ V1)) @ ((co @ V2) @ V3)) @ ((cwithin @ (cat @ V4)) @ V5))))))))))))))))
(TPIECEWISE_DIFFERENTIABLE_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpiecewise_differentiable_on @ V1) @ V2)) @ ((c/__caret__ @ ((cpiecewise_differentiable_on @ V0) @ ((cIMAGE @ V1) @ V2))) @ (c! @ (^[V3]: (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c= @ (V1 @ V5)) @ V3))) @ V5))))))))))) @ ((cpiecewise_differentiable_on @ ((co @ V0) @ V1)) @ V2)))))))))
(TMEASURABLE_ON_COMPOSE_CONTINUOUS_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ cUNIV)) @ ((c= @ (V0 @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((cmeasurable_on @ ((co @ V0) @ V1)) @ V2)))))))))
(TLINEAR_CONTINUOUS_ON_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V2)) @ (clinear @ V0))) @ ((ccontinuous_on @ (^[V3]: (V0 @ (V1 @ V3)))) @ V2)))))))))
(TABSOLUTELY_INTEGRABLE_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cabsolutely_integrable_on @ V1) @ V2)) @ (clinear @ V0))) @ ((cabsolutely_integrable_on @ ((co @ V0) @ V1)) @ V2)))))))))
(TINTEGRAL_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (clinear @ V0))) @ ((c= @ ((cintegral @ V1) @ ((co @ V0) @ V2))) @ (V0 @ ((cintegral @ V1) @ V2)))))))))))
(TLINEAR_CONTINUOUS_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V1) @ V2)) @ (clinear @ V0))) @ ((ccontinuous @ (^[V3]: (V0 @ (V1 @ V3)))) @ V2)))))))))
(TBROUWER_CUBE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((cSUBSET @ ((cIMAGE @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V0 @ V1)) @ V1))))))))
(TSCHAUDER_UNIV,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ cUNIV)) @ (cbounded @ ((cIMAGE @ V0) @ cUNIV)))) @ (c? @ (^[V1]: ((c= @ (V0 @ V1)) @ V1)))))))
(TSELF_ADJOINT_HAS_EIGENVECTOR_BASIS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c= @ (cadjoint @ V0)) @ V0))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cpairwise @ corthogonal) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c? @ (^[V3]: ((c= @ (V0 @ V2)) @ ((c% @ V3) @ V2))))))))) @ ((c/__caret__ @ (cindependent @ V1)) @ ((c/__caret__ @ ((c= @ (cspan @ V1)) @ cUNIV)) @ ((cHAS_SIZE @ V1) @ (cdimindex @ cUNIV))))))))))))
(TSELF_ADJOINT_HAS_EIGENVECTOR,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c= @ (cadjoint @ V0)) @ V0))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c= @ (cvector_norm @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (V0 @ V1)) @ ((c% @ V2) @ V1)))))))))))
(TINTEGRAL_BASIS_UNIMODULAR,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c= @ ((cIMAGE @ V0) @ cintegral_vector)) @ cintegral_vector))) @ ((c= @ (creal_abs @ (cdet @ (cmatrix @ V0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TLINEAR_SINGULAR_IMAGE_HYPERPLANE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c~ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ (c! @ (^[V2]: ((cSUBSET @ ((cIMAGE @ V0) @ V2)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V1) @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V4)))))))))))))))
(TLINEAR_SURJECTIVE_ISOMORPHISM,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c= @ (V1 @ (V0 @ V2))) @ V2)))) @ (c! @ (^[V2]: ((c= @ (V0 @ (V1 @ V2))) @ V2)))))))))))
(TLINEAR_INJECTIVE_ISOMORPHISM,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c= @ (V1 @ (V0 @ V2))) @ V2)))) @ (c! @ (^[V2]: ((c= @ (V0 @ (V1 @ V2))) @ V2)))))))))))
(TISOMETRY_SPHERE_EXTEND,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((c= @ (cvector_norm @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cvector_norm @ (V0 @ V1))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c= @ (cvector_norm @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c= @ (cdistance @ ((c__comma__ @ (V0 @ V1)) @ (V0 @ V2)))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (corthogonal_transformation @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (V1 @ V2)) @ (V0 @ V2))))))))))))
(TORTHOGONAL_MATRIX_MATRIX,(c! @ (^[V0]: ((c==> @ (corthogonal_transformation @ V0)) @ (corthogonal_matrix @ (cmatrix @ V0))))))
(TORTHOGONAL_TRANSFORMATION_LINEAR,(c! @ (^[V0]: ((c==> @ (corthogonal_transformation @ V0)) @ (clinear @ V0)))))
(TORTHOGONAL_TRANSFORMATION_INVERSE_o,(c! @ (^[V0]: ((c==> @ (corthogonal_transformation @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (corthogonal_transformation @ V1)) @ ((c/__caret__ @ ((c= @ ((co @ V1) @ V0)) @ cI)) @ ((c= @ ((co @ V0) @ V1)) @ cI)))))))))
(TORTHOGONAL_TRANSFORMATION_INVERSE,(c! @ (^[V0]: ((c==> @ (corthogonal_transformation @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (corthogonal_transformation @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c= @ (V1 @ (V0 @ V2))) @ V2)))) @ (c! @ (^[V2]: ((c= @ (V0 @ (V1 @ V2))) @ V2)))))))))))
(TDET_MATRIX_EQ_0_LEFT,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ ((c= @ (cdet @ (cmatrix @ V0))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c~ @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c= @ ((co @ V1) @ V0)) @ cI))))))))))
(TDET_MATRIX_EQ_0_RIGHT,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ ((c= @ (cdet @ (cmatrix @ V0))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c~ @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c= @ ((co @ V0) @ V1)) @ cI))))))))))
(TDET_MATRIX_EQ_0,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ ((c= @ (cdet @ (cmatrix @ V0))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c~ @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ ((c= @ ((co @ V0) @ V1)) @ cI)) @ ((c= @ ((co @ V1) @ V0)) @ cI)))))))))))
(TLINEAR_SINGULAR_INTO_HYPERPLANE,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (c~ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ (c! @ (^[V2]: ((c= @ ((cdot @ V1) @ (V0 @ V2))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))
(TMATRIX_INVERTIBLE,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (cinvertible @ (cmatrix @ V0))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ ((c= @ ((co @ V0) @ V1)) @ cI)) @ ((c= @ ((co @ V1) @ V0)) @ cI))))))))))
(TADJOINT_INJECTIVE_INJECTIVE_0,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (c! @ (^[V1]: ((c==> @ ((c= @ ((cadjoint @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))))) @ (c! @ (^[V1]: ((c==> @ ((c= @ (V0 @ V1)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0)))))))))))
(TLINEAR_INTEGRAL_VECTOR,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (c! @ (^[V1]: ((c==> @ (cintegral_vector @ V1)) @ (cintegral_vector @ (V0 @ V1)))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))))) @ (cinteger @ ((c$ @ ((c$ @ (cmatrix @ V0)) @ V1)) @ V2))))))))))))
(TLINEAR_SURJECTIVE_IFF_INJECTIVE,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))))))
(TADJOINT_INJECTIVE_INJECTIVE,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ ((cadjoint @ V0) @ V1)) @ ((cadjoint @ V0) @ V2))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))))))
(TSUBSPACE_LINEAR_FIXED_POINTS,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ (csubspace @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c= @ (V0 @ V2)) @ V2)) @ V2))))))))))
(TORTHOGONAL_TRANSFORMATION_ISOMETRY,(c! @ (^[V0]: ((c= @ (corthogonal_transformation @ V0)) @ ((c/__caret__ @ ((c= @ (V0 @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0)))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cdistance @ ((c__comma__ @ (V0 @ V1)) @ (V0 @ V2)))) @ (cdistance @ ((c__comma__ @ V1) @ V2))))))))))))
(TORTHOGONAL_TRANSFORMATION_MATRIX,(c! @ (^[V0]: ((c= @ (corthogonal_transformation @ V0)) @ ((c/__caret__ @ (clinear @ V0)) @ (corthogonal_matrix @ (cmatrix @ V0)))))))
(Torthogonal_transformation,(c! @ (^[V0]: ((c= @ (corthogonal_transformation @ V0)) @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ (V0 @ V1)) @ (V0 @ V2))) @ ((cdot @ V1) @ V2)))))))))))
(TORTHOGONAL_TRANSFORMATION_SPHERE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (corthogonal_transformation @ V0)) @ ((c= @ ((cIMAGE @ V0) @ (csphere @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))) @ (csphere @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))))))))
(TORTHOGONAL_TRANSFORMATION_CBALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (corthogonal_transformation @ V0)) @ ((c= @ ((cIMAGE @ V0) @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))) @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))))))))
(TORTHOGONAL_TRANSFORMATION_BALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (corthogonal_transformation @ V0)) @ ((c= @ ((cIMAGE @ V0) @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))) @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))))))))
(TORTHOGONAL_TRANSFORMATION_ORTHOGONAL_EIGENVECTORS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (corthogonal_transformation @ V0)) @ ((c/__caret__ @ ((c= @ (V0 @ V3)) @ ((c% @ V1) @ V3))) @ ((c/__caret__ @ ((c= @ (V0 @ V4)) @ ((c% @ V2) @ V4))) @ (c~ @ ((c= @ V1) @ V2)))))) @ ((corthogonal @ V3) @ V4)))))))))))))
(TSELF_ADJOINT_ORTHOGONAL_EIGENVECTORS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ ((c= @ (cadjoint @ V0)) @ V0)) @ ((c/__caret__ @ ((c= @ (V0 @ V3)) @ ((c% @ V1) @ V3))) @ ((c/__caret__ @ ((c= @ (V0 @ V4)) @ ((c% @ V2) @ V4))) @ (c~ @ ((c= @ V1) @ V2))))))) @ ((corthogonal @ V3) @ V4)))))))))))))
(THAS_MEASURE_LINEAR_SUFFICIENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((chas_measure @ ((cIMAGE @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ ((creal_mul @ V1) @ (cmeasure @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))) @ ((c==> @ (cmeasurable @ V2)) @ ((chas_measure @ ((cIMAGE @ V0) @ V2)) @ ((creal_mul @ V1) @ (cmeasure @ V2))))))))))))
(TWLOG_LINEAR_INJECTIVE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V1 @ V3)) @ (clinear @ V2))) @ (V1 @ ((cIMAGE @ V2) @ V3)))))))) @ ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ (c! @ (^[V2]: ((c= @ (V1 @ ((cIMAGE @ V0) @ V2))) @ (V1 @ V2)))))))))))
(TSELF_ADJOINT_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ ((c= @ (cadjoint @ V1)) @ V1)) @ ((c= @ (cadjoint @ V0)) @ V0))))) @ ((c= @ ((c= @ (cadjoint @ ((co @ V1) @ V0))) @ ((co @ V1) @ V0))) @ ((c= @ ((co @ V1) @ V0)) @ ((co @ V0) @ V1)))))))))
(TLINEAR_INVERSE_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ (clinear @ V0))) @ ((c= @ ((c= @ ((co @ V1) @ V0)) @ cI)) @ ((c= @ ((co @ V0) @ V1)) @ cI))))))))
(TLEFT_INVERSE_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c= @ ((co @ V1) @ V0)) @ cI))) @ (clinear @ V1)))))))
(TRIGHT_INVERSE_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c= @ ((co @ V0) @ V1)) @ cI))) @ (clinear @ V1)))))))
(TADJOINT_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ (clinear @ V0))) @ ((c= @ (cadjoint @ ((co @ V1) @ V0))) @ ((co @ (cadjoint @ V0)) @ (cadjoint @ V1)))))))))
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(TMEASURABLE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (cmeasurable @ V1))) @ (cmeasurable @ ((cIMAGE @ V0) @ V1))))))))
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(TFRONTIER_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cfrontier @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (cfrontier @ V1)))))))))
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(TMEASURABLE_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cmeasurable @ ((cIMAGE @ V0) @ V1))) @ (cmeasurable @ V1))))))))
(TLEBESGUE_MEASURABLE_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (clebesgue_measurable @ ((cIMAGE @ V0) @ V1))) @ (clebesgue_measurable @ V1))))))))
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(THAS_MEASURE_ORTHOGONAL_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (corthogonal_transformation @ V0)) @ ((chas_measure @ V1) @ V2))) @ ((chas_measure @ ((cIMAGE @ V0) @ V1)) @ V2)))))))))
(THAS_MEASURE_ORTHOGONAL_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (corthogonal_transformation @ V0)) @ ((c= @ ((chas_measure @ ((cIMAGE @ V0) @ V1)) @ V2)) @ ((chas_measure @ V1) @ V2))))))))))
(TFRONTIER_SUBSET_RETRACTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cbounded @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cfrontier @ V1)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ (cclosure @ V1))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V0) @ V1)) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c= @ (V0 @ V3)) @ V3))))))))) @ ((cSUBSET @ V1) @ V2)))))))))
(TLINEAR_INJECTIVE_IMP_SURJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))))))
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(TLINEAR_SURJECTIVE_IMP_INJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c? @ (^[V4]: ((c= @ (V0 @ V4)) @ V3))))))) @ ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))))
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(TLOCALLY_CONNECTED_RIGHT_INVERTIBLE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ ((cIMAGE @ V1) @ V2))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V0) @ ((cIMAGE @ V1) @ V2))) @ V2)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cIMAGE @ V1) @ V2))) @ ((c= @ (V1 @ (V0 @ V3))) @ V3))))) @ ((clocally @ cconnected) @ V2)))))) @ ((clocally @ cconnected) @ ((cIMAGE @ V1) @ V2))))))))))
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(TLOCALLY_CONNECTED_LEFT_INVERTIBLE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ ((cIMAGE @ V1) @ V2))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c= @ (V0 @ (V1 @ V3))) @ V3))))) @ ((clocally @ cconnected) @ V2))))) @ ((clocally @ cconnected) @ ((cIMAGE @ V1) @ V2))))))))))
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(TCONTINUOUS_LEFT_INVERSE_IMP_QUOTIENT_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ ((cIMAGE @ V1) @ V2))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((c= @ (V0 @ (V1 @ V4))) @ V4))))))) @ ((c==> @ ((cSUBSET @ V3) @ ((cIMAGE @ V1) @ V2))) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((cIN @ (V1 @ V5)) @ V3))) @ V5))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V1) @ V2))) @ V3)))))))))))))
(THOMEOMORPHISM_IMP_OPEN_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((chomeomorphism @ ((c__comma__ @ V1) @ V2)) @ ((c__comma__ @ V3) @ V0))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V4))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ ((cIMAGE @ V3) @ V4))))))))))))))
(THOMEOMORPHISM_IMP_CLOSED_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((chomeomorphism @ ((c__comma__ @ V1) @ V2)) @ ((c__comma__ @ V3) @ V0))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V4))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ ((cIMAGE @ V3) @ V4))))))))))))))
(THAS_DERIVATIVE_LOCALLY_INJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ (copen @ V1)) @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ ((c= @ ((co @ V0) @ (V2 @ V3))) @ cI)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ (((chas_derivative @ V4) @ (V2 @ V5)) @ (cat @ V5)))))) @ (c! @ (^[V5]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c? @ (^[V6]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V6)) @ (c! @ (^[V7]: ((c==> @ ((creal_lt @ (cdistance @ ((c__comma__ @ V3) @ V7))) @ V6)) @ ((creal_lt @ (conorm @ (^[V8]: ((cvector_sub @ ((V2 @ V7) @ V8)) @ ((V2 @ V3) @ V8))))) @ V5)))))))))))))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V3) @ V5)) @ ((c/__caret__ @ (copen @ V5)) @ (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V5)) @ ((c/__caret__ @ ((cIN @ V7) @ V5)) @ ((c= @ (V4 @ V7)) @ (V4 @ V6))))) @ ((c= @ V7) @ V6))))))))))))))))))))))
(THOMEOMORPHISM_IMP_COVERING_SPACE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((chomeomorphism @ ((c__comma__ @ V1) @ V3)) @ ((c__comma__ @ V2) @ V0))) @ ((ccovering_space @ ((c__comma__ @ V1) @ V2)) @ V3)))))))))))
(THOMEOMORPHISM_IMP_QUOTIENT_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((chomeomorphism @ ((c__comma__ @ V1) @ V3)) @ ((c__comma__ @ V2) @ V0))) @ ((c==> @ ((cSUBSET @ V4) @ V3)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cIN @ (V2 @ V6)) @ V4))) @ V6))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V3)) @ V4)))))))))))))))
(TCONTINUOUS_RIGHT_INVERSE_IMP_QUOTIENT_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V0) @ V3)) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((c= @ (V2 @ (V0 @ V5))) @ V5))))))))) @ ((c==> @ ((cSUBSET @ V4) @ V3)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cIN @ (V2 @ V6)) @ V4))) @ V6))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V3)) @ V4)))))))))))))))
(TIN_INTERIOR_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (clinear @ V2)) @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ ((c= @ ((co @ V2) @ V0)) @ cI)) @ ((cIN @ V1) @ (cinterior @ V3)))))) @ ((cIN @ (V2 @ V1)) @ (cinterior @ ((cIMAGE @ V2) @ V3)))))))))))))
(TCONTINUOUS_AT_SEQUENTIALLY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous @ V0) @ (cat @ V1))) @ (c! @ (^[V2]: ((c==> @ (((c--> @ V2) @ V1) @ csequentially)) @ (((c--> @ ((co @ V0) @ V2)) @ (V0 @ V1)) @ csequentially))))))))))
(TCONTINUOUS_ON,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous_on @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (((c--> @ V0) @ (V0 @ V2)) @ ((cwithin @ (cat @ V2)) @ V1)))))))))))
(TCONTINUOUS_AT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous @ V0) @ (cat @ V1))) @ (((c--> @ V0) @ (V0 @ V1)) @ (cat @ V1))))))))
(TPAIRWISE_DISJOINT_COMPONENTS,(c! @ (^[V0]: ((cpairwise @ cDISJOINT) @ (ccomponents @ V0)))))
(TOPEN_IN_SET_RELATIVE_INTERIOR,(c! @ (^[V0]: ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (crelative_interior @ V0)))))
(TOPEN_IN_REFL,(c! @ (^[V0]: ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V0))))
(TAFF_DIM_GE,(c! @ (^[V0]: ((cint_le @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (caff_dim @ V0)))))
(TAFF_DIM_LE_UNIV,(c! @ (^[V0]: ((cint_le @ (caff_dim @ V0)) @ (cint_of_num @ (cdimindex @ cUNIV))))))
(TAFF_DIM_LE_DIM,(c! @ (^[V0]: ((cint_le @ (caff_dim @ V0)) @ (cint_of_num @ (cdim @ V0))))))
(THOMOTOPY_EQUIVALENT_REFL,(c! @ (^[V0]: ((chomotopy_equivalent @ V0) @ V0))))
(THOMEOMORPHISM_ID,(c! @ (^[V0]: ((chomeomorphism @ ((c__comma__ @ V0) @ V0)) @ ((c__comma__ @ (^[V1]: V1)) @ (^[V1]: V1))))))
(THOMEOMORPHISM_I,(c! @ (^[V0]: ((chomeomorphism @ ((c__comma__ @ V0) @ V0)) @ ((c__comma__ @ cI) @ cI)))))
(THOMEOMORPHIC_REFL,(c! @ (^[V0]: ((chomeomorphic @ V0) @ V0))))
(THAS_BOUNDED_SETVARIATION_ON_0,(c! @ (^[V0]: ((chas_bounded_setvariation_on @ (^[V1]: (cvec @ (cNUMERAL @ c_0)))) @ V0))))
(TEMPTY_EXPOSED_FACE_OF,(c! @ (^[V0]: ((cexposed_face_of @ cEMPTY) @ V0))))
(TDIFFERENTIABLE_ON_SQNORM,(c! @ (^[V0]: ((cdifferentiable_on @ (^[V1]: (clift @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ V0))))
(TCONVEX_NORM,(c! @ (^[V0]: ((cconvex_on @ cvector_norm) @ V0))))
(TCLOSED_IN_REFL,(c! @ (^[V0]: ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V0))))
(TCONVEX_HULL_INTERIOR_SUBSET,(c! @ (^[V0]: ((cSUBSET @ ((chull @ cconvex) @ (cinterior @ V0))) @ (cinterior @ ((chull @ cconvex) @ V0))))))
(TINSIDE_INSIDE_SUBSET,(c! @ (^[V0]: ((cSUBSET @ (cinside @ (cinside @ V0))) @ V0))))
(TFRONTIER_INTERIOR_SUBSET,(c! @ (^[V0]: ((cSUBSET @ (cfrontier @ (cinterior @ V0))) @ (cfrontier @ V0)))))
(TFRONTIER_FRONTIER_SUBSET,(c! @ (^[V0]: ((cSUBSET @ (cfrontier @ (cfrontier @ V0))) @ (cfrontier @ V0)))))
(TFRONTIER_CLOSURE_SUBSET,(c! @ (^[V0]: ((cSUBSET @ (cfrontier @ (cclosure @ V0))) @ (cfrontier @ V0)))))
(TPAIRWISE_ORTHOGONAL_IMP_FINITE,(c! @ (^[V0]: ((c==> @ ((cpairwise @ corthogonal) @ V0)) @ (cFINITE @ V0)))))
(TLOCALLY_PATH_CONNECTED_IMP_LOCALLY_CONNECTED,(c! @ (^[V0]: ((c==> @ ((clocally @ cpath_connected) @ V0)) @ ((clocally @ cconnected) @ V0)))))
(TCOUNTABLE_COMPONENTS,(c! @ (^[V0]: ((c==> @ ((clocally @ cconnected) @ V0)) @ (cCOUNTABLE @ (ccomponents @ V0))))))
(TSIGMA_COMPACT,(c! @ (^[V0]: ((c==> @ ((clocally @ ccompact) @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (ccompact @ V2))))) @ ((c= @ (cUNIONS @ V1)) @ V0)))))))))
(TLOCALLY_COMPACT_CLOSED_IN_OPEN,(c! @ (^[V0]: ((c==> @ ((clocally @ ccompact) @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (copen @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0))))))))
(TLOCALLY_COMPACT_OPEN_INTER_CLOSURE,(c! @ (^[V0]: ((c==> @ ((clocally @ ccompact) @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (copen @ V1)) @ ((c= @ V0) @ ((cINTER @ V1) @ (cclosure @ V0))))))))))
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(TINTERIOR_FRONTIER_EMPTY,(c! @ (^[V0]: ((c==> @ ((c__caret__/ @ (copen @ V0)) @ (cclosed @ V0))) @ ((c= @ (cinterior @ (cfrontier @ V0))) @ cEMPTY)))))
(TFRONTIER_FRONTIER,(c! @ (^[V0]: ((c==> @ ((c__caret__/ @ (copen @ V0)) @ (cclosed @ V0))) @ ((c= @ (cfrontier @ (cfrontier @ V0))) @ (cfrontier @ V0))))))
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(TAFFINE_HULL_EQ_SPAN,(c! @ (^[V0]: ((c==> @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ ((chull @ caffine) @ V0))) @ ((c= @ ((chull @ caffine) @ V0)) @ (cspan @ V0))))))
(TAFFINE_EQ_SUBSPACE,(c! @ (^[V0]: ((c==> @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ (caffine @ V0)) @ (csubspace @ V0))))))
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(TAFFINE_DEPENDENT_BIGGERSET,(c! @ (^[V0]: ((c==> @ ((c==> @ (cFINITE @ V0)) @ ((c>= @ (cCARD @ V0)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (caffine_dependent @ V0)))))
(TAFFINE_DEPENDENT_BIGGERSET_GENERAL,(c! @ (^[V0]: ((c==> @ ((c==> @ (cFINITE @ V0)) @ ((c>= @ (cCARD @ V0)) @ ((c+ @ (cdim @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (caffine_dependent @ V0)))))
(TDEPENDENT_BIGGERSET,(c! @ (^[V0]: ((c==> @ ((c==> @ (cFINITE @ V0)) @ ((c> @ (cCARD @ V0)) @ (cdimindex @ cUNIV)))) @ (cdependent @ V0)))))
(TDEPENDENT_BIGGERSET_GENERAL,(c! @ (^[V0]: ((c==> @ ((c==> @ (cFINITE @ V0)) @ ((c> @ (cCARD @ V0)) @ (cdim @ V0)))) @ (cdependent @ V0)))))
(TCONNECTED_CONVEX_1_GEN,(c! @ (^[V0]: ((c==> @ ((c= @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ (cconvex @ V0)) @ (cconnected @ V0))))))
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(TRELATIVE_INTERIOR_INTERIOR,(c! @ (^[V0]: ((c==> @ ((c= @ ((chull @ caffine) @ V0)) @ cUNIV)) @ ((c= @ (crelative_interior @ V0)) @ (cinterior @ V0))))))
(TRELATIVE_FRONTIER_FRONTIER,(c! @ (^[V0]: ((c==> @ ((c= @ ((chull @ caffine) @ V0)) @ cUNIV)) @ ((c= @ (crelative_frontier @ V0)) @ (cfrontier @ V0))))))
(TEMPTY_INTERIOR_LOWDIM,(c! @ (^[V0]: ((c==> @ ((c< @ (cdim @ V0)) @ (cdimindex @ cUNIV))) @ ((c= @ (cinterior @ V0)) @ cEMPTY)))))
(TNEGLIGIBLE_LOWDIM,(c! @ (^[V0]: ((c==> @ ((c< @ (cdim @ V0)) @ (cdimindex @ cUNIV))) @ (cnegligible @ V0)))))
(TORTHOGONAL_TRANSFORMATION_LOWDIM_HORIZONTAL,(c! @ (^[V0]: ((c==> @ ((c< @ (cdim @ V0)) @ (cdimindex @ cUNIV))) @ (c? @ (^[V1]: ((c/__caret__ @ (corthogonal_transformation @ V1)) @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((c$ @ V3) @ (cdimindex @ cUNIV))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V3)))))))))))))
(TROTATION_LOWDIM_HORIZONTAL,(c! @ (^[V0]: ((c==> @ ((c< @ (cdim @ V0)) @ (cdimindex @ cUNIV))) @ (c? @ (^[V1]: ((c/__caret__ @ (corthogonal_transformation @ V1)) @ ((c/__caret__ @ ((c= @ (cdet @ (cmatrix @ V1))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((c$ @ V3) @ (cdimindex @ cUNIV))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V3))))))))))))))
(TLOWDIM_SUBSET_HYPERPLANE,(c! @ (^[V0]: ((c==> @ ((c< @ (cdim @ V0)) @ (cdimindex @ cUNIV))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((cSUBSET @ (cspan @ V0)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((cdot @ V1) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V3)))))))))))))
(TORTHOGONAL_TO_SUBSPACE_EXISTS,(c! @ (^[V0]: ((c==> @ ((c< @ (cdim @ V0)) @ (cdimindex @ cUNIV))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((corthogonal @ V1) @ V2)))))))))))
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(TPATH_CONNECTED_COMPLEMENT_ABSOLUTE_RETRACT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (ccompact @ V0)) @ (cAR @ V0)))) @ (cpath_connected @ ((cDIFF @ cUNIV) @ V0))))))
(TCONNECTED_COMPLEMENT_ABSOLUTE_RETRACT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (ccompact @ V0)) @ (cAR @ V0)))) @ (cconnected @ ((cDIFF @ cUNIV) @ V0))))))
(TCOBOUNDED_HAS_BOUNDED_COMPONENT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (cbounded @ ((cDIFF @ cUNIV) @ V0))) @ (c~ @ (cconnected @ V0))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ (ccomponents @ V0))) @ (cbounded @ V1))))))))
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(TCONNECTED_COMPLEMENT_BOUNDED_CONVEX,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (cbounded @ V0)) @ (cconvex @ V0)))) @ (cconnected @ ((cDIFF @ cUNIV) @ V0))))))
(TNOT_OUTSIDE_CONNECTED_COMPONENT_LT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (cbounded @ V0))) @ ((c= @ ((cDIFF @ cUNIV) @ (coutside @ V0))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ V3) @ (cvector_norm @ V4))) @ (c~ @ (((cconnected_component @ ((cDIFF @ cUNIV) @ V0)) @ V2) @ V4)))))))) @ V2))))))))))
(TNOT_OUTSIDE_CONNECTED_COMPONENT_LE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (cbounded @ V0))) @ ((c= @ ((cDIFF @ cUNIV) @ (coutside @ V0))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((creal_le @ V3) @ (cvector_norm @ V4))) @ (c~ @ (((cconnected_component @ ((cDIFF @ cUNIV) @ V0)) @ V2) @ V4)))))))) @ V2))))))))))
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(TAFFINE_INDEPENDENT_SPAN_EQ,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ (cCARD @ V0)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c= @ ((chull @ caffine) @ V0)) @ cUNIV)))))
(TAFFINE_INDEPENDENT_SPAN_GT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V0))) @ ((c< @ (cdimindex @ cUNIV)) @ (cCARD @ V0)))) @ ((c= @ ((chull @ caffine) @ V0)) @ cUNIV)))))
(TISOMETRY_UNIV_SUBSPACE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (csubspace @ V0)) @ ((c= @ (cdimindex @ cUNIV)) @ (cdim @ V0)))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ cUNIV)) @ V0)) @ (c! @ (^[V2]: ((c= @ (cvector_norm @ (V1 @ V2))) @ (cvector_norm @ V2))))))))))))
(TISOMETRY_UNIV_SUPERSET_SUBSPACE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (csubspace @ V0)) @ ((c/__caret__ @ ((c<= @ (cdim @ V0)) @ (cdimindex @ cUNIV))) @ ((c<= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ ((cIMAGE @ V1) @ cUNIV))) @ (c! @ (^[V2]: ((c= @ (cvector_norm @ (V1 @ V2))) @ (cvector_norm @ V2))))))))))))
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(TFINITELY_GENERATED_CONIC_POLYHEDRON,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V0)) @ ((c/__caret__ @ (cconic @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY))))) @ (c? @ (^[V1]: ((c/__caret__ @ (cFINITE @ V1)) @ ((c= @ V0) @ ((chull @ cconvex_cone) @ V1)))))))))
(TCARD_EQ_OPEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c=_c @ V0) @ cUNIV)))))
(TDIM_OPEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ (cdim @ V0)) @ (cdimindex @ cUNIV))))))
(TAFF_DIM_OPEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ (caff_dim @ V0)) @ (cint_of_num @ (cdimindex @ cUNIV)))))))
(TAFFINE_HULL_OPEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((chull @ caffine) @ V0)) @ cUNIV)))))
(TSPAN_OPEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ (cspan @ V0)) @ cUNIV)))))
(TOPEN_NOT_NEGLIGIBLE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c~ @ (cnegligible @ V0))))))
(TUNCOUNTABLE_OPEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c~ @ (cCOUNTABLE @ V0))))))
(TOPEN_SET_IRRATIONAL_COORDINATES,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (c~ @ (crational @ ((c$ @ V1) @ V2)))))))))))))
(TOPEN_SET_RATIONAL_COORDINATES,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (crational @ ((c$ @ V1) @ V2))))))))))))
(TCONNECTED_OPEN_PATH_CONNECTED,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (cconnected @ V0))) @ (cpath_connected @ V0)))))
(TMEASURABLE_NONNEGLIGIBLE_IMP_LARGE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cmeasure @ V0)))) @ ((c=_c @ V0) @ cUNIV)))))
(TSTEINHAUS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cmeasure @ V0)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V0))) @ ((cvector_sub @ V3) @ V4))))))))))))))))
(TMEASURABLE_SMALL_IMP_NEGLIGIBLE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c<_c @ V0) @ cUNIV))) @ (cnegligible @ V0)))))
(TSTARLIKE_NEGLIGIBLE_BOUNDED_MEASURABLE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ (cbounded @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ ((c% @ V1) @ V2)) @ V0)))) @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))) @ (cnegligible @ V0)))))
(TSTEINHAUS_LEBESGUE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clebesgue_measurable @ V0)) @ (c~ @ (cnegligible @ V0)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V0))) @ ((cvector_sub @ V3) @ V4))))))))))))))))
(TINTERIOR_SIMPLEX_NONEMPTY,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cindependent @ V0)) @ ((cHAS_SIZE @ V0) @ (cdimindex @ cUNIV)))) @ (c? @ (^[V1]: ((cIN @ V1) @ (cinterior @ ((chull @ cconvex) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ V0))))))))))
(TBASIS_HAS_SIZE_UNIV,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cindependent @ V0)) @ ((c= @ (cspan @ V0)) @ cUNIV))) @ ((cHAS_SIZE @ V0) @ (cdimindex @ cUNIV))))))
(TEMPTY_INTERIOR_SUBSET_HYPERPLANE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c= @ (cinterior @ V0)) @ cEMPTY))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((cSUBSET @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V1) @ V4)) @ V2)) @ V4)))))))))))))))
(TSEPARATING_HYPERPLANE_SET_0_INSPAN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c~ @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V0))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V1) @ (cspan @ V0))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cdot @ V1) @ V3)))))))))))))))
(TUNBOUNDED_CONVEX_CLOSED_CONTAINS_RAYS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (c~ @ (cbounded @ V0))) @ (cclosed @ V0)))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ ((cIN @ ((cvector_add @ V2) @ ((c% @ V3) @ V1))) @ V0)))))))))))))
(TMINKOWSKI_COMPACT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((cIN @ (cvector_neg @ V1)) @ V0))))) @ ((creal_le @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cdimindex @ cUNIV))) @ (cmeasure @ V0)))))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (cinteger @ ((c$ @ V1) @ V2)))))) @ ((cIN @ V1) @ V0)))))))))
(TKREIN_MILMAN_RELATIVE_FRONTIER,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (ccompact @ V0)) @ (c~ @ (c? @ (^[V1]: ((c= @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))) @ ((c= @ V0) @ ((chull @ cconvex) @ ((cDIFF @ V0) @ (crelative_interior @ V0))))))))
(TSEPARATING_HYPERPLANE_CLOSED_0_INSET,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c~ @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V0)))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_gt @ ((cdot @ V1) @ V3)) @ V2)))))))))))))))
(TSEPARATING_HYPERPLANE_CLOSED_0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (cclosed @ V0)) @ (c~ @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V0))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_gt @ ((cdot @ V1) @ V3)) @ V2))))))))))))))
(TMINKOWSKI,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((cIN @ (cvector_neg @ V1)) @ V0))))) @ ((creal_lt @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cdimindex @ cUNIV))) @ (cmeasure @ V0)))))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (cinteger @ ((c$ @ V1) @ V2)))))) @ ((cIN @ V1) @ V0)))))))))
(TPATH_CONNECTED_SPHERE_GEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (cbounded @ V0)) @ (c~ @ ((c= @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ (cpath_connected @ (crelative_frontier @ V0))))))
(TCONNECTED_SPHERE_GEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (cbounded @ V0)) @ (c~ @ ((c= @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ (cconnected @ (crelative_frontier @ V0))))))
(TSEPARATING_HYPERPLANE_SET_0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c~ @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V0)))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cdot @ V1) @ V3))))))))))))))
(TCLOSURE_DYADIC_RATIONALS_IN_CONVEX_SET,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c~ @ ((c= @ (cinterior @ V0)) @ cEMPTY)))) @ ((c= @ (cclosure @ ((cINTER @ V0) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V1) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ (cdimindex @ cUNIV)))) @ (cinteger @ ((c$ @ V3) @ V4)))))) @ ((c% @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2))) @ V3))))))))))) @ (cclosure @ V0))))))
(TCLOSURE_RATIONALS_IN_CONVEX_SET,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c~ @ ((c= @ (cinterior @ V0)) @ cEMPTY)))) @ ((c= @ (cclosure @ ((cINTER @ V0) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (crational @ ((c$ @ V2) @ V3)))))) @ V2)))))))) @ (cclosure @ V0))))))
(TCONVEX_CLOSURE_INTERIOR,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c~ @ ((c= @ (cinterior @ V0)) @ cEMPTY)))) @ ((c= @ (cclosure @ (cinterior @ V0))) @ (cclosure @ V0))))))
(TCONVEX_IMP_AR,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (cAR @ V0)))))
(TRELATIVE_INTERIOR_UNBOUNDED_CONVEX_CONTAINS_RAYS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c~ @ (cbounded @ V0)))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ (crelative_interior @ V0))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ ((cIN @ ((cvector_add @ V2) @ ((c% @ V3) @ V1))) @ (crelative_interior @ V0))))))))))))))
(TKREIN_MILMAN_FRONTIER,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (ccompact @ V0))) @ ((c= @ V0) @ ((chull @ cconvex) @ (cfrontier @ V0)))))))
(TKREIN_MILMAN_MINKOWSKI,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (ccompact @ V0))) @ ((c= @ V0) @ ((chull @ cconvex) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cextreme_point_of @ V2) @ V0)) @ V2)))))))))))
(TKREIN_MILMAN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (ccompact @ V0))) @ ((c= @ V0) @ (cclosure @ ((chull @ cconvex) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cextreme_point_of @ V2) @ V0)) @ V2))))))))))))
(TMEASURABLE_CONVEX,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (cbounded @ V0))) @ (cmeasurable @ V0)))))
(TINSIDE_COMPLEMENT_UNBOUNDED_CONNECTED_EMPTY,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconnected @ ((cDIFF @ cUNIV) @ V0))) @ (c~ @ (cbounded @ ((cDIFF @ cUNIV) @ V0))))) @ ((c= @ (cinside @ V0)) @ cEMPTY)))))
(TINSIDE_BOUNDED_COMPLEMENT_CONNECTED_EMPTY,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconnected @ ((cDIFF @ cUNIV) @ V0))) @ (cbounded @ V0))) @ ((c= @ (cinside @ V0)) @ cEMPTY)))))
(TFINITE_LOCALLY_PATH_CONNECTED_PATH_COMPONENTS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((clocally @ cpath_connected) @ V0))) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ ((cpath_component @ V0) @ V2)))))))))))
(TFINITE_COMPONENTS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((clocally @ cconnected) @ V0))) @ (cFINITE @ (ccomponents @ V0))))))
(TFINITE_LOCALLY_CONNECTED_CONNECTED_COMPONENTS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((clocally @ cconnected) @ V0))) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ ((cconnected_component @ V0) @ V2)))))))))))
(TEXTREME_POINT_EXISTS_CONVEX,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (cconvex @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY))))) @ (c? @ (^[V1]: ((cextreme_point_of @ V1) @ V0)))))))
(TDIAMETER_COMPACT_ATTAINED,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (cvector_norm @ ((cvector_sub @ V1) @ V2))) @ (cdiameter @ V0))))))))))))
(TCOMPACT_SUP_MAXDISTANCE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V0))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ V3) @ V4))) @ (cvector_norm @ ((cvector_sub @ V1) @ V2))))))))))))))))))
(TFINITE_COMPLEMENT_ENR_COMPONENTS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ (cENR @ V0))) @ (cFINITE @ (ccomponents @ ((cDIFF @ cUNIV) @ V0)))))))
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(TEXTREME_POINTS_OF_CONVEX_HULL_EQ,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cPSUBSET @ V1) @ V0)) @ (c~ @ ((c= @ ((chull @ cconvex) @ V1)) @ ((chull @ cconvex) @ V0)))))))) @ ((c= @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cextreme_point_of @ V2) @ ((chull @ cconvex) @ V0))) @ V2)))))) @ V0)))))
(TCARD_EQ_PERFECT_SET,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((climit_point_of @ V1) @ V0))))) @ (c~ @ ((c= @ V0) @ cEMPTY))))) @ ((c=_c @ V0) @ cUNIV)))))
(TCONVEX_HALFSPACE_INTERSECTION,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (cconvex @ V0))) @ ((c= @ V0) @ (cINTERS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V2) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((cdot @ V3) @ V6)) @ V4)) @ V6)))))))))))) @ V2)))))))))))
(TENR_CONVEX_CLOSED,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (cconvex @ V0))) @ (cENR @ V0)))))
(TINSIDE_INSIDE_EQ_EMPTY,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (cconnected @ V0))) @ ((c= @ (cinside @ (cinside @ V0))) @ cEMPTY)))))
(TCONNECTED_WITH_OUTSIDE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (cconnected @ V0))) @ (cconnected @ ((cUNION @ V0) @ (coutside @ V0)))))))
(TCONNECTED_WITH_INSIDE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (cconnected @ V0))) @ (cconnected @ ((cUNION @ V0) @ (cinside @ V0)))))))
(TNOT_ABSOLUTE_RETRACT_COBOUNDED,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ ((cretract_of @ ((cDIFF @ cUNIV) @ V0)) @ cUNIV))) @ ((c= @ V0) @ cEMPTY)))))
(TBLICHFELDT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cmeasure @ V0))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (cinteger @ ((creal_sub @ ((c$ @ V1) @ V3)) @ ((c$ @ V2) @ V3)))))))))))))))))
(TDIAMETER_ATTAINED_RELATIVE_FRONTIER,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (c~ @ ((c= @ (cdiameter @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V1) @ (crelative_frontier @ V0))) @ ((c/__caret__ @ ((cIN @ V2) @ (crelative_frontier @ V0))) @ ((c= @ (cvector_norm @ ((cvector_sub @ V1) @ V2))) @ (cdiameter @ V0))))))))))))
(TDIAMETER_ATTAINED_FRONTIER,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (c~ @ ((c= @ (cdiameter @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V1) @ (cfrontier @ V0))) @ ((c/__caret__ @ ((cIN @ V2) @ (cfrontier @ V0))) @ ((c= @ (cvector_norm @ ((cvector_sub @ V1) @ V2))) @ (cdiameter @ V0))))))))))))
(TNO_RETRACTION_FRONTIER_BOUNDED,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (c~ @ ((c= @ (cinterior @ V0)) @ cEMPTY)))) @ (c~ @ ((cretract_of @ (cfrontier @ V0)) @ V0))))))
(TDIAMETER_SUBSET_CBALL_NONEMPTY,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cSUBSET @ V0) @ (ccball @ ((c__comma__ @ V1) @ (cdiameter @ V0)))))))))))
(TDIAMETER_RELATIVE_FRONTIER,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (c~ @ (c? @ (^[V1]: ((c= @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))) @ ((c= @ (cdiameter @ (crelative_frontier @ V0))) @ (cdiameter @ V0))))))
(TMEASURABLE_OPEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (copen @ V0))) @ (cmeasurable @ V0)))))
(TMEASURE_INTERIOR,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cnegligible @ (cfrontier @ V0)))) @ ((c= @ (cmeasure @ (cinterior @ V0))) @ (cmeasure @ V0))))))
(TMEASURE_CLOSURE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cnegligible @ (cfrontier @ V0)))) @ ((c= @ (cmeasure @ (cclosure @ V0))) @ (cmeasure @ V0))))))
(TMEASURABLE_JORDAN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cnegligible @ (cfrontier @ V0)))) @ (cmeasurable @ V0)))))
(TLOCALLY_PATH_CONNECTED_SPHERE_GEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cconvex @ V0))) @ ((clocally @ cpath_connected) @ (crelative_frontier @ V0))))))
(TLOCALLY_CONNECTED_SPHERE_GEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cconvex @ V0))) @ ((clocally @ cconnected) @ (crelative_frontier @ V0))))))
(TOUTSIDE_FRONTIER_EQ_COMPLEMENT_CLOSURE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cconvex @ V0))) @ ((c= @ (coutside @ (cfrontier @ V0))) @ ((cDIFF @ cUNIV) @ (cclosure @ V0)))))))
(TINSIDE_FRONTIER_EQ_INTERIOR,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cconvex @ V0))) @ ((c= @ (cinside @ (cfrontier @ V0))) @ (cinterior @ V0))))))
(TENR_RELATIVE_FRONTIER_CONVEX,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cconvex @ V0))) @ (cENR @ (crelative_frontier @ V0))))))
(TANR_RELATIVE_FRONTIER_CONVEX,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cconvex @ V0))) @ (cANR @ (crelative_frontier @ V0))))))
(TBOUNDED_CLOSED_IMP_COMPACT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cclosed @ V0))) @ (ccompact @ V0)))))
(TBOLZANO_WEIERSTRASS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cINFINITE @ V0))) @ (c? @ (^[V1]: ((climit_point_of @ V1) @ V0)))))))
(TEXPLICIT_SUBSET_INTERIOR_CONVEX_HULL_MINIMAL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c= @ ((chull @ caffine) @ V0)) @ cUNIV))) @ ((cSUBSET @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4)))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))))) @ V2)))))) @ (cinterior @ ((chull @ cconvex) @ V0)))))))
(TEXPLICIT_SUBSET_INTERIOR_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c= @ ((chull @ caffine) @ V0)) @ cUNIV))) @ ((cSUBSET @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4))) @ ((creal_lt @ (V3 @ V4)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))))) @ V2)))))) @ (cinterior @ ((chull @ cconvex) @ V0)))))))
(TEMPTY_INTERIOR_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c<= @ (cCARD @ V0)) @ (cdimindex @ cUNIV)))) @ ((c= @ (cinterior @ ((chull @ cconvex) @ V0))) @ cEMPTY)))))
(TEMPTY_INTERIOR_AFFINE_HULL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c<= @ (cCARD @ V0)) @ (cdimindex @ cUNIV)))) @ ((c= @ (cinterior @ ((chull @ caffine) @ V0))) @ cEMPTY)))))
(TNEGLIGIBLE_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c<= @ (cCARD @ V0)) @ (cdimindex @ cUNIV)))) @ (cnegligible @ ((chull @ cconvex) @ V0))))))
(TNEGLIGIBLE_AFFINE_HULL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c<= @ (cCARD @ V0)) @ (cdimindex @ cUNIV)))) @ (cnegligible @ ((chull @ caffine) @ V0))))))
(TSIMPLEX_EXPLICIT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V0)))) @ ((c= @ ((chull @ cconvex) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ V0))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4)))))) @ ((c/__caret__ @ ((creal_le @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))))) @ V2))))))))))
(TFINITE_IMP_NOT_OPEN,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c~ @ (copen @ V0))))))
(TSIMPLEX_EXTREMAL_LE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ ((chull @ cconvex) @ V0))) @ ((cIN @ V4) @ ((chull @ cconvex) @ V0)))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ V3) @ V4))) @ (cvector_norm @ ((cvector_sub @ V1) @ V2))))))))))))))))))
(TRADON_EX_LEMMA,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (caffine_dependent @ V0))) @ (c? @ (^[V1]: ((c/__caret__ @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c~ @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((cvsum @ V0) @ (^[V2]: ((c% @ (V1 @ V2)) @ V2)))) @ (cvec @ (cNUMERAL @ c_0)))))))))))
(TRADON_PARTITION,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (caffine_dependent @ V0))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cDISJOINT @ V1) @ V2)) @ ((c/__caret__ @ ((c= @ ((cUNION @ V1) @ V2)) @ V0)) @ (c~ @ ((cDISJOINT @ ((chull @ cconvex) @ V1)) @ ((chull @ cconvex) @ V2)))))))))))))
(TFINITE_ENR_COMPONENTS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cENR @ V0)) @ (ccompact @ V0))) @ (cFINITE @ (ccomponents @ V0))))))
(TFINITE_ANR_COMPONENTS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cANR @ V0)) @ (ccompact @ V0))) @ (cFINITE @ (ccomponents @ V0))))))
(TSPAN_NOT_UNIV_SUBSET_HYPERPLANE,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cspan @ V0)) @ cUNIV))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((cSUBSET @ (cspan @ V0)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((cdot @ V1) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V3)))))))))))))
(TSPAN_NOT_UNIV_ORTHOGONAL,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cspan @ V0)) @ cUNIV))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (cspan @ V0))) @ ((c= @ ((cdot @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))
(TCARD_EQ_NONEMPTY_INTERIOR,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cinterior @ V0)) @ cEMPTY))) @ ((c=_c @ V0) @ cUNIV)))))
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(TUNCOUNTABLE_NONEMPTY_INTERIOR,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cinterior @ V0)) @ cEMPTY))) @ (c~ @ (cCOUNTABLE @ V0))))))
(TDIAMETER_SIMPLEX,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c= @ (cdiameter @ ((chull @ cconvex) @ V0))) @ (csup @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V0))) @ (cdistance @ ((c__comma__ @ V2) @ V3)))))))))))))))
(TCONVEX_CONE_HULL_SEPARATE_NONEMPTY,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c= @ ((chull @ cconvex_cone) @ V0)) @ ((chull @ cconic) @ ((chull @ cconvex) @ V0)))))))
(TCONVEX_CONE_HULL_CONVEX_HULL_NONEMPTY,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c= @ ((chull @ cconvex_cone) @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((cIN @ V3) @ ((chull @ cconvex) @ V0)))) @ ((c% @ V2) @ V3)))))))))))))
(TAFF_DIM_AFFINE_INDEPENDENT,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ (caff_dim @ V0)) @ ((cint_sub @ (cint_of_num @ (cCARD @ V0))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TRELATIVE_BOUNDARY_OF_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ ((cDIFF @ ((chull @ cconvex) @ V0)) @ (crelative_interior @ ((chull @ cconvex) @ V0)))) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ ((chull @ cconvex) @ ((cDELETE @ V0) @ V2)))))))))))))
(TRELATIVE_INTERIOR_CONVEX_HULL_EXPLICIT,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ (crelative_interior @ ((chull @ cconvex) @ V0))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4)))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))))) @ V2))))))))))
(TRELATIVE_FRONTIER_CONVEX_HULL_CASES,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ (crelative_frontier @ ((chull @ cconvex) @ V0))) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ ((chull @ cconvex) @ ((cDELETE @ V0) @ V2)))))))))))))
(TRELATIVE_FRONTIER_CONVEX_HULL_EXPLICIT,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ (crelative_frontier @ ((chull @ cconvex) @ V0))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4)))))) @ ((c/__caret__ @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V3 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2))))))) @ V2))))))))))
(TINTERIOR_CONVEX_HULL_EXPLICIT_MINIMAL,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ (cinterior @ ((chull @ cconvex) @ V0))) @ (((cCOND @ ((c<= @ (cCARD @ V0)) @ (cdimindex @ cUNIV))) @ cEMPTY) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4)))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))))) @ V2)))))))))))
(TINTERIOR_CONVEX_HULL_EXPLICIT,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ (cinterior @ ((chull @ cconvex) @ V0))) @ (((cCOND @ ((c<= @ (cCARD @ V0)) @ (cdimindex @ cUNIV))) @ cEMPTY) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4))) @ ((creal_lt @ (V3 @ V4)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))))) @ V2)))))))))))
(TFRONTIER_CONVEX_HULL_CASES,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ (cfrontier @ ((chull @ cconvex) @ V0))) @ (((cCOND @ ((c<= @ (cCARD @ V0)) @ (cdimindex @ cUNIV))) @ ((chull @ cconvex) @ V0)) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ V0)) @ ((chull @ cconvex) @ ((cDELETE @ V0) @ V2))))))))))))))
(TFRONTIER_CONVEX_HULL_EXPLICIT,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ (cfrontier @ ((chull @ cconvex) @ V0))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4)))))) @ ((c/__caret__ @ ((c==> @ ((c< @ (cdimindex @ cUNIV)) @ (cCARD @ V0))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V3 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2))))))) @ V2))))))))))
(TAFFINE_INDEPENDENT_CARD_LE,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c<= @ (cCARD @ V0)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TAFFINE_INDEPENDENT_IMP_FINITE,(c! @ (^[V0]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ (cFINITE @ V0)))))
(TCARD_EQ_CONDENSATION_POINTS_IN_SET,(c! @ (^[V0]: ((c==> @ (c~ @ (cCOUNTABLE @ V0))) @ ((c=_c @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((ccondensation_point_of @ V2) @ V0))) @ V2)))))) @ V0)))))
(TUNCOUNTABLE_HAS_CONDENSATION_POINT,(c! @ (^[V0]: ((c==> @ (c~ @ (cCOUNTABLE @ V0))) @ (c? @ (^[V1]: ((ccondensation_point_of @ V1) @ V0)))))))
(TAFF_DIM_DIM_SUBSPACE,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ ((c= @ (caff_dim @ V0)) @ (cint_of_num @ (cdim @ V0)))))))
(TSPAN_OF_SUBSPACE,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ ((c= @ (cspan @ V0)) @ V0)))))
(TSUBSPACE_BOUNDED_EQ_TRIVIAL,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ ((c= @ (cbounded @ V0)) @ ((c= @ V0) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ cEMPTY)))))))
(TCOMPLETE_SUBSPACE,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ (ccomplete @ V0)))))
(TCLOSED_SUBSPACE,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ (cclosed @ V0)))))
(TORTHOGONAL_SPANNINGSET_SUBSPACE,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ V1)) @ ((c= @ (cspan @ V1)) @ V0)))))))))
(TORTHONORMAL_BASIS_SUBSPACE,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((c/__caret__ @ (cindependent @ V1)) @ ((c/__caret__ @ ((cHAS_SIZE @ V1) @ (cdim @ V0))) @ ((c= @ (cspan @ V1)) @ V0))))))))))))
(TORTHOGONAL_BASIS_SUBSPACE,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V1))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ V1)) @ ((c/__caret__ @ (cindependent @ V1)) @ ((c/__caret__ @ ((cHAS_SIZE @ V1) @ (cdim @ V0))) @ ((c= @ (cspan @ V1)) @ V0))))))))))))
(TBASIS_SUBSPACE_EXISTS,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cindependent @ V1)) @ ((c/__caret__ @ ((c= @ (cspan @ V1)) @ V0)) @ ((cHAS_SIZE @ V1) @ (cdim @ V0))))))))))))
(TSTARLIKE_CLOSURE,(c! @ (^[V0]: ((c==> @ (cstarlike @ V0)) @ (cstarlike @ (cclosure @ V0))))))
(TSTARLIKE_IMP_SIMPLY_CONNECTED,(c! @ (^[V0]: ((c==> @ (cstarlike @ V0)) @ (csimply_connected @ V0)))))
(TSTARLIKE_IMP_PATH_CONNECTED,(c! @ (^[V0]: ((c==> @ (cstarlike @ V0)) @ (cpath_connected @ V0)))))
(TSTARLIKE_IMP_CONTRACTIBLE,(c! @ (^[V0]: ((c==> @ (cstarlike @ V0)) @ (ccontractible @ V0)))))
(TSTARLIKE_IMP_CONNECTED,(c! @ (^[V0]: ((c==> @ (cstarlike @ V0)) @ (cconnected @ V0)))))
(TSIMPLY_CONNECTED_IMP_PATH_CONNECTED,(c! @ (^[V0]: ((c==> @ (csimply_connected @ V0)) @ (cpath_connected @ V0)))))
(TSIMPLY_CONNECTED_IMP_CONNECTED,(c! @ (^[V0]: ((c==> @ (csimply_connected @ V0)) @ (cconnected @ V0)))))
(TPOLYTOPE_VERTEX_LOWER_BOUND,(c! @ (^[V0]: ((c==> @ (cpolytope @ V0)) @ ((cint_le @ ((cint_add @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cint_of_num @ (cCARD @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cextreme_point_of @ V2) @ V0)) @ V2))))))))))))
(TPOLYTOPE_NEGATIONS,(c! @ (^[V0]: ((c==> @ (cpolytope @ V0)) @ (cpolytope @ ((cIMAGE @ cvector_neg) @ V0))))))
(TFINITE_POLYTOPE_FACETS,(c! @ (^[V0]: ((c==> @ (cpolytope @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cfacet_of @ V2) @ V0)) @ V2))))))))))
(TFINITE_POLYTOPE_FACES,(c! @ (^[V0]: ((c==> @ (cpolytope @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cface_of @ V2) @ V0)) @ V2))))))))))
(TRELATIVE_BOUNDARY_OF_POLYHEDRON,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ ((c= @ ((cDIFF @ V0) @ (crelative_interior @ V0))) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cfacet_of @ V2) @ V0)) @ V2)))))))))))
(TRELATIVE_INTERIOR_OF_POLYHEDRON,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ ((c= @ (crelative_interior @ V0)) @ ((cDIFF @ V0) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cfacet_of @ V2) @ V0)) @ V2))))))))))))
(TRELATIVE_FRONTIER_OF_POLYHEDRON,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ ((c= @ (crelative_frontier @ V0)) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cfacet_of @ V2) @ V0)) @ V2)))))))))))
(TRELATIVE_FRONTIER_OF_POLYHEDRON_ALT,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ ((c= @ (crelative_frontier @ V0)) @ (cUNIONS @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((cface_of @ V2) @ V0)) @ (c~ @ ((c= @ V2) @ V0)))) @ V2)))))))))))
(TPOLYHEDRON_NEGATIONS,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ (cpolyhedron @ ((cIMAGE @ cvector_neg) @ V0))))))
(TPOLYHEDRON_IMP_CONVEX,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ (cconvex @ V0)))))
(TPOLYHEDRON_IMP_CLOSED,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ (cclosed @ V0)))))
(TFINITE_POLYHEDRON_FACETS,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cfacet_of @ V2) @ V0)) @ V2))))))))))
(TFINITE_POLYHEDRON_FACES,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cface_of @ V2) @ V0)) @ V2))))))))))
(TFINITE_POLYHEDRON_EXPOSED_FACES,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cexposed_face_of @ V2) @ V0)) @ V2))))))))))
(TFINITE_POLYHEDRON_EXTREME_POINTS,(c! @ (^[V0]: ((c==> @ (cpolyhedron @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cextreme_point_of @ V2) @ V0)) @ V2))))))))))
(TPATH_CONNECTED_NEGATIONS,(c! @ (^[V0]: ((c==> @ (cpath_connected @ V0)) @ (cpath_connected @ ((cIMAGE @ cvector_neg) @ V0))))))
(TPATH_CONNECTED_IMP_CONNECTED,(c! @ (^[V0]: ((c==> @ (cpath_connected @ V0)) @ (cconnected @ V0)))))
(TOPEN_IMP_LOCALLY_PATH_CONNECTED,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ ((clocally @ cpath_connected) @ V0)))))
(TOPEN_IMP_LOCALLY_CONNECTED,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ ((clocally @ cconnected) @ V0)))))
(TOPEN_IMP_LOCALLY_COMPACT,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ ((clocally @ ccompact) @ V0)))))
(TRELATIVE_INTERIOR_OPEN,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ ((c= @ (crelative_interior @ V0)) @ V0)))))
(TCLOSURE_DYADIC_RATIONALS_IN_OPEN_SET,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ ((c= @ (cclosure @ ((cINTER @ V0) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V1) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ (cdimindex @ cUNIV)))) @ (cinteger @ ((c$ @ V3) @ V4)))))) @ ((c% @ (creal_inv @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2))) @ V3))))))))))) @ (cclosure @ V0))))))
(TCONNECTED_OPEN_SET,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ ((c= @ (cconnected @ V0)) @ (c~ @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (copen @ V1)) @ ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ ((c/__caret__ @ ((c= @ ((cUNION @ V1) @ V2)) @ V0)) @ ((c= @ ((cINTER @ V1) @ V2)) @ cEMPTY))))))))))))))))
(TOPEN_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ (copen @ ((chull @ cconvex) @ V0))))))
(TOPEN_NEGATIONS,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ (copen @ ((cIMAGE @ cvector_neg) @ V0))))))
(TOPEN_POSITIVE_MULTIPLES,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ (copen @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((cIN @ V3) @ V0))) @ ((c% @ V2) @ V3)))))))))))))
(TLEBESGUE_MEASURABLE_OPEN,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ (clebesgue_measurable @ V0)))))
(TOPEN_IMP_ENR,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ (cENR @ V0)))))
(TOPEN_IMP_ANR,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ (cANR @ V0)))))
(TOPEN_UNION_COMPACT_SUBSETS,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: (ccompact @ (V1 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((cSUBSET @ (V1 @ V2)) @ V0)))) @ ((c/__caret__ @ (c! @ (^[V2]: ((cSUBSET @ (V1 @ V2)) @ (cinterior @ (V1 @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((c/__caret__ @ ((c= @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (V1 @ V3)))))))) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V2)) @ ((cSUBSET @ V2) @ V0))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c>= @ V4) @ V3)) @ ((cSUBSET @ V2) @ (V1 @ V4))))))))))))))))))))
(TOPEN_COUNTABLE_UNION_OPEN_INTERVALS,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V2) @ (copen_interval @ ((c__comma__ @ V3) @ V4)))))))))))) @ ((c= @ (cUNIONS @ V1)) @ V0)))))))))
(TOPEN_COUNTABLE_UNION_CLOSED_INTERVALS,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))) @ ((c= @ (cUNIONS @ V1)) @ V0)))))))))
(TLEBESGUE_MEASURABLE_JORDAN,(c! @ (^[V0]: ((c==> @ (cnegligible @ (cfrontier @ V0))) @ (clebesgue_measurable @ V0)))))
(TNEGLIGIBLE_IMP_MEASURABLE,(c! @ (^[V0]: ((c==> @ (cnegligible @ V0)) @ (cmeasurable @ V0)))))
(TNEGLIGIBLE_IMP_LEBESGUE_MEASURABLE,(c! @ (^[V0]: ((c==> @ (cnegligible @ V0)) @ (clebesgue_measurable @ V0)))))
(TMEASURABLE_IMP_LEBESGUE_MEASURABLE,(c! @ (^[V0]: ((c==> @ (cmeasurable @ V0)) @ (clebesgue_measurable @ V0)))))
(TLEBESGUE_MEASURABLE_REGULAR_OUTER,(c! @ (^[V0]: ((c==> @ (clebesgue_measurable @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cnegligible @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: (copen @ (V2 @ V3))))) @ ((c= @ V0) @ ((cDIFF @ (cINTERS @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ cUNIV)) @ (V2 @ V4)))))))) @ V1))))))))))))
(TLEBESGUE_MEASURABLE_REGULAR_INNER,(c! @ (^[V0]: ((c==> @ (clebesgue_measurable @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cnegligible @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: (ccompact @ (V2 @ V3))))) @ ((c= @ V0) @ ((cUNION @ (cUNIONS @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ cUNIV)) @ (V2 @ V4)))))))) @ V1))))))))))))
(TIS_INTERVAL_IMP_LOCALLY_COMPACT,(c! @ (^[V0]: ((c==> @ (cis_interval @ V0)) @ ((clocally @ ccompact) @ V0)))))
(TIS_INTERVAL_CONVEX,(c! @ (^[V0]: ((c==> @ (cis_interval @ V0)) @ (cconvex @ V0)))))
(TIS_INTERVAL_CONNECTED,(c! @ (^[V0]: ((c==> @ (cis_interval @ V0)) @ (cconnected @ V0)))))
(TDIM_EQ_CARD,(c! @ (^[V0]: ((c==> @ (cindependent @ V0)) @ ((c= @ (cdim @ V0)) @ (cCARD @ V0))))))
(TINDEPENDENT_BOUND_conjunct1,(c! @ (^[V0]: ((c==> @ (cindependent @ V0)) @ ((c<= @ (cCARD @ V0)) @ (cdimindex @ cUNIV))))))
(TINDEPENDENT_BOUND_GENERAL_conjunct1,(c! @ (^[V0]: ((c==> @ (cindependent @ V0)) @ ((c<= @ (cCARD @ V0)) @ (cdim @ V0))))))
(TINDEPENDENT_IMP_FINITE,(c! @ (^[V0]: ((c==> @ (cindependent @ V0)) @ (cFINITE @ V0)))))
(TBASIS_COORDINATES_LIPSCHITZ,(c! @ (^[V0]: ((c==> @ (cindependent @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (creal_abs @ (V2 @ V3))) @ ((creal_mul @ V1) @ (cvector_norm @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V2 @ V4)) @ V4))))))))))))))))))
(TCONVEX_CONE_CONTAINS_0,(c! @ (^[V0]: ((c==> @ (cconvex_cone @ V0)) @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V0)))))
(TCONVEX_IMP_LOCALLY_PATH_CONNECTED,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((clocally @ cpath_connected) @ V0)))))
(TCONVEX_IMP_LOCALLY_CONNECTED,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((clocally @ cconnected) @ V0)))))
(TEXPOSED_FACE_OF_REFL,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((cexposed_face_of @ V0) @ V0)))))
(TCONVEX_RELATIVE_INTERIOR_CLOSURE,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((c= @ (crelative_interior @ (cclosure @ V0))) @ (crelative_interior @ V0))))))
(TRELATIVE_INTERIOR_CONVEX_PROLONG,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((c= @ (crelative_interior @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V4)) @ ((cIN @ ((cvector_add @ V3) @ ((c% @ V4) @ ((cvector_sub @ V2) @ V3)))) @ V0))))))))) @ V2))))))))))
(TRELATIVE_FRONTIER_RELATIVE_INTERIOR,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((c= @ (crelative_frontier @ (crelative_interior @ V0))) @ (crelative_frontier @ V0))))))
(TOUTSIDE_CONVEX,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((c= @ (coutside @ V0)) @ ((cDIFF @ cUNIV) @ V0))))))
(TCONVEX_INTERIOR_CLOSURE,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((c= @ (cinterior @ (cclosure @ V0))) @ (cinterior @ V0))))))
(TFRONTIER_CLOSURE_CONVEX,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((c= @ (cfrontier @ (cclosure @ V0))) @ (cfrontier @ V0))))))
(TCONVEX_CLOSURE_RELATIVE_INTERIOR,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((c= @ (cclosure @ (crelative_interior @ V0))) @ (cclosure @ V0))))))
(TAFF_DIM_NONEMPTY_INTERIOR_EQ,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((c= @ ((c= @ (caff_dim @ V0)) @ (cint_of_num @ (cdimindex @ cUNIV)))) @ (c~ @ ((c= @ (cinterior @ V0)) @ cEMPTY)))))))
(TRELATIVE_INTERIOR_EQ_EMPTY,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((c= @ ((c= @ (crelative_interior @ V0)) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY))))))
(TCONVEX_IMP_SIMPLY_CONNECTED,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (csimply_connected @ V0)))))
(TCONVEX_IMP_PATH_CONNECTED,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (cpath_connected @ V0)))))
(TNEGLIGIBLE_CONVEX_FRONTIER,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (cnegligible @ (cfrontier @ V0))))))
(TLEBESGUE_MEASURABLE_CONVEX,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (clebesgue_measurable @ V0)))))
(TCONVEX_CONIC_HULL,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (cconvex @ ((chull @ cconic) @ V0))))))
(TCONVEX_RELATIVE_INTERIOR,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (cconvex @ (crelative_interior @ V0))))))
(TCONVEX_INTERIOR,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (cconvex @ (cinterior @ V0))))))
(TCONVEX_CLOSURE,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (cconvex @ (cclosure @ V0))))))
(TCONVEX_IMP_CONTRACTIBLE,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (ccontractible @ V0)))))
(TCONVEX_CONNECTED,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (cconnected @ V0)))))
(TCONVEX_IMP_ANR,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (cANR @ V0)))))
(TCONTRACTIBLE_IMP_SIMPLY_CONNECTED,(c! @ (^[V0]: ((c==> @ (ccontractible @ V0)) @ (csimply_connected @ V0)))))
(TCONTRACTIBLE_IMP_PATH_CONNECTED,(c! @ (^[V0]: ((c==> @ (ccontractible @ V0)) @ (cpath_connected @ V0)))))
(TCONTRACTIBLE_IMP_CONNECTED,(c! @ (^[V0]: ((c==> @ (ccontractible @ V0)) @ (cconnected @ V0)))))
(TCONNECTED_CARD_EQ_IFF_NONTRIVIAL,(c! @ (^[V0]: ((c==> @ (cconnected @ V0)) @ ((c= @ ((c=_c @ V0) @ cUNIV)) @ (c~ @ (c? @ (^[V1]: ((cSUBSET @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))))
(TCONNECTED_INFINITE_IFF_CARD_EQ,(c! @ (^[V0]: ((c==> @ (cconnected @ V0)) @ ((c= @ (cINFINITE @ V0)) @ ((c=_c @ V0) @ cUNIV))))))
(TCONNECTED_FINITE_IFF_SING,(c! @ (^[V0]: ((c==> @ (cconnected @ V0)) @ ((c= @ (cFINITE @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ (c? @ (^[V1]: ((c= @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))))
(TCONNECTED_FINITE_IFF_COUNTABLE,(c! @ (^[V0]: ((c==> @ (cconnected @ V0)) @ ((c= @ (cFINITE @ V0)) @ (cCOUNTABLE @ V0))))))
(TCONNECTED_NEGATIONS,(c! @ (^[V0]: ((c==> @ (cconnected @ V0)) @ (cconnected @ ((cIMAGE @ cvector_neg) @ V0))))))
(TCONNECTED_CLOSURE,(c! @ (^[V0]: ((c==> @ (cconnected @ V0)) @ (cconnected @ (cclosure @ V0))))))
(TCONIC_CONTAINS_0,(c! @ (^[V0]: ((c==> @ (cconic @ V0)) @ ((c= @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))))))
(TMEASURABLE_INSIDE,(c! @ (^[V0]: ((c==> @ (ccompact @ V0)) @ (cmeasurable @ (cinside @ V0))))))
(TMEASURABLE_COMPACT,(c! @ (^[V0]: ((c==> @ (ccompact @ V0)) @ (cmeasurable @ V0)))))
(TLEBESGUE_MEASURABLE_COMPACT,(c! @ (^[V0]: ((c==> @ (ccompact @ V0)) @ (clebesgue_measurable @ V0)))))
(TCOMPACT_IMP_COMPLETE,(c! @ (^[V0]: ((c==> @ (ccompact @ V0)) @ (ccomplete @ V0)))))
(TCOMPACT_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ (ccompact @ V0)) @ (ccompact @ ((chull @ cconvex) @ V0))))))
(TCOMPACT_NEGATIONS,(c! @ (^[V0]: ((c==> @ (ccompact @ V0)) @ (ccompact @ ((cIMAGE @ cvector_neg) @ V0))))))
(TCOMPACT_RELATIVE_FRONTIER,(c! @ (^[V0]: ((c==> @ (ccompact @ V0)) @ (ccompact @ (crelative_frontier @ V0))))))
(TCONVEX_CONNECTED_COLLINEAR,(c! @ (^[V0]: ((c==> @ (ccollinear @ V0)) @ ((c= @ (cconvex @ V0)) @ (cconnected @ V0))))))
(TCOLLINEAR_EXTREME_POINTS_conjunct1,(c! @ (^[V0]: ((c==> @ (ccollinear @ V0)) @ ((c<= @ (cCARD @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cextreme_point_of @ V2) @ V0)) @ V2))))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))
(TCOLLINEAR_EXTREME_POINTS_conjunct0,(c! @ (^[V0]: ((c==> @ (ccollinear @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cextreme_point_of @ V2) @ V0)) @ V2))))))))))
(TCLOSED_IMP_LOCALLY_COMPACT,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ ((clocally @ ccompact) @ V0)))))
(TCARD_EQ_CLOSED,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ ((c__caret__/ @ ((c<=_c @ V0) @ cUNIV)) @ ((c=_c @ V0) @ cUNIV))))))
(TFRONTIER_OUTSIDE_SUBSET,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ ((cSUBSET @ (cfrontier @ (coutside @ V0))) @ V0)))))
(TFRONTIER_INSIDE_SUBSET,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ ((cSUBSET @ (cfrontier @ (cinside @ V0))) @ V0)))))
(TCLOSURE_OUTSIDE_SUBSET,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ ((cSUBSET @ (cclosure @ (coutside @ V0))) @ ((cUNION @ V0) @ (coutside @ V0)))))))
(TCLOSURE_INSIDE_SUBSET,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ ((cSUBSET @ (cclosure @ (cinside @ V0))) @ ((cUNION @ V0) @ (cinside @ V0)))))))
(TCONNECTED_CLOSED_SET,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ ((c= @ (cconnected @ V0)) @ (c~ @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cclosed @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ ((c/__caret__ @ ((c= @ ((cUNION @ V1) @ V2)) @ V0)) @ ((c= @ ((cINTER @ V1) @ V2)) @ cEMPTY))))))))))))))))
(TOPEN_OUTSIDE,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ (copen @ (coutside @ V0))))))
(TOPEN_INSIDE,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ (copen @ (cinside @ V0))))))
(TLEBESGUE_MEASURABLE_CLOSED,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ (clebesgue_measurable @ V0)))))
(TCLOSED_NEGATIONS,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ (cclosed @ ((cIMAGE @ cvector_neg) @ V0))))))
(TCLOSED_UNION_COMPACT_SUBSETS,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: (ccompact @ (V1 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((cSUBSET @ (V1 @ V2)) @ V0)))) @ ((c/__caret__ @ (c! @ (^[V2]: ((cSUBSET @ (V1 @ V2)) @ (V1 @ ((c+ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((c/__caret__ @ ((c= @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (V1 @ V3)))))))) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V2)) @ ((cSUBSET @ V2) @ V0))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c>= @ V4) @ V3)) @ ((cSUBSET @ V2) @ (V1 @ V4))))))))))))))))))))
(TCLOSED_AS_GDELTA,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (copen @ V2))))) @ ((c= @ (cINTERS @ V1)) @ V0)))))))))
(TCANTOR_BENDIXSON,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((climit_point_of @ V3) @ V1))))) @ ((c/__caret__ @ (cCOUNTABLE @ V2)) @ ((c= @ V0) @ ((cUNION @ V1) @ V2)))))))))))))
(TCOBOUNDED_IMP_UNBOUNDED,(c! @ (^[V0]: ((c==> @ (cbounded @ ((cDIFF @ cUNIV) @ V0))) @ (c~ @ (cbounded @ V0))))))
(TCOBOUNDED_UNBOUNDED_COMPONENTS,(c! @ (^[V0]: ((c==> @ (cbounded @ ((cDIFF @ cUNIV) @ V0))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ (ccomponents @ V0))) @ (c~ @ (cbounded @ V1)))))))))
(TCOBOUNDED_UNBOUNDED_COMPONENT,(c! @ (^[V0]: ((c==> @ (cbounded @ ((cDIFF @ cUNIV) @ V0))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c~ @ (cbounded @ ((cconnected_component @ V0) @ V1))))))))))
(TDIAMETER_POS_LE,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdiameter @ V0))))))
(TOUTSIDE_FRONTIER_MISSES_CLOSURE,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ ((cSUBSET @ (coutside @ (cfrontier @ V0))) @ ((cDIFF @ cUNIV) @ (cclosure @ V0)))))))
(TINTERIOR_INSIDE_FRONTIER,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ ((cSUBSET @ (cinterior @ V0)) @ (cinside @ (cfrontier @ V0)))))))
(TMEASURE_FRONTIER,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ ((c= @ (cmeasure @ (cfrontier @ V0))) @ ((creal_sub @ (cmeasure @ (cclosure @ V0))) @ (cmeasure @ (cinterior @ V0))))))))
(TDIAMETER_FRONTIER,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ ((c= @ (cdiameter @ (cfrontier @ V0))) @ (cdiameter @ V0))))))
(TDIAMETER_CLOSURE,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ ((c= @ (cdiameter @ (cclosure @ V0))) @ (cdiameter @ V0))))))
(TDIAMETER_EQ_0,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ ((c= @ ((c= @ (cdiameter @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ (c? @ (^[V1]: ((c= @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))))
(TCONTENT_EQ_0_GEN,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ ((c= @ ((c= @ (ccontent @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ ((c$ @ V3) @ V1)) @ V2)))))))))))))))
(TLEBESGUE_MEASURABLE_IFF_MEASURABLE,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ ((c= @ (clebesgue_measurable @ V0)) @ (cmeasurable @ V0))))))
(TENR_BOUNDED,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ ((c= @ (cENR @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (copen @ V1)) @ ((c/__caret__ @ (cbounded @ V1)) @ ((cretract_of @ V0) @ V1))))))))))
(TOUTSIDE_BOUNDED_NONEMPTY,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (c~ @ ((c= @ (coutside @ V0)) @ cEMPTY))))))
(TUNBOUNDED_OUTSIDE,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (c~ @ (cbounded @ (coutside @ V0)))))))
(TMEASURABLE_FRONTIER,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cmeasurable @ (cfrontier @ V0))))))
(TCOMPACT_RELATIVE_FRONTIER_BOUNDED,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (ccompact @ (crelative_frontier @ V0))))))
(TBOUNDED_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cbounded @ ((chull @ cconvex) @ V0))))))
(TCOBOUNDED_OUTSIDE,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cbounded @ ((cDIFF @ cUNIV) @ (coutside @ V0)))))))
(TBOUNDED_RELATIVE_FRONTIER,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cbounded @ (crelative_frontier @ V0))))))
(TBOUNDED_INTERIOR,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cbounded @ (cinterior @ V0))))))
(TBOUNDED_INSIDE,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cbounded @ (cinside @ V0))))))
(TBOUNDED_FRONTIER,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cbounded @ (cfrontier @ V0))))))
(TBOUNDED_CLOSURE,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cbounded @ (cclosure @ V0))))))
(TFINITE_BOUNDED_INTEGER_POINTS,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (cintegral_vector @ V2))) @ V2))))))))))
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(TBOUNDED_SUBSET_CLOSED_INTERVAL_SYMMETRIC,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (c? @ (^[V1]: ((cSUBSET @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvector_neg @ V1)) @ V1)) @ cNIL)))))))))
(TDIAMETER_SUBSET_CBALL,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (c? @ (^[V1]: ((cSUBSET @ V0) @ (ccball @ ((c__comma__ @ V1) @ (cdiameter @ V0))))))))))
(TBOUNDED_SUBSET_OPEN_INTERVAL,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((cSUBSET @ V0) @ (copen_interval @ ((c__comma__ @ V1) @ V2)))))))))))
(TBOUNDED_SUBSET_CLOSED_INTERVAL,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((cSUBSET @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
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(TDIAMETER_BOUNDED_conjunct0,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ V1) @ V2))) @ (cdiameter @ V0)))))))))))
(TRADON,(c! @ (^[V0]: ((c==> @ (caffine_dependent @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ ((cDISJOINT @ V1) @ V2)) @ (c~ @ ((cDISJOINT @ ((chull @ cconvex) @ V1)) @ ((chull @ cconvex) @ V2))))))))))))))
(TRELATIVE_INTERIOR_AFFINE,(c! @ (^[V0]: ((c==> @ (caffine @ V0)) @ ((c= @ (crelative_interior @ V0)) @ V0)))))
(TAFFINE_BOUNDED_EQ_LOWDIM,(c! @ (^[V0]: ((c==> @ (caffine @ V0)) @ ((c= @ (cbounded @ V0)) @ ((cint_le @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0))))))))
(TAFFINE_BOUNDED_EQ_TRIVIAL,(c! @ (^[V0]: ((c==> @ (caffine @ V0)) @ ((c= @ (cbounded @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ (c? @ (^[V1]: ((c= @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))))
(TAFFINE_IMP_POLYHEDRON,(c! @ (^[V0]: ((c==> @ (caffine @ V0)) @ (cpolyhedron @ V0)))))
(TCLOSED_AFFINE,(c! @ (^[V0]: ((c==> @ (caffine @ V0)) @ (cclosed @ V0)))))
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(TEXPLICIT_SUBSET_RELATIVE_INTERIOR_CONVEX_HULL_MINIMAL,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((cSUBSET @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4)))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))))) @ V2)))))) @ (crelative_interior @ ((chull @ cconvex) @ V0)))))))
(TEXPLICIT_SUBSET_RELATIVE_INTERIOR_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((cSUBSET @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4))) @ ((creal_lt @ (V3 @ V4)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))))) @ V2)))))) @ (crelative_interior @ ((chull @ cconvex) @ V0)))))))
(TSPAN_FINITE,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cspan @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))) @ V2))))))))))
(TEMPTY_INTERIOR_FINITE,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cinterior @ V0)) @ cEMPTY)))))
(TDEPENDENT_FINITE,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cdependent @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c~ @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((cvsum @ V0) @ (^[V2]: ((c% @ (V1 @ V2)) @ V2)))) @ (cvec @ (cNUMERAL @ c_0)))))))))))
(TCONVEX_FINITE,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cconvex @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V2)))))) @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cIN @ ((cvsum @ V0) @ (^[V2]: ((c% @ (V1 @ V2)) @ V2)))) @ V0)))))))))
(TAFFINE_DEPENDENT_EXPLICIT_FINITE,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (caffine_dependent @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c~ @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((cvsum @ V0) @ (^[V2]: ((c% @ (V1 @ V2)) @ V2)))) @ (cvec @ (cNUMERAL @ c_0))))))))))))
(TPOLYHEDRON_CONVEX_CONE_HULL,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cpolyhedron @ ((chull @ cconvex_cone) @ V0))))))
(TFINITE_IMP_COMPACT_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (ccompact @ ((chull @ cconvex) @ V0))))))
(TCLOSED_CONVEX_CONE_HULL,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cclosed @ ((chull @ cconvex_cone) @ V0))))))
(TFINITE_IMP_BOUNDED,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cbounded @ V0)))))
(TFINITE_IMP_ENR,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cENR @ V0)))))
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(TDIAMETER_CONVEX_HULL,(c! @ (^[V0]: ((c= @ (cdiameter @ ((chull @ cconvex) @ V0))) @ (cdiameter @ V0)))))
(TDIM_INSERT_0,(c! @ (^[V0]: ((c= @ (cdim @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ V0))) @ (cdim @ V0)))))
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(TAFF_DIM_CONVEX_HULL,(c! @ (^[V0]: ((c= @ (caff_dim @ ((chull @ cconvex) @ V0))) @ (caff_dim @ V0)))))
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(TCONVEX_HULL_FINITE,(c! @ (^[V0]: ((c= @ ((chull @ cconvex) @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V4)))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4)))) @ V2)))))) @ V2)))))))))
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(TCARATHEODORY,(c! @ (^[V0]: ((c= @ ((chull @ cconvex) @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ (cFINITE @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c/__caret__ @ ((c<= @ (cCARD @ V3)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cIN @ V2) @ ((chull @ cconvex) @ V3)))))))) @ V2)))))))))
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(TPOLYHEDRON_INTER_AFFINE_PARALLEL,(c! @ (^[V0]: ((c= @ (cpolyhedron @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((c= @ V0) @ ((cINTER @ ((chull @ caffine) @ V0)) @ (cINTERS @ V1)))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((c= @ V2) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((cdot @ V3) @ V6)) @ V4)) @ V6))))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ ((chull @ caffine) @ V0))) @ ((cIN @ ((cvector_add @ V5) @ V3)) @ ((chull @ caffine) @ V0))))))))))))))))))))))
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(Tlebesgue_measurable,(c! @ (^[V0]: ((c= @ (clebesgue_measurable @ V0)) @ ((cmeasurable_on @ (cindicator @ V0)) @ cUNIV)))))
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(Tcomplete,(c! @ (^[V0]: ((c= @ (ccomplete @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((cIN @ (V1 @ V2)) @ V0)))) @ (ccauchy @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (((c--> @ V1) @ V2) @ csequentially)))))))))))
(TCOMPACT_EQ_BOUNDED_CLOSED,(c! @ (^[V0]: ((c= @ (ccompact @ V0)) @ ((c/__caret__ @ (cbounded @ V0)) @ (cclosed @ V0))))))
(Tcompact,(c! @ (^[V0]: ((c= @ (ccompact @ V0)) @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((cIN @ (V1 @ V2)) @ V0)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c< @ V4) @ V5)) @ ((c< @ (V3 @ V4)) @ (V3 @ V5)))))))) @ (((c--> @ ((co @ V1) @ V3)) @ V2) @ csequentially))))))))))))))
(TCOMPACT_EQ_HEINE_BOREL_SUBTOPOLOGY,(c! @ (^[V0]: ((c= @ (ccompact @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2))))) @ ((cSUBSET @ V0) @ (cUNIONS @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((c/__caret__ @ (cFINITE @ V2)) @ ((cSUBSET @ V0) @ (cUNIONS @ V2)))))))))))))
(TCOMPACT_EQ_HEINE_BOREL,(c! @ (^[V0]: ((c= @ (ccompact @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (copen @ V2))))) @ ((cSUBSET @ V0) @ (cUNIONS @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((c/__caret__ @ (cFINITE @ V2)) @ ((cSUBSET @ V0) @ (cUNIONS @ V2)))))))))))))
(TCOMPACT_EQ_BOLZANO_WEIERSTRASS,(c! @ (^[V0]: ((c= @ (ccompact @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V1)) @ ((cSUBSET @ V1) @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((climit_point_of @ V2) @ V1)))))))))))
(TCOLLINEAR_CONVEX_HULL_COLLINEAR,(c! @ (^[V0]: ((c= @ (ccollinear @ ((chull @ cconvex) @ V0))) @ (ccollinear @ V0)))))
(TCOLLINEAR_AFF_DIM,(c! @ (^[V0]: ((c= @ (ccollinear @ V0)) @ ((cint_le @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TCOLLINEAR_AFFINE_HULL,(c! @ (^[V0]: ((c= @ (ccollinear @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((cSUBSET @ V0) @ ((chull @ caffine) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))))
(TCLOSED_IN,(c! @ (^[V0]: ((c= @ (cclosed @ V0)) @ ((cclosed_in @ ceuclidean) @ V0)))))
(Tclosed,(c! @ (^[V0]: ((c= @ (cclosed @ V0)) @ (copen @ ((cDIFF @ cUNIV) @ V0))))))
(TCLOSED_AS_FRONTIER,(c! @ (^[V0]: ((c= @ (cclosed @ V0)) @ (c? @ (^[V1]: ((c= @ V0) @ (cfrontier @ V1))))))))
(TCLOSED_AS_FRONTIER_OF_SUBSET,(c! @ (^[V0]: ((c= @ (cclosed @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c= @ V0) @ (cfrontier @ V1)))))))))
(TCLOSED_INTERS_COMPACT,(c! @ (^[V0]: ((c= @ (cclosed @ V0)) @ (c! @ (^[V1]: (ccompact @ ((cINTER @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1))) @ V0))))))))
(TBOUNDED_CLOSURE_EQ,(c! @ (^[V0]: ((c= @ (cbounded @ (cclosure @ V0))) @ (cbounded @ V0)))))
(Tbounded,(c! @ (^[V0]: ((c= @ (cbounded @ V0)) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (cvector_norm @ V2)) @ V1))))))))))
(TBOUNDED_COMPONENTWISE,(c! @ (^[V0]: ((c= @ (cbounded @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (cbounded @ ((cIMAGE @ (^[V2]: (clift @ ((c$ @ V2) @ V1)))) @ V0)))))))))
(TBOUNDED_EQ_BOLZANO_WEIERSTRASS,(c! @ (^[V0]: ((c= @ (cbounded @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (cINFINITE @ V1))) @ (c? @ (^[V2]: ((climit_point_of @ V2) @ V1))))))))))
(TAFFINE_DEPENDENT_EXPLICIT,(c! @ (^[V0]: ((c= @ (caffine_dependent @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ ((csum @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ (c~ @ ((c= @ (V2 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((cvsum @ V1) @ (^[V3]: ((c% @ (V2 @ V3)) @ V3)))) @ (cvec @ (cNUMERAL @ c_0)))))))))))))))
(Taffine_dependent,(c! @ (^[V0]: ((c= @ (caffine_dependent @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V1) @ ((chull @ caffine) @ ((cDELETE @ V0) @ V1))))))))))
(TAFFINE_INDEXED,(c! @ (^[V0]: ((c= @ (caffine @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ V1))) @ ((cIN @ (V3 @ V4)) @ V0))))) @ ((c= @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cIN @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ (^[V4]: ((c% @ (V2 @ V4)) @ (V3 @ V4))))) @ V0))))))))))))
(TAFFINE_EXPLICIT,(c! @ (^[V0]: ((c= @ (caffine @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c= @ ((csum @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((cIN @ ((cvsum @ V1) @ (^[V3]: ((c% @ (V2 @ V3)) @ V3)))) @ V0))))))))))
(TAFFINE,(c! @ (^[V0]: ((c= @ (caffine @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c= @ ((csum @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cIN @ ((cvsum @ V1) @ (^[V3]: ((c% @ (V2 @ V3)) @ V3)))) @ V0))))))))))
(TENR_ANR,(c! @ (^[V0]: ((c= @ (cENR @ V0)) @ ((c/__caret__ @ (cANR @ V0)) @ ((clocally @ ccompact) @ V0))))))
(TAR_ANR,(c! @ (^[V0]: ((c= @ (cAR @ V0)) @ ((c/__caret__ @ (cANR @ V0)) @ ((c/__caret__ @ (ccontractible @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY))))))))
(TAR_EQ_ABSOLUTE_EXTENSOR,(c! @ (^[V0]: ((c= @ (cAR @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V3)) @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3)))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V2)) @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((c= @ (V4 @ V5)) @ (V1 @ V5))))))))))))))))))))
(TAR,(c! @ (^[V0]: ((c= @ (cAR @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chomeomorphic @ V0) @ V2)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2))) @ ((cretract_of @ V2) @ V1))))))))))
(TANR_EQ_ABSOLUTE_NEIGHBOURHOOD_EXTENSOR,(c! @ (^[V0]: ((c= @ (cANR @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V3)) @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3)))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((cSUBSET @ V3) @ V4)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V5) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V5) @ V4)) @ V0)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V3)) @ ((c= @ (V5 @ V6)) @ (V1 @ V6))))))))))))))))))))))))
(TANR,(c! @ (^[V0]: ((c= @ (cANR @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chomeomorphic @ V0) @ V2)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2))) @ (c? @ (^[V3]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cretract_of @ V2) @ V3)))))))))))))
(TCOMPONENTS_EQ_SING_EXISTS,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ (ccomponents @ V0)) @ ((cINSERT @ V1) @ cEMPTY))))) @ ((c/__caret__ @ (cconnected @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))))))
(TDIM_SUBSET_UNIV,(c! @ (^[V0]: ((c<= @ (cdim @ V0)) @ (cdimindex @ cUNIV)))))
(TCLOSED_RELATIVE_FRONTIER,(c! @ (^[V0]: (cclosed @ (crelative_frontier @ V0)))))
(TCLOSED_LIMPTS,(c! @ (^[V0]: (cclosed @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((climit_point_of @ V2) @ V0)) @ V2)))))))))
(TCLOSED_CONDENSATION_POINTS,(c! @ (^[V0]: (cclosed @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((ccondensation_point_of @ V2) @ V0)) @ V2)))))))))
(TCOUNTABLE_NON_CONDENSATION_POINTS,(c! @ (^[V0]: (cCOUNTABLE @ ((cDIFF @ V0) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((ccondensation_point_of @ V2) @ V0)) @ V2))))))))))
(TAFFINE_HULL_FINITE_INTERSECTION_HYPERPLANES,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((c= @ ((cint_add @ (cint_of_num @ (cCARD @ V1))) @ (caff_dim @ V0))) @ (cint_of_num @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((c= @ ((chull @ caffine) @ V0)) @ (cINTERS @ V1))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V2) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c= @ ((cdot @ V3) @ V6)) @ V4)) @ V6))))))))))))))))))))))
(TSUBSET_SECOND_COUNTABLE,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)))))) @ (c! @ (^[V2]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ V1)) @ ((c= @ V2) @ (cUNIONS @ V3)))))))))))))))
(TMAXIMAL_INDEPENDENT_SUBSET,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cindependent @ V1)) @ ((cSUBSET @ V0) @ (cspan @ V1)))))))))
(TAFFINE_BASIS_EXISTS,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (c~ @ (caffine_dependent @ V1))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c= @ ((chull @ caffine) @ V1)) @ ((chull @ caffine) @ V0)))))))))
(TORTHOGONAL_BASIS_EXISTS,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (cindependent @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ (cspan @ V0))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cspan @ V1))) @ ((c/__caret__ @ ((cHAS_SIZE @ V1) @ (cdim @ V0))) @ ((cpairwise @ corthogonal) @ V1))))))))))
(TSEPARABLE,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((cSUBSET @ V0) @ (cclosure @ V1)))))))))
(THAS_MEASURE_POS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_measure @ V0) @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)))))))
(TDIAMETER_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c__caret__/ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V0))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ V2) @ V3))) @ V1)))))))) @ ((creal_le @ (cdiameter @ V0)) @ V1)))))))
(TOPEN_MEASURABLE_INNER_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cdivision_of @ V2) @ (cUNIONS @ V2))) @ ((c/__caret__ @ ((cSUBSET @ (cUNIONS @ V2)) @ V0)) @ ((creal_lt @ (cmeasure @ V0)) @ ((creal_add @ (cmeasure @ (cUNIONS @ V2))) @ V1))))))))))))
(TMEASURE_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V2))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ ((creal_lt @ (creal_abs @ ((creal_sub @ (cmeasure @ ((cINTER @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))) @ (cmeasure @ V0)))) @ V1)))))))))))))))
(TMEASURABLE_OUTER_OPEN_INTERVALS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ (cCOUNTABLE @ V2)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ cEMPTY))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c= @ V3) @ (copen_interval @ ((c__comma__ @ V4) @ V5)))))))))))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cUNIONS @ V2))) @ ((c/__caret__ @ (cmeasurable @ (cUNIONS @ V2))) @ ((creal_le @ (cmeasure @ (cUNIONS @ V2))) @ ((creal_add @ (cmeasure @ V0)) @ V1))))))))))))))
(TMEASURABLE_OUTER_CLOSED_INTERVALS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ (cCOUNTABLE @ V2)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ cEMPTY))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c= @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ (c~ @ ((c= @ V3) @ V4))))) @ ((c= @ ((cINTER @ (cinterior @ V3)) @ (cinterior @ V4))) @ cEMPTY))))))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cUNIONS @ V2))) @ ((c/__caret__ @ (cmeasurable @ (cUNIONS @ V2))) @ ((creal_le @ (cmeasure @ (cUNIONS @ V2))) @ ((creal_add @ (cmeasure @ V0)) @ V1)))))))))))))))
(TMEASURABLE_OUTER_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((c/__caret__ @ (cmeasurable @ V2)) @ ((creal_lt @ (cmeasure @ V2)) @ ((creal_add @ (cmeasure @ V0)) @ V1)))))))))))))
(TMEASURABLE_INNER_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ (ccompact @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ (cmeasurable @ V2)) @ ((creal_lt @ (cmeasure @ V0)) @ ((creal_add @ (cmeasure @ V2)) @ V1)))))))))))))
(TLEBESGUE_MEASURABLE_OUTER_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clebesgue_measurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((c/__caret__ @ (cmeasurable @ ((cDIFF @ V2) @ V0))) @ ((creal_lt @ (cmeasure @ ((cDIFF @ V2) @ V0))) @ V1))))))))))))
(TLEBESGUE_MEASURABLE_INNER_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clebesgue_measurable @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ (cclosed @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ (cmeasurable @ ((cDIFF @ V0) @ V2))) @ ((creal_lt @ (cmeasure @ ((cDIFF @ V0) @ V2))) @ V1))))))))))))
(TBASIS_COORDINATES_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cindependent @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (cvector_norm @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V3 @ V4)) @ V4))))) @ V2)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_lt @ (creal_abs @ (V3 @ V4))) @ V1))))))))))))))))
(TSCHAUDER_PROJECTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ ((chull @ cconvex) @ V2))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ (V3 @ V4)) @ V4))) @ V1))))))))))))))))))
(TJUNG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ ((creal_le @ ((creal_mul @ (csqrt @ ((creal_div @ (creal_of_num @ (cdimindex @ cUNIV))) @ (creal_of_num @ ((c+ @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ (cdiameter @ V0))) @ V1))) @ (c? @ (^[V2]: ((cSUBSET @ V0) @ (ccball @ ((c__comma__ @ V2) @ V1)))))))))))
(TCONTINUOUS_DIAMETER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cbounded @ V3)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ cEMPTY))) @ ((creal_lt @ (chausdist @ ((c__comma__ @ V0) @ V3))) @ V2)))) @ ((creal_lt @ (creal_abs @ ((creal_sub @ (cdiameter @ V0)) @ (cdiameter @ V3)))) @ V1)))))))))))))
(TCONVEX_OUTER_POLYTOPE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (cconvex @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ (cpolytope @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((creal_lt @ (chausdist @ ((c__comma__ @ V2) @ V0))) @ V1)))))))))))
(TCONVEX_OUTER_APPROXIMATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (cconvex @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ ((chull @ cconvex) @ V2))) @ ((creal_lt @ (chausdist @ ((c__comma__ @ ((chull @ cconvex) @ V2)) @ V0))) @ V1)))))))))))
(TCOMPACT_IMP_TOTALLY_BOUNDED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (ccompact @ V0)) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((cSUBSET @ V0) @ (cUNIONS @ ((cIMAGE @ (^[V3]: (cball @ ((c__comma__ @ V3) @ V1)))) @ V2))))))))))))))
(THAS_MEASURE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_measure @ V0) @ V1)) @ (((chas_integral @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V0)) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))) @ (clift @ V1)) @ cUNIV)))))))
(THAS_MEASURE_INNER_OUTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_measure @ V0) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c/__caret__ @ (cmeasurable @ V3)) @ ((creal_lt @ ((creal_sub @ V1) @ V2)) @ (cmeasure @ V3)))))))))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V0) @ V3)) @ ((c/__caret__ @ (cmeasurable @ V3)) @ ((creal_lt @ (cmeasure @ V3)) @ ((creal_add @ V1) @ V2))))))))))))))))
(THAS_MEASURE_INNER_OUTER_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_measure @ V0) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c/__caret__ @ (cmeasurable @ V3)) @ ((creal_le @ ((creal_sub @ V1) @ V2)) @ (cmeasure @ V3)))))))))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V0) @ V3)) @ ((c/__caret__ @ (cmeasurable @ V3)) @ ((creal_le @ (cmeasure @ V3)) @ ((creal_add @ V1) @ V2))))))))))))))))
(THAS_MEASURE_SCALING,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chas_measure @ V0) @ V2)) @ ((chas_measure @ ((cIMAGE @ (^[V3]: ((c% @ V1) @ V3))) @ V0)) @ ((creal_mul @ ((creal_pow @ (creal_abs @ V1)) @ (cdimindex @ cUNIV))) @ V2))))))))))
(TCONTINUOUS_ON_CLOSURE_COMPONENT_GE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ (cclosure @ V0))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((creal_le @ V1) @ ((c$ @ (V2 @ V5)) @ V4)))))) @ ((cIN @ V3) @ (cclosure @ V0))))) @ ((creal_le @ V1) @ ((c$ @ (V2 @ V3)) @ V4))))))))))))))
(TCHOOSE_SUBSPACE_OF_SUBSPACE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<= @ V1) @ (cdim @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ (csubspace @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ (cspan @ V0))) @ ((c= @ (cdim @ V2)) @ V1)))))))))))
(TMEASURABLE_INTER_HALFSPACE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cmeasurable @ V0)) @ (cmeasurable @ ((cINTER @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((creal_le @ ((c$ @ V4) @ V1)) @ V2)) @ V4)))))))))))))))
(TMEASURABLE_INTER_HALFSPACE_GE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cmeasurable @ V0)) @ (cmeasurable @ ((cINTER @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((creal_ge @ ((c$ @ V4) @ V1)) @ V2)) @ V4)))))))))))))))
(TCOMPACT_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (c! @ (^[V3]: ((cIN @ (V2 @ V3)) @ V0))))) @ ((c==> @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c< @ V5) @ V6)) @ ((c< @ (V4 @ V5)) @ (V4 @ V6)))))))) @ (c! @ (^[V5]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c? @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V8)) @ ((c<= @ V8) @ V1))) @ ((c==> @ ((c<= @ V6) @ V7)) @ ((creal_lt @ (creal_abs @ ((creal_sub @ ((c$ @ (V2 @ (V4 @ V7))) @ V8)) @ ((c$ @ V3) @ V8)))) @ V5))))))))))))))))))))))))))
(TMIDPOINT_CONVEX_DYADIC_RATIONALS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((cIN @ V7) @ V0)) @ ((cIN @ V8) @ V0))) @ ((c/__caret__ @ ((cIN @ (cmidpoint @ ((c__comma__ @ V7) @ V8))) @ V0)) @ ((creal_le @ (V5 @ (cmidpoint @ ((c__comma__ @ V7) @ V8)))) @ ((creal_div @ ((creal_add @ (V5 @ V7)) @ (V5 @ V8))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c= @ ((c+ @ V1) @ V3)) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V4))))) @ ((c/__caret__ @ ((cIN @ ((cvector_add @ ((c% @ ((creal_div @ (creal_of_num @ V1)) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V4))) @ V2)) @ ((c% @ ((creal_div @ (creal_of_num @ V3)) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V4))) @ V6))) @ V0)) @ ((creal_le @ (V5 @ ((cvector_add @ ((c% @ ((creal_div @ (creal_of_num @ V1)) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V4))) @ V2)) @ ((c% @ ((creal_div @ (creal_of_num @ V3)) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V4))) @ V6)))) @ ((creal_add @ ((creal_mul @ ((creal_div @ (creal_of_num @ V1)) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V4))) @ (V5 @ V2))) @ ((creal_mul @ ((creal_div @ (creal_of_num @ V3)) @ ((creal_pow @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V4))) @ (V5 @ V6))))))))))))))))))))))
(THAS_SIZE_FACES_OF_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V1) @ V0)) @ ((cHAS_SIZE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cface_of @ V3) @ V0)) @ V3)))))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cnum_of_int @ ((cint_add @ V1) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TSIMPLEX_EXTREME_POINTS_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V1) @ V0)) @ ((c= @ (cint_of_num @ (cCARD @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cextreme_point_of @ V3) @ V0)) @ V3)))))))) @ ((cint_add @ V1) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TCHOOSE_AFFINE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V0)) @ ((c/__caret__ @ ((cint_le @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V1)) @ ((cint_le @ V1) @ (caff_dim @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ (caffine @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c= @ (caff_dim @ V2)) @ V1)))))))))))
(TSIMPLEX_FACE_OF_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csimplex @ V1) @ V0)) @ ((cface_of @ V2) @ V0))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cint_le @ V3) @ V1)) @ ((csimplex @ V3) @ V2))))))))))))
(TSUM_OVER_TAGGED_PARTIAL_DIVISION_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ctagged_partial_division_of @ V1) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ cEMPTY))) @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (V2 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))) @ ((c= @ ((csum @ V1) @ (cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ (V2 @ V5)))))))))) @ ((csum @ ((cIMAGE @ cSND) @ V1)) @ V2))))))))))
(TSUM_OVER_TAGGED_DIVISION_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V1) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ cEMPTY))) @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (V2 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))) @ ((c= @ ((csum @ V1) @ (cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ (V2 @ V5)))))))))) @ ((csum @ ((cIMAGE @ cSND) @ V1)) @ V2))))))))))
(TTAGGED_PARTIAL_DIVISION_COMMON_TAGS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ctagged_partial_division_of @ V1) @ V0)) @ ((c<= @ (cCARD @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ ((c__comma__ @ V2) @ V4)) @ V1)) @ (c~ @ ((c= @ (ccontent @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((c__comma__ @ V2) @ V4)))))))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV)))))))))))
(TTAGGED_PARTIAL_DIVISION_COMMON_POINT_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ctagged_partial_division_of @ V1) @ V0)) @ ((c<= @ (cCARD @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ ((c__comma__ @ V4) @ V5)) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V5)) @ (c~ @ ((c= @ (ccontent @ V5)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ ((c__comma__ @ V4) @ V5)))))))))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV)))))))))))
(THAS_MEASURE_STRETCH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chas_measure @ V0) @ V2)) @ ((chas_measure @ ((cIMAGE @ (^[V3]: (clambda @ (^[V4]: ((creal_mul @ (V1 @ V4)) @ ((c$ @ V3) @ V4)))))) @ V0)) @ ((creal_mul @ (creal_abs @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ V1))) @ V2))))))))))
(TOPEN_SET_COSMALL_COORDINATES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c<_c @ ((cDIFF @ cUNIV) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((V1 @ V2) @ V4)) @ V4))))))) @ cUNIV))))) @ ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((V1 @ V3) @ ((c$ @ V2) @ V3)))))))))))))))
(TOPEN_SET_COCOUNTABLE_COORDINATES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (cCOUNTABLE @ ((cDIFF @ cUNIV) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((V1 @ V2) @ V4)) @ V4))))))))))) @ ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((V1 @ V3) @ ((c$ @ V2) @ V3)))))))))))))))
(TBEPPO_LEVI_DECREASING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((cintegrable_on @ (V1 @ V2)) @ V0)))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (cdrop @ ((V1 @ (cSUC @ V2)) @ V3))) @ (cdrop @ ((V1 @ V2) @ V3))))))))) @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ ((cintegral @ V0) @ (V1 @ V3))))))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (cnegligible @ V3)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ V0) @ V3))) @ (((c--> @ (^[V5]: ((V1 @ V5) @ V4))) @ (V2 @ V4)) @ csequentially)))))))))))))))
(TBEPPO_LEVI_INCREASING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((cintegrable_on @ (V1 @ V2)) @ V0)))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (cdrop @ ((V1 @ V2) @ V3))) @ (cdrop @ ((V1 @ (cSUC @ V2)) @ V3))))))))) @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ ((cintegral @ V0) @ (V1 @ V3))))))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (cnegligible @ V3)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ V0) @ V3))) @ (((c--> @ (^[V5]: ((V1 @ V5) @ V4))) @ (V2 @ V4)) @ csequentially)))))))))))))))
(TDINI,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((ccontinuous_on @ (V1 @ V4)) @ V0)))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ (((c--> @ (^[V5]: ((V1 @ V5) @ V4))) @ (V2 @ V4)) @ csequentially))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((creal_le @ (cdrop @ ((V1 @ V4) @ V5))) @ (cdrop @ ((V1 @ ((c+ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V5))))))))))))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((ceventually @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((V1 @ V4) @ V5)) @ (V2 @ V5)))) @ V3)))))) @ csequentially))))))))))))
(TKUHN_LABELLING_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V0 @ (V2 @ V3)))))) @ ((c==> @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (c! @ (^[V4]: ((c==> @ (V1 @ V4)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V3) @ V4))) @ ((creal_le @ ((c$ @ V3) @ V4)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c<= @ ((V3 @ V4) @ V5)) @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (V0 @ V4)) @ ((c/__caret__ @ (V1 @ V5)) @ ((c= @ ((c$ @ V4) @ V5)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((c= @ ((V3 @ V4) @ V5)) @ (cNUMERAL @ c_0)))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (V0 @ V4)) @ ((c/__caret__ @ (V1 @ V5)) @ ((c= @ ((c$ @ V4) @ V5)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((c= @ ((V3 @ V4) @ V5)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (V0 @ V4)) @ ((c/__caret__ @ (V1 @ V5)) @ ((c= @ ((V3 @ V4) @ V5)) @ (cNUMERAL @ c_0))))) @ ((creal_le @ ((c$ @ V4) @ V5)) @ ((c$ @ (V2 @ V4)) @ V5)))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (V0 @ V4)) @ ((c/__caret__ @ (V1 @ V5)) @ ((c= @ ((V3 @ V4) @ V5)) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((creal_le @ ((c$ @ (V2 @ V4)) @ V5)) @ ((c$ @ V4) @ V5))))))))))))))))))))))
(TDIVISION_POINTS_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdivision_of @ V1) @ V0)) @ (cFINITE @ ((cdivision_points @ V0) @ V1))))))))
(TSUBORDINATE_PARTITION_OF_UNITY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cUNIONS @ V1))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (copen @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ (copen @ V3)) @ ((c/__caret__ @ ((cIN @ V2) @ V3)) @ (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (c~ @ ((c= @ ((cINTER @ V5) @ V3)) @ cEMPTY)))) @ V5)))))))))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ ((co @ clift) @ (V2 @ V3))) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((V2 @ V3) @ V4)))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V4))))) @ ((c= @ ((V2 @ V4) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ ((csum @ V1) @ (^[V4]: ((V2 @ V4) @ V3)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ (copen @ V4)) @ ((c/__caret__ @ ((cIN @ V3) @ V4)) @ (cFINITE @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ (c~ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V4)) @ ((c= @ ((V2 @ V6) @ V7)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ V6))))))))))))))))))))))))
(TCOMPONENTS_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (cUNIONS @ V1)) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ (cconnected @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconnected @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V3)) @ ((cSUBSET @ V3) @ V0)))) @ ((c= @ V3) @ V2))))))))))) @ ((c= @ (ccomponents @ V0)) @ V1)))))))
(TINTERS_FACES_FINITE_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cface_of @ V2) @ V0)))))) @ (c? @ (^[V2]: ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((c/__caret__ @ ((c<= @ (cCARD @ V2)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cINTERS @ V2)) @ (cINTERS @ V1)))))))))))))
(TLEBESGUE_COVERING_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cUNIONS @ V1))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (copen @ V2)))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((creal_le @ (cdiameter @ V3)) @ V2))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cSUBSET @ V3) @ V4))))))))))))))))
(TCOMPACT_IMP_FIP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (cclosed @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((cSUBSET @ V2) @ V1))) @ (c~ @ ((c= @ ((cINTER @ V0) @ (cINTERS @ V2))) @ cEMPTY)))))))) @ (c~ @ ((c= @ ((cINTER @ V0) @ (cINTERS @ V1))) @ cEMPTY))))))))
(TCLOSED_UNION_COMPLEMENT_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((cSUBSET @ V1) @ (ccomponents @ ((cDIFF @ cUNIV) @ V0))))) @ (cclosed @ ((cUNION @ V0) @ (cUNIONS @ V1)))))))))
(TBAIRE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cCOUNTABLE @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((cSUBSET @ V0) @ (cclosure @ V2))))))))) @ ((cSUBSET @ V0) @ (cclosure @ (cINTERS @ V1)))))))))
(TPARACOMPACT_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (copen @ V2))))) @ ((cSUBSET @ V0) @ (cUNIONS @ V1))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V0) @ (cUNIONS @ V2))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ (copen @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cSUBSET @ V3) @ V4))))))))) @ (c! @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (copen @ V4)) @ ((c/__caret__ @ ((cIN @ V3) @ V4)) @ (cFINITE @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ (c~ @ ((c= @ ((cINTER @ V6) @ V4)) @ cEMPTY)))) @ V6))))))))))))))))))))))
(TCLOSED_IMP_FIP_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (ccompact @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((cSUBSET @ V2) @ V1))) @ (c~ @ ((c= @ ((cINTER @ V0) @ (cINTERS @ V2))) @ cEMPTY)))))))) @ (c~ @ ((c= @ ((cINTER @ V0) @ (cINTERS @ V1))) @ cEMPTY))))))))
(TCLOSED_IMP_FIP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (cclosed @ V2))))) @ ((c/__caret__ @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V1)) @ (cbounded @ V2))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((cSUBSET @ V2) @ V1))) @ (c~ @ ((c= @ ((cINTER @ V0) @ (cINTERS @ V2))) @ cEMPTY))))))))) @ (c~ @ ((c= @ ((cINTER @ V0) @ (cINTERS @ V1))) @ cEMPTY))))))))
(TINTER_INTERIOR_UNIONS_INTERVALS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c= @ ((cINTER @ V0) @ (cinterior @ V2))) @ cEMPTY)))))))) @ ((c= @ ((cINTER @ V0) @ (cinterior @ (cUNIONS @ V1)))) @ cEMPTY)))))))
(TBROUWER_REDUCTION_THEOREM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c/__caret__ @ (ccompact @ (V2 @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ (V2 @ V3)) @ cEMPTY))) @ (V1 @ (V2 @ V3))))))) @ (c! @ (^[V3]: ((cSUBSET @ (V2 @ (cSUC @ V3))) @ (V2 @ V3)))))) @ (V1 @ (cINTERS @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ cUNIV)) @ (V2 @ V4)))))))))))) @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (V1 @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ (ccompact @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ ((c/__caret__ @ (V1 @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c/__caret__ @ (cclosed @ V3)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ cEMPTY))) @ (V1 @ V3))))) @ (c~ @ ((cPSUBSET @ V3) @ V2)))))))))))))))))
(TBROUWER_REDUCTION_THEOREM_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c/__caret__ @ (cclosed @ (V2 @ V3))) @ (V1 @ (V2 @ V3)))))) @ (c! @ (^[V3]: ((cSUBSET @ (V2 @ (cSUC @ V3))) @ (V2 @ V3)))))) @ (V1 @ (cINTERS @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ cUNIV)) @ (V2 @ V4)))))))))))) @ ((c/__caret__ @ (cclosed @ V0)) @ (V1 @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ (cclosed @ V2)) @ ((c/__caret__ @ (V1 @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c/__caret__ @ (cclosed @ V3)) @ (V1 @ V3)))) @ (c~ @ ((cPSUBSET @ V3) @ V2))))))))))))))))
(TCOMPONENTS_OPEN_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ (cconnected @ V2)) @ (c~ @ ((c= @ V2) @ cEMPTY)))))))) @ ((c/__caret__ @ ((cpairwise @ cDISJOINT) @ V1)) @ ((c= @ (cUNIONS @ V1)) @ V0)))) @ ((c= @ (ccomponents @ V0)) @ V1)))))))
(TBOUNDED_CLOSED_CHAIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ (cclosed @ V2)) @ (c~ @ ((c= @ V2) @ cEMPTY))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((cIN @ V3) @ V1))) @ ((c__caret__/ @ ((cSUBSET @ V2) @ V3)) @ ((cSUBSET @ V3) @ V2)))))))) @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ (cbounded @ V0))))) @ (c~ @ ((c= @ (cINTERS @ V1)) @ cEMPTY))))))))
(THEINE_BOREL_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (ccompact @ V0)) @ ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cUNIONS @ V1))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (copen @ V2)))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cSUBSET @ (cball @ ((c__comma__ @ V3) @ V2))) @ V4)))))))))))))))))
(TLINDELOF_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((c/__caret__ @ (cCOUNTABLE @ V2)) @ ((c= @ (cUNIONS @ V2)) @ (cUNIONS @ V1))))))))))))
(TINTERS_FACES_FINITE_ALTBOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cface_of @ V2) @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((c/__caret__ @ ((c<= @ (cCARD @ V2)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c= @ (cINTERS @ V2)) @ (cINTERS @ V1)))))))))))))
(Tdivision_points,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdivision_points @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((creal_lt @ ((c$ @ (cinterval_lowerbound @ V0)) @ V3)) @ V4)) @ ((c/__caret__ @ ((creal_lt @ V4) @ ((c$ @ (cinterval_upperbound @ V0)) @ V3))) @ (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c__caret__/ @ ((c= @ ((c$ @ (cinterval_lowerbound @ V5)) @ V3)) @ V4)) @ ((c= @ ((c$ @ (cinterval_upperbound @ V5)) @ V3)) @ V4)))))))))) @ ((c__comma__ @ V3) @ V4))))))))))))))
(Tlocally,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((clocally @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((cIN @ V3) @ V2))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ ((c/__caret__ @ (V1 @ V5)) @ ((c/__caret__ @ ((cIN @ V3) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V5)) @ ((cSUBSET @ V5) @ V2))))))))))))))))))))
(TRELATIVE_INTERIOR_POLYHEDRON_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((c= @ V0) @ ((cINTER @ ((chull @ caffine) @ V0)) @ (cINTERS @ V1)))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ (V2 @ V4)) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V4) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((cdot @ (V2 @ V4)) @ V6)) @ (V3 @ V4))) @ V6))))))))))) @ (c! @ (^[V4]: ((c==> @ ((cPSUBSET @ V4) @ V1)) @ ((cPSUBSET @ V0) @ ((cINTER @ ((chull @ caffine) @ V0)) @ (cINTERS @ V4)))))))))) @ ((c= @ (crelative_interior @ V0)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V1)) @ ((creal_lt @ ((cdot @ (V2 @ V6)) @ V5)) @ (V3 @ V6))))))) @ V5))))))))))))))))
(TLOCALLY_OPEN_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((clocally @ V1) @ V0)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2))) @ ((clocally @ V1) @ V2)))))))))
(TPARACOMPACT_CLOSED_IN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3))))) @ ((cSUBSET @ V0) @ (cUNIONS @ V1))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V0) @ (cUNIONS @ V3))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cSUBSET @ V4) @ V5))))))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ (c? @ (^[V5]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V5)) @ ((c/__caret__ @ ((cIN @ V4) @ V5)) @ (cFINITE @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V3)) @ (c~ @ ((c= @ ((cINTER @ V7) @ V5)) @ cEMPTY)))) @ V7)))))))))))))))))))))))))
(TDIVISION_SPLIT_LEFT_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V1) @ V0)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V2))) @ ((c= @ ((cINTER @ V3) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_le @ ((c$ @ V7) @ V4)) @ V5)) @ V7))))))) @ ((cINTER @ V2) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_le @ ((c$ @ V7) @ V4)) @ V5)) @ V7)))))))))))))) @ ((c= @ (ccontent @ ((cINTER @ V3) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_le @ ((c$ @ V7) @ V4)) @ V5)) @ V7)))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))))
(TDIVISION_SPLIT_RIGHT_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V1) @ V0)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V2))) @ ((c= @ ((cINTER @ V3) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_ge @ ((c$ @ V7) @ V4)) @ V5)) @ V7))))))) @ ((cINTER @ V2) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_ge @ ((c$ @ V7) @ V4)) @ V5)) @ V7)))))))))))))) @ ((c= @ (ccontent @ ((cINTER @ V3) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_ge @ ((c$ @ V7) @ V4)) @ V5)) @ V7)))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))))
(TDIVISION_COMMON_POINT_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cdivision_of @ V1) @ V0)) @ ((c<= @ (cCARD @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ (ccontent @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((cIN @ V2) @ V4)))) @ V4))))))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV)))))))))))
(TDIVISION_INTER_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V1) @ V0)) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V0))) @ ((cdivision_of @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (c~ @ ((c= @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V5)) @ cEMPTY)))) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V5))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(THOMOTOPIC_WITH_COMPOSE_CONTINUOUS_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((((chomotopic_with @ (^[V7]: (V1 @ ((co @ V7) @ V6)))) @ ((c__comma__ @ V0) @ V3)) @ V4) @ V5)) @ ((c/__caret__ @ ((ccontinuous_on @ V6) @ V2)) @ ((cSUBSET @ ((cIMAGE @ V6) @ V2)) @ V0)))) @ ((((chomotopic_with @ V1) @ ((c__comma__ @ V2) @ V3)) @ ((co @ V4) @ V6)) @ ((co @ V5) @ V6))))))))))))))))))
(THOMOTOPIC_WITH_COMPOSE_CONTINUOUS_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((((chomotopic_with @ (^[V7]: (V1 @ ((co @ V5) @ V7)))) @ ((c__comma__ @ V2) @ V0)) @ V4) @ V6)) @ ((c/__caret__ @ ((ccontinuous_on @ V5) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V5) @ V0)) @ V3)))) @ ((((chomotopic_with @ V1) @ ((c__comma__ @ V2) @ V3)) @ ((co @ V5) @ V4)) @ ((co @ V5) @ V6))))))))))))))))))
(THOMOTOPIC_WITH_SUBSET_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((((chomotopic_with @ V1) @ ((c__comma__ @ V2) @ V0)) @ V4) @ V5)) @ ((cSUBSET @ V0) @ V3))) @ ((((chomotopic_with @ V1) @ ((c__comma__ @ V2) @ V3)) @ V4) @ V5)))))))))))))))
(TOPEN_OPEN_RIGHT_PROJECTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (copen @ V1))) @ (copen @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((cIN @ ((cpastecart @ V4) @ V3)) @ V1))))) @ V3))))))))))))
(TEXISTS_ARC_PSUBSET_SIMPLE_PATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csimple_path @ V1)) @ ((c/__caret__ @ (cclosed @ V0)) @ ((cPSUBSET @ V0) @ (cpath_image @ V1))))) @ (c? @ (^[V2]: ((c/__caret__ @ (carc @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cpath_image @ V2))) @ ((cSUBSET @ (cpath_image @ V2)) @ (cpath_image @ V1))))))))))))
(THOMOTOPIC_PATHS_LINV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((cSUBSET @ (cpath_image @ V1)) @ V0))) @ (((chomotopic_paths @ V0) @ ((c++ @ (creversepath @ V1)) @ V1)) @ (clinepath @ ((c__comma__ @ (cpathfinish @ V1)) @ (cpathfinish @ V1))))))))))
(THOMOTOPIC_PATHS_LID,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((cSUBSET @ (cpath_image @ V1)) @ V0))) @ (((chomotopic_paths @ V0) @ ((c++ @ (clinepath @ ((c__comma__ @ (cpathstart @ V1)) @ (cpathstart @ V1)))) @ V1)) @ V1)))))))
(THOMOTOPIC_PATHS_RINV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((cSUBSET @ (cpath_image @ V1)) @ V0))) @ (((chomotopic_paths @ V0) @ ((c++ @ V1) @ (creversepath @ V1))) @ (clinepath @ ((c__comma__ @ (cpathstart @ V1)) @ (cpathstart @ V1))))))))))
(THOMOTOPIC_NEARBY_LOOPS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))) @ ((c/__caret__ @ (copen @ V0)) @ ((cSUBSET @ (cpath_image @ V1)) @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cpath @ V3)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V3)) @ (cpathstart @ V3))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ (V3 @ V4)) @ (V1 @ V4)))) @ V2))))))) @ (((chomotopic_loops @ V0) @ V1) @ V3)))))))))))))
(THOMOTOPIC_NEARBY_PATHS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ (copen @ V0)) @ ((cSUBSET @ (cpath_image @ V1)) @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cpath @ V3)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V3)) @ (cpathstart @ V1))) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V3)) @ (cpathfinish @ V1))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ (V3 @ V4)) @ (V1 @ V4)))) @ V2)))))))) @ (((chomotopic_paths @ V0) @ V1) @ V3)))))))))))))
(THOMOTOPIC_LOOPS_ADD_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V2)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V2)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V2)) @ (cpathstart @ V2))) @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V1)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))) @ ((c= @ (cpathstart @ V1)) @ (cpathstart @ V2))))))))) @ (((chomotopic_loops @ V0) @ ((c++ @ V2) @ V1)) @ ((c++ @ V1) @ V2))))))))))
(THOMOTOPIC_LOOPS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V1)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V1 @ V3)) @ (V2 @ V3))))))))) @ (((chomotopic_loops @ V0) @ V1) @ V2)))))))))
(THOMOTOPIC_LOOPS_CONJUGATE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V1)) @ V0)) @ ((c/__caret__ @ (cpath @ V2)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V2)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V2))) @ ((c= @ (cpathfinish @ V2)) @ (cpathstart @ V2)))))))) @ (((chomotopic_loops @ V0) @ ((c++ @ V1) @ ((c++ @ V2) @ (creversepath @ V1)))) @ V2)))))))))
(THOMOTOPIC_PATHS_REPARAMETRIZE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V1)) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ ((ccontinuous_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c/__caret__ @ ((c= @ (V3 @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((c= @ (V3 @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V2 @ V4)) @ (V1 @ (V3 @ V4))))))))))))))) @ (((chomotopic_paths @ V0) @ V1) @ V2)))))))))
(THOMOTOPIC_PATHS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V1)) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V1 @ V3)) @ (V2 @ V3)))))))) @ (((chomotopic_paths @ V0) @ V1) @ V2)))))))))
(THOMOTOPIC_PATHS_NEARBY_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ (cpath @ V2)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V2)) @ (cpathstart @ V1))) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V2)) @ (cpathfinish @ V1))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ (c~ @ ((cIN @ V4) @ V0)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ (V2 @ V3)) @ (V1 @ V3)))) @ (cvector_norm @ ((cvector_sub @ (V1 @ V3)) @ V4))))))))))))) @ (((chomotopic_paths @ V0) @ V1) @ V2)))))))))
(THOMOTOPIC_PATHS_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ (cpath @ V2)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V2)) @ (cpathstart @ V1))) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V2)) @ (cpathfinish @ V1))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ (V1 @ V3)) @ (V2 @ V3))) @ cNIL))) @ V0))))))))))) @ (((chomotopic_paths @ V0) @ V1) @ V2)))))))))
(THOMOTOPIC_LOOPS_NEARBY_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ (cpath @ V2)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V2)) @ (cpathstart @ V2))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ (c~ @ ((cIN @ V4) @ V0)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ (V2 @ V3)) @ (V1 @ V3)))) @ (cvector_norm @ ((cvector_sub @ (V1 @ V3)) @ V4))))))))))))) @ (((chomotopic_loops @ V0) @ V1) @ V2)))))))))
(THOMOTOPIC_LOOPS_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ (cpath @ V2)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V2)) @ (cpathstart @ V2))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ (V1 @ V3)) @ (V2 @ V3))) @ cNIL))) @ V0))))))))))) @ (((chomotopic_loops @ V0) @ V1) @ V2)))))))))
(THOMOTOPIC_PATHS_REVERSEPATH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chomotopic_paths @ V0) @ (creversepath @ V1)) @ (creversepath @ V2))) @ (((chomotopic_paths @ V0) @ V1) @ V2)))))))))
(THOMOTOPIC_PATHS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chomotopic_paths @ V0) @ V2) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((ccontinuous_on @ V3) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V3 @ ((cpastecart @ (cvec @ (cNUMERAL @ c_0))) @ V4))) @ (V2 @ V4)))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V3 @ ((cpastecart @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V4))) @ (V1 @ V4)))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c/__caret__ @ ((c= @ (cpathstart @ ((co @ V3) @ (cpastecart @ V4)))) @ (cpathstart @ V2))) @ ((c= @ (cpathfinish @ ((co @ V3) @ (cpastecart @ V4)))) @ (cpathfinish @ V2))))))))))))))))))))
(THOMOTOPIC_LOOPS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chomotopic_loops @ V0) @ V1) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((ccontinuous_on @ V3) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V3 @ ((cpastecart @ (cvec @ (cNUMERAL @ c_0))) @ V4))) @ (V1 @ V4)))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V3 @ ((cpastecart @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V4))) @ (V2 @ V4)))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (cpathfinish @ ((co @ V3) @ (cpastecart @ V4)))) @ (cpathstart @ ((co @ V3) @ (cpastecart @ V4)))))))))))))))))))))
(THOMOTOPIC_PATHS_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V1)) @ V0)) @ ((c/__caret__ @ (cpath @ V2)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V2)) @ V0)) @ ((c/__caret__ @ (cpath @ V3)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V3)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V2))) @ ((c= @ (cpathfinish @ V2)) @ (cpathstart @ V3)))))))))) @ (((chomotopic_paths @ V0) @ ((c++ @ V1) @ ((c++ @ V2) @ V3))) @ ((c++ @ ((c++ @ V1) @ V2)) @ V3))))))))))))
(THOMOTOPIC_PATHS_JOIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chomotopic_paths @ V0) @ V1) @ V3)) @ ((c/__caret__ @ (((chomotopic_paths @ V0) @ V2) @ V4)) @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V2))))) @ (((chomotopic_paths @ V0) @ ((c++ @ V1) @ V2)) @ ((c++ @ V3) @ V4))))))))))))))
(THOMOTOPIC_LOOPS_IMP_PATH_COMPONENT_VALUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chomotopic_loops @ V0) @ V1) @ V2)) @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ (((cpath_component @ V0) @ (V1 @ V3)) @ (V2 @ V3))))))))))))
(TCOVERING_SPACE_LIFT_HOMOTOPIC_PATHS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V4) @ V2)) @ V0)) @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V1)) @ V0)) @ ((c/__caret__ @ (cpath @ V3)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V3)) @ V0)) @ ((c/__caret__ @ (((chomotopic_paths @ V0) @ V1) @ V3)) @ ((c/__caret__ @ (cpath @ V5)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V5)) @ V4)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V2 @ (V5 @ V7))) @ (V1 @ V7)))))) @ ((c/__caret__ @ (cpath @ V6)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V6)) @ V4)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V2 @ (V6 @ V7))) @ (V3 @ V7)))))) @ ((c= @ (cpathstart @ V5)) @ (cpathstart @ V6))))))))))))))) @ (((chomotopic_paths @ V4) @ V5) @ V6)))))))))))))))))
(TCOVERING_SPACE_MONODROMY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V2) @ V3)) @ V0)) @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V1)) @ V0)) @ ((c/__caret__ @ (cpath @ V4)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V4)) @ V0)) @ ((c/__caret__ @ (((chomotopic_paths @ V0) @ V1) @ V4)) @ ((c/__caret__ @ (cpath @ V5)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V5)) @ V2)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V3 @ (V5 @ V7))) @ (V1 @ V7)))))) @ ((c/__caret__ @ (cpath @ V6)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V6)) @ V2)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V3 @ (V6 @ V7))) @ (V4 @ V7)))))) @ ((c= @ (cpathstart @ V5)) @ (cpathstart @ V6))))))))))))))) @ ((c= @ (cpathfinish @ V5)) @ (cpathfinish @ V6))))))))))))))))))
(THOMOTOPIC_LOOPS_SHIFTPATH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chomotopic_loops @ V0) @ V1) @ V3)) @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ (((chomotopic_loops @ V0) @ ((cshiftpath @ V2) @ V1)) @ ((cshiftpath @ V2) @ V3))))))))))))
(TCOVERING_SPACE_LIFT_HOMOTOPIC_PATH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V3) @ V6)) @ V0)) @ ((c/__caret__ @ (((chomotopic_paths @ V0) @ V2) @ V7)) @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V1)) @ V3)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V1)) @ V4)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ V5)) @ (c! @ (^[V8]: ((c==> @ ((cIN @ V8) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V6 @ (V1 @ V8))) @ (V2 @ V8)))))))))))) @ (c? @ (^[V8]: ((c/__caret__ @ (cpath @ V8)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V8)) @ V3)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V8)) @ V4)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V8)) @ V5)) @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V6 @ (V8 @ V9))) @ (V7 @ V9)))))))))))))))))))))))))))))
(TPROPER_MAP_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V2)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V6) @ V0)) @ (ccompact @ V6))) @ (ccompact @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V2)) @ ((cIN @ (V4 @ V8)) @ V6))) @ V8)))))))))) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V6) @ V1)) @ (ccompact @ V6))) @ (ccompact @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V0)) @ ((cIN @ (V3 @ V8)) @ V6))) @ V8)))))))))))) @ ((c==> @ ((c/__caret__ @ ((cSUBSET @ V5) @ V1)) @ (ccompact @ V5))) @ (ccompact @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V2)) @ ((cIN @ (((co @ V3) @ V4) @ V7)) @ V5))) @ V7)))))))))))))))))))))
(TLIFT_TO_QUOTIENT_SPACE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V4) @ V2)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cSUBSET @ V5) @ V0)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V2)) @ ((cIN @ (V4 @ V7)) @ V5))) @ V7))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)))))) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V3) @ V2)) @ V1)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ ((c= @ (V4 @ V5)) @ (V4 @ V6))))) @ ((c= @ (V3 @ V5)) @ (V3 @ V6)))))))))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V5) @ V0)) @ V1)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((c= @ (V3 @ V6)) @ (V5 @ (V4 @ V6))))))))))))))))))))))
(TCONTINUOUS_ATTAINS_SUP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((ccontinuous_on @ ((co @ clift) @ V1)) @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (V1 @ V3)) @ (V1 @ V2))))))))))))))
(TCONTINUOUS_ATTAINS_INF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((ccontinuous_on @ ((co @ clift) @ V1)) @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (V1 @ V2)) @ (V1 @ V3))))))))))))))
(TCONVEX_ON_JENSEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cconvex @ V0)) @ ((c= @ ((cconvex_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ V2))) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V3 @ V5))) @ ((cIN @ (V4 @ V5)) @ V0)))))) @ ((c= @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((creal_le @ (V1 @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ (^[V5]: ((c% @ (V3 @ V5)) @ (V4 @ V5)))))) @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ (^[V5]: ((creal_mul @ (V3 @ V5)) @ (V1 @ (V4 @ V5))))))))))))))))))))
(Tepigraph,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cepigraph @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ (cfstcart @ V3)) @ V0)) @ ((creal_le @ (V1 @ (cfstcart @ V3))) @ (cdrop @ (csndcart @ V3))))) @ V3)))))))))))
(TCONVEX_ON_LEFT_SECANT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cconvex_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ (copen_segment @ ((c__comma__ @ V2) @ V3)))))) @ ((creal_le @ ((creal_div @ ((creal_sub @ (V1 @ V4)) @ (V1 @ V2))) @ (cvector_norm @ ((cvector_sub @ V4) @ V2)))) @ ((creal_div @ ((creal_sub @ (V1 @ V3)) @ (V1 @ V2))) @ (cvector_norm @ ((cvector_sub @ V3) @ V2)))))))))))))))))
(TCONVEX_ON_RIGHT_SECANT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cconvex_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ (copen_segment @ ((c__comma__ @ V2) @ V3)))))) @ ((creal_le @ ((creal_div @ ((creal_sub @ (V1 @ V3)) @ (V1 @ V2))) @ (cvector_norm @ ((cvector_sub @ V3) @ V2)))) @ ((creal_div @ ((creal_sub @ (V1 @ V3)) @ (V1 @ V4))) @ (cvector_norm @ ((cvector_sub @ V3) @ V4)))))))))))))))))
(TCONVEX_ON_LEFT_SECANT_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cconvex_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))) @ ((creal_le @ ((creal_mul @ ((creal_sub @ (V1 @ V4)) @ (V1 @ V2))) @ (cvector_norm @ ((cvector_sub @ V3) @ V2)))) @ ((creal_mul @ ((creal_sub @ (V1 @ V3)) @ (V1 @ V2))) @ (cvector_norm @ ((cvector_sub @ V4) @ V2)))))))))))))))))
(TCONVEX_ON_RIGHT_SECANT_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cconvex_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))) @ ((creal_le @ ((creal_mul @ ((creal_sub @ (V1 @ V3)) @ (V1 @ V2))) @ (cvector_norm @ ((cvector_sub @ V3) @ V4)))) @ ((creal_mul @ ((creal_sub @ (V1 @ V3)) @ (V1 @ V4))) @ (cvector_norm @ ((cvector_sub @ V3) @ V2)))))))))))))))))
(TCONVEX_ON_EPIGRAPH_SLICE_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V1) @ V0)) @ (cconvex @ V0))) @ (cconvex @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((creal_lt @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TCONVEX_ON_EPIGRAPH_SLICE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V1) @ V0)) @ (cconvex @ V0))) @ (cconvex @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((creal_le @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TAFFINE_HULL_EXPLICIT_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V0))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V1 @ V4)) @ V4)))) @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V2 @ V4)) @ V4)))))))) @ ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ (V2 @ V3)))))))))))))
(TCONVEX_ON_SECANT_DERIVATIVE_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V4) @ V3)) @ cNIL))) @ V0)) @ (((chas_derivative @ ((co @ clift) @ V1)) @ ((co @ clift) @ V2)) @ ((cwithin @ (cat @ V3)) @ V0))))) @ ((creal_le @ ((creal_sub @ (V1 @ V3)) @ (V1 @ V4))) @ (V2 @ ((cvector_sub @ V3) @ V4)))))))))))))))
(TCONVEX_ON_SECANT_DERIVATIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (((chas_derivative @ ((co @ clift) @ V1)) @ ((co @ clift) @ (V2 @ V3))) @ ((cwithin @ (cat @ V3)) @ V0))))))) @ ((c= @ ((cconvex_on @ V1) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V0))) @ ((creal_le @ ((creal_sub @ (V1 @ V4)) @ (V1 @ V3))) @ ((V2 @ V4) @ ((cvector_sub @ V4) @ V3)))))))))))))))))
(TCONTINUOUS_ON_COMPACT_SURFACE_PROJECTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ ((cDELETE @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ (cconic @ V2)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V3) @ ((cDELETE @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((cIN @ ((c% @ V4) @ V3)) @ V0))) @ ((c= @ (V1 @ V3)) @ V4))))))))))) @ ((ccontinuous_on @ (^[V3]: ((c% @ (V1 @ V3)) @ V3))) @ ((cDELETE @ V2) @ (cvec @ (cNUMERAL @ c_0))))))))))))
(TCONVEX_ON_CONVEX_HULL_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V1) @ ((chull @ cconvex) @ V0))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ (V1 @ V4)) @ V3)))))) @ ((c==> @ ((cIN @ V2) @ ((chull @ cconvex) @ V0))) @ ((creal_le @ (V1 @ V2)) @ V3))))))))))))
(TCONVEX_ON_DERIVATIVE_SECANT_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V4) @ V2)) @ cNIL))) @ V0)) @ (((chas_derivative @ ((co @ clift) @ V3)) @ ((co @ clift) @ V1)) @ ((cwithin @ (cat @ V4)) @ V0))))) @ ((creal_le @ (V1 @ ((cvector_sub @ V2) @ V4))) @ ((creal_sub @ (V3 @ V2)) @ (V3 @ V4)))))))))))))))
(TCONVEX_ON_DERIVATIVE_SECANT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (((chas_derivative @ ((co @ clift) @ V2)) @ ((co @ clift) @ (V1 @ V3))) @ ((cwithin @ (cat @ V3)) @ V0))))))) @ ((c= @ ((cconvex_on @ V2) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V0))) @ ((creal_le @ ((V1 @ V3) @ ((cvector_sub @ V4) @ V3))) @ ((creal_sub @ (V2 @ V4)) @ (V2 @ V3)))))))))))))))))
(TINVERSE_FUNCTION_C1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ (((chas_derivative @ V3) @ (V1 @ V4)) @ (cat @ V4)))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((creal_lt @ (cdistance @ ((c__comma__ @ V2) @ V6))) @ V5)) @ ((creal_lt @ (conorm @ (^[V7]: ((cvector_sub @ ((V1 @ V6) @ V7)) @ ((V1 @ V2) @ V7))))) @ V4))))))))))) @ (c~ @ ((c= @ (cdet @ (cmatrix @ (V1 @ V2)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ (copen @ V4)) @ ((c/__caret__ @ ((cIN @ V2) @ V4)) @ ((c/__caret__ @ (copen @ V5)) @ ((c/__caret__ @ ((cIN @ (V3 @ V2)) @ V5)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V4)) @ ((c= @ (V6 @ (V3 @ V7))) @ V7))))) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V5)) @ ((c= @ (V3 @ (V6 @ V7))) @ V7))))) @ ((cdifferentiable_on @ V6) @ V5)))))))))))))))))))))))
(TCONNECTED_EQUIVALENCE_RELATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V4))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V6))) @ ((V1 @ V4) @ V6))))))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ (c? @ (^[V5]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((c/__caret__ @ ((cIN @ V4) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V5)) @ ((V1 @ V4) @ V6))))))))))))))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V0))) @ ((V1 @ V2) @ V3))))))))))))
(TCONNECTED_COMPONENT_EQUIVALENCE_RELATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V4))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V6))) @ ((V1 @ V4) @ V6))))))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ (c? @ (^[V5]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((c/__caret__ @ ((cIN @ V4) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V5)) @ ((V1 @ V4) @ V6)))))))))))))) @ ((c==> @ (((cconnected_component @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TINJECTIVE_INTO_1D_EQ_HOMEOMORPHISM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (cpath_connected @ V0))) @ ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))) @ (c? @ (^[V2]: ((chomeomorphism @ ((c__comma__ @ V0) @ ((cIMAGE @ V1) @ V0))) @ ((c__comma__ @ V1) @ V2)))))))))))
(TINJECTIVE_INTO_1D_IMP_OPEN_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ (cpath_connected @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V3)) @ (V1 @ V4))))) @ ((c= @ V3) @ V4))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V1) @ V0))) @ ((cIMAGE @ V1) @ V2))))))))))
(TTIETZE_OPEN_INTERVAL_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (cdrop @ V3)) @ (cdrop @ V4))) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ (copen_interval @ ((c__comma__ @ V3) @ V4)))))))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ V2)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((c= @ (V5 @ V6)) @ (V1 @ V6)))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((cIN @ (V5 @ V6)) @ (copen_interval @ ((c__comma__ @ V3) @ V4))))))))))))))))))))))
(TTIETZE_CLOSED_INTERVAL_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ V2)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((c= @ (V5 @ V6)) @ (V1 @ V6)))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((cIN @ (V5 @ V6)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))))))))))))))
(TMEASURABLE_ON_COMPOSE_CONTINUOUS_CLOSED_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ ((cmeasurable_on @ V2) @ cUNIV)) @ ((c/__caret__ @ (c! @ (^[V3]: ((cIN @ (V2 @ V3)) @ V0)))) @ ((ccontinuous_on @ V1) @ V0))))) @ ((cmeasurable_on @ ((co @ V1) @ V2)) @ cUNIV)))))))))
(TMEASURABLE_ON_COMPOSE_CONTINUOUS_CLOSED_SET_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ ((cmeasurable_on @ V2) @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: ((cIN @ (V2 @ V4)) @ V0)))) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ ((c= @ (V1 @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))))))) @ ((cmeasurable_on @ ((co @ V1) @ V2)) @ V3)))))))))))
(TBROUWER_ABSOLUTE_RETRACT_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V0) @ cUNIV)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0)) @ (cbounded @ ((cIMAGE @ V1) @ V0)))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V2))))))))))
(TIDEMPOTENT_IMP_RETRACTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ (V1 @ V2))) @ (V1 @ V2)))))))) @ ((cretraction @ ((c__comma__ @ V0) @ ((cIMAGE @ V1) @ V0))) @ V1)))))))
(TSELF_ADJOINT_HAS_EIGENVECTOR_IN_SUBSPACE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ ((c= @ (cadjoint @ V1)) @ V1)) @ ((c/__caret__ @ (csubspace @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ cEMPTY)))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cIN @ (V1 @ V2)) @ V0))))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (V1 @ V2)) @ ((c% @ V3) @ V2))))))))))))))
(TBROUWER_ABSOLUTE_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ ((cretract_of @ V0) @ cUNIV)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V2))))))))))
(TISOMETRY_IMP_HOMEOMORPHISM_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V0))) @ ((c= @ (cdistance @ ((c__comma__ @ (V1 @ V2)) @ (V1 @ V3)))) @ (cdistance @ ((c__comma__ @ V2) @ V3))))))))))) @ (c? @ (^[V2]: ((chomeomorphism @ ((c__comma__ @ V0) @ V0)) @ ((c__comma__ @ V1) @ V2))))))))))
(TEDELSTEIN_FIX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V1 @ V2)) @ (V1 @ V3)))) @ (cdistance @ ((c__comma__ @ V2) @ V3)))))))))))) @ (c?! @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V2))))))))))
(TBROUWER_INESSENTIAL_ANR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (cANR @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0)) @ (c? @ (^[V2]: ((((chomotopic_with @ (^[V3]: cT)) @ ((c__comma__ @ V0) @ V0)) @ V1) @ (^[V3]: V2)))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V2))))))))))
(TBROUWER_WEAK,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ (cinterior @ V0)) @ cEMPTY))) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0)))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V2))))))))))
(TBROUWER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0)))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V2))))))))))
(TBROUWER_CONTRACTIBLE_ANR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (ccontractible @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (cANR @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V2))))))))))
(TBROUWER_AR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (cAR @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V2))))))))))
(TROTHE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ (cbounded @ ((cIMAGE @ V1) @ V0))) @ ((cSUBSET @ ((cIMAGE @ V1) @ (cfrontier @ V0))) @ V0))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V2))))))))))
(THAS_MEASURE_LINEAR_IMAGE_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ ((chas_measure @ V0) @ V2))) @ ((chas_measure @ ((cIMAGE @ V1) @ V0)) @ ((creal_mul @ (creal_abs @ (cdet @ (cmatrix @ V1)))) @ V2))))))))))
(THAS_DERIVATIVE_INVERSE_STRONG_X,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ ((cIN @ (V3 @ V5)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((c= @ (V3 @ (V2 @ V6))) @ V6))))) @ ((c/__caret__ @ (((chas_derivative @ V2) @ V1) @ (cat @ (V3 @ V5)))) @ ((c/__caret__ @ ((c= @ ((co @ V1) @ V4)) @ cI)) @ ((c= @ (V2 @ (V3 @ V5))) @ V5)))))))) @ (((chas_derivative @ V3) @ V4) @ (cat @ V5))))))))))))))))
(THAS_DERIVATIVE_INVERSE_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((c= @ (V2 @ (V4 @ V6))) @ V6))))) @ ((c/__caret__ @ (((chas_derivative @ V4) @ V1) @ (cat @ V5))) @ ((c= @ ((co @ V1) @ V3)) @ cI))))))) @ (((chas_derivative @ V2) @ V3) @ (cat @ (V4 @ V5)))))))))))))))))
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(TCONTINUOUS_ON_CLOSURE_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ (cclosure @ V0))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((creal_le @ ((c$ @ (V1 @ V5)) @ V3)) @ V4))))) @ ((cIN @ V2) @ (cclosure @ V0))))) @ ((creal_le @ ((c$ @ (V1 @ V2)) @ V3)) @ V4)))))))))))))
(TPRESERVES_LEBESGUE_MEASURABLE_IMP_PRESERVES_NEGLIGIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnegligible @ V3)) @ ((cSUBSET @ V3) @ V0))) @ (clebesgue_measurable @ ((cIMAGE @ V1) @ V3)))))) @ ((c==> @ ((c/__caret__ @ (cnegligible @ V2)) @ ((cSUBSET @ V2) @ V0))) @ (cnegligible @ ((cIMAGE @ V1) @ V2)))))))))))
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(TCONTINUOUS_ON_SEQUENTIALLY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((cIN @ (V2 @ V4)) @ V0)))) @ (((c--> @ V2) @ V3) @ csequentially)))) @ (((c--> @ ((co @ V1) @ V2)) @ (V1 @ V3)) @ csequentially))))))))))))
(TCONTINUOUS_WITHIN_SEQUENTIALLY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccontinuous @ V1) @ ((cwithin @ (cat @ V2)) @ V0))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((cIN @ (V3 @ V4)) @ V0)))) @ (((c--> @ V3) @ V2) @ csequentially))) @ (((c--> @ ((co @ V1) @ V3)) @ (V1 @ V2)) @ csequentially))))))))))))
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(THAUSDIST_POS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (chausdist @ ((c__comma__ @ V0) @ V1))))))))
(TCONTINUOUS_ON_LIFT_SETDIST,(c! @ (^[V0]: (c! @ (^[V1]: ((ccontinuous_on @ (^[V2]: (clift @ (csetdist @ ((c__comma__ @ ((cINSERT @ V2) @ cEMPTY)) @ V0))))) @ V1))))))
(TUNION_INTERIOR_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ ((cUNION @ (cinterior @ V0)) @ (cinterior @ V1))) @ (cinterior @ ((cUNION @ V0) @ V1))))))))
(TDIFF_CLOSURE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ ((cDIFF @ (cclosure @ V0)) @ (cclosure @ V1))) @ (cclosure @ ((cDIFF @ V0) @ V1))))))))
(TFRONTIER_UNION_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ (cfrontier @ ((cUNION @ V0) @ V1))) @ ((cUNION @ (cfrontier @ V0)) @ (cfrontier @ V1))))))))
(TFRONTIER_INTER_SUBSET_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ (cfrontier @ ((cINTER @ V0) @ V1))) @ ((cUNION @ ((cINTER @ (cclosure @ V0)) @ (cfrontier @ V1))) @ ((cINTER @ (cfrontier @ V0)) @ (cclosure @ V1)))))))))
(TCLOSED_IN_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cretract_of @ V1) @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)))))))
(TORTHOGONAL_EXTENSION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpairwise @ corthogonal) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cpairwise @ corthogonal) @ ((cUNION @ V0) @ V2))) @ ((c= @ (cspan @ ((cUNION @ V0) @ V2))) @ (cspan @ ((cUNION @ V0) @ V1))))))))))))
(TORTHOGONAL_EXTENSION_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpairwise @ corthogonal) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cDISJOINT @ V2) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ V0))) @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ ((cUNION @ V0) @ V2))) @ ((c= @ (cspan @ ((cUNION @ V0) @ V2))) @ (cspan @ ((cUNION @ V0) @ V1)))))))))))))
(TCOUNTABLE_PATH_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ cpath_connected) @ V1)) @ (cCOUNTABLE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cpath_component @ V1) @ V3)))))))))))))
(TCOUNTABLE_CONNECTED_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ cconnected) @ V1)) @ (cCOUNTABLE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cconnected_component @ V1) @ V3)))))))))))))
(TOPEN_IN_LOCALLY_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ ccompact) @ V0)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V2)) @ ((cSUBSET @ V2) @ V0))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ ((cINTER @ V2) @ V1)))))))))))))
(TOPEN_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c__caret__/ @ (copen @ V0)) @ (copen @ V1))) @ (copen @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TINTERIOR_UNION_EQ_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c__caret__/ @ (cclosed @ V0)) @ (cclosed @ V1))) @ ((c= @ ((c= @ (cinterior @ ((cUNION @ V0) @ V1))) @ cEMPTY)) @ ((c/__caret__ @ ((c= @ (cinterior @ V0)) @ cEMPTY)) @ ((c= @ (cinterior @ V1)) @ cEMPTY)))))))))
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(TSETDIST_EQ_0_BOUNDED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c__caret__/ @ (cbounded @ V0)) @ (cbounded @ V1))) @ ((c= @ ((c= @ (csetdist @ ((c__comma__ @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ (c~ @ ((c= @ ((cINTER @ (cclosure @ V0)) @ (cclosure @ V1))) @ cEMPTY)))))))))))
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(TINSIDE_INSIDE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ (cinside @ V1))) @ ((cSUBSET @ ((cDIFF @ (cinside @ V0)) @ V1)) @ (cinside @ V1))))))))
(TAFF_DIM_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ V1)) @ ((cint_le @ (caff_dim @ V0)) @ (caff_dim @ V1))))))))
(TDIM_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ V1)) @ ((c<= @ (cdim @ V0)) @ (cdim @ V1))))))))
(TORTHOGONAL_TO_SUBSPACE_EXISTS_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cPSUBSET @ (cspan @ V1)) @ (cspan @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((cIN @ V2) @ (cspan @ V0))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (cspan @ V1))) @ ((corthogonal @ V2) @ V3))))))))))))))
(TCLOSED_IN_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ (ccomponents @ V0))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)))))))
(TIN_COMPONENTS_UNIONS_COMPLEMENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ (ccomponents @ V0))) @ ((c= @ ((cDIFF @ V0) @ V1)) @ (cUNIONS @ ((cDELETE @ (ccomponents @ V0)) @ V1)))))))))
(TFRONTIER_OF_COMPONENTS_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V0) @ (ccomponents @ V1))) @ ((cSUBSET @ (cfrontier @ V0)) @ (cfrontier @ V1))))))))
(TFRONTIER_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ ((cINTER @ (cclosure @ V0)) @ (cclosure @ V1))) @ cEMPTY)) @ ((c= @ (cfrontier @ ((cUNION @ V0) @ V1))) @ ((cUNION @ (cfrontier @ V0)) @ (cfrontier @ V1)))))))))
(TABSOLUTE_RETRACT_FROM_UNION_AND_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cretract_of @ ((cUNION @ V1) @ V0)) @ cUNIV)) @ ((c/__caret__ @ ((cretract_of @ ((cINTER @ V1) @ V0)) @ cUNIV)) @ ((c/__caret__ @ (cclosed @ V1)) @ (cclosed @ V0))))) @ ((cretract_of @ V1) @ cUNIV)))))))
(TRETRACT_OF_LOCALLY_PATH_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V1) @ V0)) @ ((clocally @ cpath_connected) @ V0))) @ ((clocally @ cpath_connected) @ V1)))))))
(TRETRACT_OF_LOCALLY_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V1) @ V0)) @ ((clocally @ cconnected) @ V0))) @ ((clocally @ cconnected) @ V1)))))))
(TABSOLUTE_RETRACT_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V0) @ cUNIV)) @ ((c/__caret__ @ ((cretract_of @ V1) @ cUNIV)) @ ((cretract_of @ ((cINTER @ V0) @ V1)) @ cUNIV)))) @ ((cretract_of @ ((cUNION @ V0) @ V1)) @ cUNIV)))))))
(TORTHONORMAL_EXTENSION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cDISJOINT @ V2) @ V0)) @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ ((cUNION @ V0) @ V2))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c= @ (cvector_norm @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((c= @ (cspan @ ((cUNION @ V0) @ V2))) @ (cspan @ ((cUNION @ V0) @ V1))))))))))))))
(TAFFINE_HULL_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((chull @ caffine) @ V1))) @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((chull @ caffine) @ V0)) @ ((chull @ caffine) @ V1))))))))
(TSIMPLY_CONNECTED_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V0)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V1)) @ ((c/__caret__ @ (csimply_connected @ V0)) @ ((c/__caret__ @ (csimply_connected @ V1)) @ ((c/__caret__ @ (cpath_connected @ ((cINTER @ V0) @ V1))) @ (c~ @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)))))))) @ (csimply_connected @ ((cUNION @ V0) @ V1))))))))
(TLOCALLY_COMPACT_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((clocally @ ccompact) @ V0))) @ ((clocally @ ccompact) @ V1)))))))
(TENR_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ (cENR @ V0))) @ (cENR @ V1)))))))
(TANR_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ (cANR @ V0))) @ (cANR @ V1)))))))
(TINFINITE_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((climit_point_of @ V2) @ V0)))))) @ (cINFINITE @ V1)))))))
(TLOCALLY_PATH_CONNECTED_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ cpath_connected) @ V0)) @ ((cIN @ V1) @ (ccomponents @ V0)))) @ ((clocally @ cpath_connected) @ V1)))))))
(TOPEN_IN_COMPONENTS_LOCALLY_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ cconnected) @ V0)) @ ((cIN @ V1) @ (ccomponents @ V0)))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)))))))
(TLOCALLY_CONNECTED_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ cconnected) @ V0)) @ ((cIN @ V1) @ (ccomponents @ V0)))) @ ((clocally @ cconnected) @ V1)))))))
(TCARD_EQ_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ cconnected) @ V0)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((climit_point_of @ V2) @ V0))))))) @ ((c=_c @ V1) @ cUNIV)))))))
(TSURA_BURA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ ccompact) @ V1)) @ ((c/__caret__ @ ((cIN @ V0) @ (ccomponents @ V1))) @ (ccompact @ V0)))) @ ((c= @ V0) @ (cINTERS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V3)) @ ((c/__caret__ @ (ccompact @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)))) @ V3)))))))))))))
(TRETRACT_OF_LOCALLY_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ ccompact) @ V0)) @ ((cretract_of @ V1) @ V0))) @ ((clocally @ ccompact) @ V1)))))))
(TLOCALLY_COMPACT_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ ccompact) @ V0)) @ ((clocally @ ccompact) @ V1))) @ ((clocally @ ccompact) @ ((cINTER @ V0) @ V1))))))))
(TLOCALLY_COMPACT_OPEN_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ ccompact) @ V0)) @ ((c/__caret__ @ ((clocally @ ccompact) @ V1)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V0)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V1))))) @ ((clocally @ ccompact) @ ((cUNION @ V0) @ V1))))))))
(TLOCALLY_COMPACT_CLOSED_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ ccompact) @ V0)) @ ((c/__caret__ @ ((clocally @ ccompact) @ V1)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V1))))) @ ((clocally @ ccompact) @ ((cUNION @ V0) @ V1))))))))
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(TFACE_OF_SUBSET_RELATIVE_FRONTIER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ (c~ @ ((c= @ V0) @ V1)))) @ ((cSUBSET @ V0) @ (crelative_frontier @ V1))))))))
(TFACE_OF_DISJOINT_RELATIVE_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ (c~ @ ((c= @ V0) @ V1)))) @ ((c= @ ((cINTER @ V0) @ (crelative_interior @ V1))) @ cEMPTY)))))))
(TFACE_OF_DISJOINT_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ (c~ @ ((c= @ V0) @ V1)))) @ ((c= @ ((cINTER @ V0) @ (cinterior @ V1))) @ cEMPTY)))))))
(TENR_FROM_UNION_AND_INTER_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V1) @ V0))) @ V1)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V1) @ V0))) @ V0)) @ ((c/__caret__ @ (cENR @ ((cUNION @ V1) @ V0))) @ (cENR @ ((cINTER @ V1) @ V0)))))) @ (cENR @ V1)))))))
(TAR_FROM_UNION_AND_INTER_LOCAL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V1) @ V0))) @ V1)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V1) @ V0))) @ V0)) @ ((c/__caret__ @ (cAR @ ((cUNION @ V1) @ V0))) @ (cAR @ ((cINTER @ V1) @ V0)))))) @ (cAR @ V1)))))))
(TANR_FROM_UNION_AND_INTER_LOCAL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V1) @ V0))) @ V1)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V1) @ V0))) @ V0)) @ ((c/__caret__ @ (cANR @ ((cUNION @ V1) @ V0))) @ (cANR @ ((cINTER @ V1) @ V0)))))) @ (cANR @ V1)))))))
(TENR_CLOSED_UNION_LOCAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V0)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V1)) @ ((c/__caret__ @ (cENR @ V0)) @ ((c/__caret__ @ (cENR @ V1)) @ (cENR @ ((cINTER @ V0) @ V1))))))) @ (cENR @ ((cUNION @ V0) @ V1))))))))
(TAR_FROM_UNION_AND_INTER_LOCAL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V0)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V1)) @ ((c/__caret__ @ (cAR @ ((cUNION @ V0) @ V1))) @ (cAR @ ((cINTER @ V0) @ V1)))))) @ (cAR @ V1)))))))
(TAR_CLOSED_UNION_LOCAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V0)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V1)) @ ((c/__caret__ @ (cAR @ V0)) @ ((c/__caret__ @ (cAR @ V1)) @ (cAR @ ((cINTER @ V0) @ V1))))))) @ (cAR @ ((cUNION @ V0) @ V1))))))))
(TANR_FROM_UNION_AND_INTER_LOCAL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V0)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V1)) @ ((c/__caret__ @ (cANR @ ((cUNION @ V0) @ V1))) @ (cANR @ ((cINTER @ V0) @ V1)))))) @ (cANR @ V1)))))))
(TANR_CLOSED_UNION_LOCAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V0)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V0) @ V1))) @ V1)) @ ((c/__caret__ @ (cANR @ V0)) @ ((c/__caret__ @ (cANR @ V1)) @ (cANR @ ((cINTER @ V0) @ V1))))))) @ (cANR @ ((cUNION @ V0) @ V1))))))))
(TCLOPEN_IN_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ ((c/__caret__ @ (cconnected @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))))) @ ((cIN @ V0) @ (ccomponents @ V1))))))))
(TABSOLUTE_RETRACT_CONTRACTIBLE_ANR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ ((c/__caret__ @ (ccontractible @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (cANR @ V0))))) @ ((cretract_of @ V0) @ V1)))))))
(TCLOPEN_UNIONS_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ (ccomponents @ V0))) @ ((c= @ V1) @ (cUNIONS @ V2)))))))))))
(TLOCALLY_COMPACT_CLOSED_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((clocally @ ccompact) @ V0))) @ ((clocally @ ccompact) @ V1)))))))
(TEXISTS_COMPONENT_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (cconnected @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ (ccomponents @ V0))) @ ((cSUBSET @ V1) @ V2))))))))))
(TMAXIMAL_AFFINE_INDEPENDENT_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V1))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ (c~ @ (caffine_dependent @ V2))))) @ ((c= @ V2) @ V1))))))) @ ((cSUBSET @ V0) @ ((chull @ caffine) @ V1))))))))
(TCARD_GE_DIM_INDEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cindependent @ V1)) @ ((c<= @ (cdim @ V0)) @ (cCARD @ V1))))) @ ((cSUBSET @ V0) @ (cspan @ V1))))))))
(TSPANNING_SUBSET_INDEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cindependent @ V0)) @ ((cSUBSET @ V0) @ (cspan @ V1))))) @ ((c= @ V0) @ V1)))))))
(TMINIMAL_CONTINUUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (ccompact @ V0)) @ (cconnected @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ (ccompact @ V2)) @ ((c/__caret__ @ (cconnected @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V3)) @ ((c/__caret__ @ (ccompact @ V3)) @ (cconnected @ V3))))) @ ((c= @ V3) @ V2))))))))))))))))
(TCONTENT_0_SUBSET_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cbounded @ V0)) @ ((c= @ (ccontent @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((c= @ (ccontent @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TOPEN_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (copen @ V1))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)))))))
(TINDEPENDENT_CARD_LE_DIM_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (cindependent @ V1))) @ (cFINITE @ V1)))))))
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(TCARD_LE_DIM_SPANNING,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cspan @ V1))) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c<= @ (cCARD @ V1)) @ (cdim @ V0))))) @ (cindependent @ V1)))))))
(TSPAN_CARD_GE_DIM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cspan @ V1))) @ (cFINITE @ V1))) @ ((c<= @ (cdim @ V0)) @ (cCARD @ V1))))))))
(TAFF_DIM_EQ_AFFINE_HULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((cint_le @ (caff_dim @ V1)) @ (caff_dim @ V0)))) @ ((c= @ ((chull @ caffine) @ V0)) @ ((chull @ caffine) @ V1))))))))
(TDIM_EQ_SPAN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c<= @ (cdim @ V1)) @ (cdim @ V0)))) @ ((c= @ (cspan @ V0)) @ (cspan @ V1))))))))
(TSPAN_SUBSET_SUBSPACE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ (csubspace @ V1))) @ ((cSUBSET @ (cspan @ V0)) @ V1)))))))
(TINDEPENDENT_CARD_LE_DIM_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ (cindependent @ V0))) @ ((c<= @ (cCARD @ V0)) @ (cdim @ V1))))))))
(TMAXIMAL_INDEPENDENT_SUBSET_EXTEND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ (cindependent @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((c/__caret__ @ (cindependent @ V2)) @ ((cSUBSET @ V1) @ (cspan @ V2)))))))))))))
(TDIAMETER_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ (cbounded @ V1))) @ ((creal_le @ (cdiameter @ V0)) @ (cdiameter @ V1))))))))
(TAFF_DIM_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ ((chull @ caffine) @ V1)) @ ((chull @ caffine) @ V0))) @ (c~ @ (caffine_dependent @ V1)))) @ ((c= @ (caff_dim @ V0)) @ ((cint_sub @ (cint_of_num @ (cCARD @ V1))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TSEPARATION_CLOSURES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ ((cINTER @ V0) @ (cclosure @ V1))) @ cEMPTY)) @ ((c= @ ((cINTER @ V1) @ (cclosure @ V0))) @ cEMPTY))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cDISJOINT @ V2) @ V3)) @ ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ (copen @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((cSUBSET @ V1) @ V3)))))))))))))))
(TREGULAR_OPEN_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (cinterior @ (cclosure @ V0))) @ V0)) @ ((c= @ (cinterior @ (cclosure @ V1))) @ V1))) @ ((c= @ (cinterior @ (cclosure @ ((cINTER @ V0) @ V1)))) @ ((cINTER @ V0) @ V1))))))))
(TREGULAR_CLOSED_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (cclosure @ (cinterior @ V0))) @ V0)) @ ((c= @ (cclosure @ (cinterior @ V1))) @ V1))) @ ((c= @ (cclosure @ (cinterior @ ((cUNION @ V0) @ V1)))) @ ((cUNION @ V0) @ V1))))))))
(TPATH_CONNECTED_OPEN_DIFF_CARD_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (cconnected @ V0)) @ ((c<_c @ V1) @ cUNIV))))) @ (cpath_connected @ ((cDIFF @ V0) @ V1))))))))
(TCONNECTED_OPEN_DIFF_CARD_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (cconnected @ V0)) @ ((c<_c @ V1) @ cUNIV))))) @ (cconnected @ ((cDIFF @ V0) @ V1))))))))
(TPATH_CONNECTED_OPEN_DIFF_COUNTABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (cconnected @ V0)) @ (cCOUNTABLE @ V1))))) @ (cpath_connected @ ((cDIFF @ V0) @ V1))))))))
(TCONNECTED_OPEN_DIFF_COUNTABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (cconnected @ V0)) @ (cCOUNTABLE @ V1))))) @ (cconnected @ ((cDIFF @ V0) @ V1))))))))
(TBOUNDED_UNIQUE_OUTSIDE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (cbounded @ V1))) @ ((c= @ ((c/__caret__ @ ((cIN @ V0) @ (ccomponents @ ((cDIFF @ cUNIV) @ V1)))) @ (c~ @ (cbounded @ V0)))) @ ((c= @ V0) @ (coutside @ V1)))))))))
(TDIM_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ (csubspace @ V1)))) @ ((c= @ (cdim @ V0)) @ (cdim @ V1))))))))
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(TSPAN_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ ((cUNION @ V0) @ V1))))) @ ((c= @ (cspan @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ (cspan @ V0))) @ ((cIN @ V4) @ (cspan @ V1)))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TUNBOUNDED_INTER_COBOUNDED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ (cbounded @ V0))) @ (cbounded @ ((cDIFF @ cUNIV) @ V1)))) @ (c~ @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY))))))))
(TAFFINE_INDEPENDENT_CONVEX_AFFINE_HULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V1))) @ ((cSUBSET @ V0) @ V1))) @ ((c= @ ((chull @ cconvex) @ V0)) @ ((cINTER @ ((chull @ caffine) @ V0)) @ ((chull @ cconvex) @ V1)))))))))
(TEXTEND_TO_AFFINE_BASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V0))) @ ((cSUBSET @ V0) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ (c~ @ (caffine_dependent @ V2))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((c= @ ((chull @ caffine) @ V2)) @ ((chull @ caffine) @ V1)))))))))))))
(TSUBSPACE_UNION_CHAIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V1)) @ ((c/__caret__ @ (csubspace @ V0)) @ (csubspace @ ((cUNION @ V1) @ V0))))) @ ((c__caret__/ @ ((cSUBSET @ V1) @ V0)) @ ((cSUBSET @ V0) @ V1))))))))
(TDIM_SUBSPACE_ORTHOGONAL_TO_VECTORS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V0)) @ ((c/__caret__ @ (csubspace @ V1)) @ ((cSUBSET @ V0) @ V1)))) @ ((c= @ ((c+ @ (cdim @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((corthogonal @ V4) @ V3)))))) @ V3))))))) @ (cdim @ V0))) @ (cdim @ V1))))))))
(TORTHOGONAL_TRANSFORMATION_ONTO_SUBSPACE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V0)) @ ((c/__caret__ @ (csubspace @ V1)) @ ((c= @ (cdim @ V0)) @ (cdim @ V1))))) @ (c? @ (^[V2]: ((c/__caret__ @ (corthogonal_transformation @ V2)) @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1))))))))))
(TORTHOGONAL_TRANSFORMATION_INTO_SUBSPACE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V0)) @ ((c/__caret__ @ (csubspace @ V1)) @ ((c<= @ (cdim @ V0)) @ (cdim @ V1))))) @ (c? @ (^[V2]: ((c/__caret__ @ (corthogonal_transformation @ V2)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1))))))))))
(TDIM_SUMS_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V0)) @ (csubspace @ V1))) @ ((c= @ ((c+ @ (cdim @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))) @ (cdim @ ((cINTER @ V0) @ V1)))) @ ((c+ @ (cdim @ V0)) @ (cdim @ V1)))))))))
(TRETRACT_OF_SIMPLY_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csimply_connected @ V0)) @ ((cretract_of @ V1) @ V0))) @ (csimply_connected @ V1)))))))
(TFACE_OF_POLYTOPE_POLYTOPE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolytope @ V0)) @ ((cface_of @ V1) @ V0))) @ (cpolytope @ V1)))))))
(TPOLYTOPE_UNION_CONVEX_HULL_FACETS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolytope @ V0)) @ ((c/__caret__ @ ((cint_lt @ (cint_of_num @ (cNUMERAL @ c_0))) @ (caff_dim @ V0))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((cSUBSET @ V1) @ V0))))) @ ((c= @ V0) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cfacet_of @ V3) @ V0)) @ ((chull @ cconvex) @ ((cUNION @ V1) @ V3)))))))))))))))
(TPOLYTOPE_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolytope @ V0)) @ (cpolytope @ V1))) @ (cpolytope @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TPOLYTOPE_INTER_POLYHEDRON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolytope @ V0)) @ (cpolyhedron @ V1))) @ (cpolytope @ ((cINTER @ V0) @ V1))))))))
(TFACET_OF_POLYHEDRON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V1)) @ ((cfacet_of @ V0) @ V1))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((creal_le @ ((cdot @ V2) @ V5)) @ V3)) @ V5))))))) @ ((c= @ V0) @ ((cINTER @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V2) @ V5)) @ V3)) @ V5)))))))))))))))))))
(TFACE_OF_POLYHEDRON_POLYHEDRON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V0)) @ ((cface_of @ V1) @ V0))) @ (cpolyhedron @ V1)))))))
(TPOLYHEDRON_RIDGE_TWO_FACETS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V0)) @ ((c/__caret__ @ ((cface_of @ V1) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c= @ (caff_dim @ V1)) @ ((cint_sub @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cface_of @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ (caff_dim @ V2)) @ ((cint_sub @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((cface_of @ V3) @ V0)) @ ((c/__caret__ @ ((c= @ (caff_dim @ V3)) @ ((cint_sub @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V3))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V3)) @ ((c/__caret__ @ ((c= @ ((cINTER @ V2) @ V3)) @ V1)) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cface_of @ V4) @ V0)) @ ((c/__caret__ @ ((c= @ (caff_dim @ V4)) @ ((cint_sub @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cSUBSET @ V1) @ V4)))) @ ((c__caret__/ @ ((c= @ V4) @ V2)) @ ((c= @ V4) @ V3)))))))))))))))))))))))
(TFACE_OF_POLYHEDRON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V0)) @ ((c/__caret__ @ ((cface_of @ V1) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c~ @ ((c= @ V1) @ V0)))))) @ ((c= @ V1) @ (cINTERS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cfacet_of @ V3) @ V0)) @ ((cSUBSET @ V1) @ V3))) @ V3)))))))))))))
(TFACE_OF_POLYHEDRON_SUBSET_FACET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V0)) @ ((c/__caret__ @ ((cface_of @ V1) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c~ @ ((c= @ V1) @ V0)))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cfacet_of @ V2) @ V0)) @ ((cSUBSET @ V1) @ V2))))))))))
(TSEPARATING_HYPERPLANE_POLYHEDRA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V0)) @ ((c/__caret__ @ (cpolyhedron @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((cDISJOINT @ V0) @ V1)))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_lt @ ((cdot @ V2) @ V4)) @ V3))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((creal_gt @ ((cdot @ V2) @ V4)) @ V3))))))))))))))))
(TPOLYHEDRON_INTER_POLYTOPE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V0)) @ (cpolytope @ V1))) @ (cpolytope @ ((cINTER @ V0) @ V1))))))))
(TPOLYHEDRON_POLYTOPE_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V0)) @ (cpolytope @ V1))) @ (cpolyhedron @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TPOLYHEDRON_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V0)) @ (cpolyhedron @ V1))) @ (cpolyhedron @ ((cINTER @ V0) @ V1))))))))
(TPOLYHEDRON_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolyhedron @ V0)) @ (cpolyhedron @ V1))) @ (cpolyhedron @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TRETRACT_OF_PATH_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath_connected @ V0)) @ ((cretract_of @ V1) @ V0))) @ (cpath_connected @ V1)))))))
(TPATH_CONNECTED_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath_connected @ V0)) @ (cpath_connected @ V1))) @ (cpath_connected @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TCLOSURE_OPEN_INTER_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V1)) @ ((cSUBSET @ V1) @ (cclosure @ V0)))) @ ((c= @ (cclosure @ ((cINTER @ V1) @ V0))) @ (cclosure @ V1))))))))
(TCONNECTED_FROM_OPEN_UNION_AND_INTER_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V1)) @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (cconnected @ ((cUNION @ V1) @ V0))) @ (cconnected @ ((cINTER @ V1) @ V0)))))) @ (cconnected @ V1)))))))
(TOPEN_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((cIN @ V1) @ (ccomponents @ V0)))) @ (copen @ V1)))))))
(TDENSE_ACCESSIBLE_FRONTIER_POINTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ (cfrontier @ V0))) @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY))))) @ (c? @ (^[V2]: ((c/__caret__ @ (carc @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ ((cDELETE @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ V0)) @ ((c/__caret__ @ ((cIN @ (cpathstart @ V2)) @ V0)) @ ((cIN @ (cpathfinish @ V2)) @ V1))))))))))))
(TCONNECTED_FROM_OPEN_UNION_AND_INTER_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (copen @ V1)) @ ((c/__caret__ @ (cconnected @ ((cUNION @ V0) @ V1))) @ (cconnected @ ((cINTER @ V0) @ V1)))))) @ (cconnected @ V1)))))))
(TINTERIOR_CLOSURE_INTER_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (copen @ V1))) @ ((c= @ (cinterior @ (cclosure @ ((cINTER @ V0) @ V1)))) @ ((cINTER @ (cinterior @ (cclosure @ V0))) @ (cinterior @ (cclosure @ V1))))))))))
(TNEGLIGIBLE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cnegligible @ V0)) @ ((cSUBSET @ V1) @ V0))) @ (cnegligible @ V1)))))))
(TNEGLIGIBLE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cnegligible @ V0)) @ (cnegligible @ V1))) @ (cnegligible @ ((cUNION @ V0) @ V1))))))))
(TMEASURABLE_NEGLIGIBLE_SYMDIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V1)) @ ((cDIFF @ V1) @ V0))))) @ (cmeasurable @ V1)))))))
(TMEASURE_UNION_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ (cmeasurable @ V1))) @ ((creal_le @ (cmeasure @ ((cUNION @ V0) @ V1))) @ ((creal_add @ (cmeasure @ V0)) @ (cmeasure @ V1)))))))))
(TMEASURE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ (cmeasurable @ V1))) @ ((c= @ (cmeasure @ ((cUNION @ V0) @ V1))) @ ((creal_add @ (cmeasure @ V0)) @ ((creal_sub @ (cmeasure @ V1)) @ (cmeasure @ ((cINTER @ V0) @ V1)))))))))))
(TMEASURABLE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ (cmeasurable @ V1))) @ (cmeasurable @ ((cUNION @ V0) @ V1))))))))
(TMEASURABLE_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ (cmeasurable @ V1))) @ (cmeasurable @ ((cINTER @ V0) @ V1))))))))
(TMEASURABLE_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ (cmeasurable @ V1))) @ (cmeasurable @ ((cDIFF @ V0) @ V1))))))))
(TMEASURABLE_MEASURABLE_INTER_LEGESGUE_MEASURABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ (clebesgue_measurable @ V1))) @ (cmeasurable @ ((cINTER @ V0) @ V1))))))))
(TMEASURABLE_LEGESGUE_MEASURABLE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clebesgue_measurable @ V1)) @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((cSUBSET @ V1) @ V0)))) @ (cmeasurable @ V1)))))))
(TMEASURABLE_LEGESGUE_MEASURABLE_INTER_MEASURABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clebesgue_measurable @ V0)) @ (cmeasurable @ V1))) @ (cmeasurable @ ((cINTER @ V0) @ V1))))))))
(TLEBESGUE_MEASURABLE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clebesgue_measurable @ V0)) @ (clebesgue_measurable @ V1))) @ (clebesgue_measurable @ ((cUNION @ V0) @ V1))))))))
(TLEBESGUE_MEASURABLE_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clebesgue_measurable @ V0)) @ (clebesgue_measurable @ V1))) @ (clebesgue_measurable @ ((cINTER @ V0) @ V1))))))))
(TLEBESGUE_MEASURABLE_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clebesgue_measurable @ V0)) @ (clebesgue_measurable @ V1))) @ (clebesgue_measurable @ ((cDIFF @ V0) @ V1))))))))
(TIS_INTERVAL_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cis_interval @ V0)) @ (cis_interval @ V1))) @ (cis_interval @ ((cINTER @ V0) @ V1))))))))
(TIS_INTERVAL_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cis_interval @ V0)) @ (cis_interval @ V1))) @ (cis_interval @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TDEPENDENT_MONO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cdependent @ V0)) @ ((cSUBSET @ V0) @ V1))) @ (cdependent @ V1)))))))
(TCONVEX_CONE_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex_cone @ V0)) @ (cconvex_cone @ V1))) @ (cconvex_cone @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TAFFINE_HULL_CONVEX_INTER_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((chull @ caffine) @ V1))) @ V0)) @ (c~ @ ((c= @ ((cINTER @ V1) @ V0)) @ cEMPTY))))) @ ((c= @ ((chull @ caffine) @ ((cINTER @ V1) @ V0))) @ ((chull @ caffine) @ V1))))))))
(TFACE_OF_AFF_DIM_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ (c~ @ ((c= @ V0) @ V1))))) @ ((cint_lt @ (caff_dim @ V0)) @ (caff_dim @ V1))))))))
(TAFFINE_HULL_FACE_OF_DISJOINT_RELATIVE_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ (c~ @ ((c= @ V0) @ V1))))) @ ((c= @ ((cINTER @ ((chull @ caffine) @ V0)) @ (crelative_interior @ V1))) @ cEMPTY)))))))
(TCLOSURE_CONVEX_INTER_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ (cinterior @ V1)) @ cEMPTY))) @ ((cSUBSET @ (cinterior @ V1)) @ (cclosure @ V0))))) @ ((c= @ (cclosure @ ((cINTER @ V1) @ V0))) @ (cclosure @ V1))))))))
(TAFF_DIM_CONVEX_INTER_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ ((cINTER @ V1) @ V0)) @ cEMPTY))))) @ ((c= @ (caff_dim @ ((cINTER @ V1) @ V0))) @ (caff_dim @ V1))))))))
(TAFFINE_HULL_CONVEX_INTER_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ ((cINTER @ V1) @ V0)) @ cEMPTY))))) @ ((c= @ ((chull @ caffine) @ ((cINTER @ V1) @ V0))) @ ((chull @ caffine) @ V1))))))))
(TABSOLUTE_RETRACTION_CONVEX_CLOSED_RELATIVE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((cSUBSET @ V1) @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cretraction @ ((c__comma__ @ V0) @ V1)) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cDIFF @ ((chull @ caffine) @ V1)) @ (crelative_interior @ V1)))) @ ((cIN @ (V2 @ V3)) @ (crelative_frontier @ V1))))))))))))))
(TABSOLUTE_RETRACTION_CONVEX_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((cSUBSET @ V1) @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cretraction @ ((c__comma__ @ V0) @ V1)) @ V2)) @ (c! @ (^[V3]: ((c==> @ (c~ @ ((cIN @ V3) @ V1))) @ ((cIN @ (V2 @ V3)) @ (cfrontier @ V1))))))))))))))
(TAFF_DIM_CONVEX_INTER_NONEMPTY_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ (c~ @ ((c= @ ((cINTER @ V1) @ (cinterior @ V0))) @ cEMPTY)))) @ ((c= @ (caff_dim @ ((cINTER @ V1) @ V0))) @ (caff_dim @ V1))))))))
(TAFFINE_HULL_CONVEX_INTER_NONEMPTY_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ (c~ @ ((c= @ ((cINTER @ V1) @ (cinterior @ V0))) @ cEMPTY)))) @ ((c= @ ((chull @ caffine) @ ((cINTER @ V1) @ V0))) @ ((chull @ caffine) @ V1))))))))
(TOUTSIDE_SUBSET_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((cSUBSET @ V1) @ V0))) @ ((cSUBSET @ ((cDIFF @ cUNIV) @ V0)) @ (coutside @ V1))))))))
(TCONTRACTIBLE_CONVEX_TWEAK_BOUNDARY_POINTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ ((cSUBSET @ (crelative_interior @ V0)) @ V1)) @ ((cSUBSET @ V1) @ (cclosure @ V0))))) @ (ccontractible @ V1)))))))
(TABSOLUTE_RETRACT_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)))) @ ((cretract_of @ V0) @ V1)))))))
(TSTARLIKE_CONVEX_TWEAK_BOUNDARY_POINTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ (crelative_interior @ V0)) @ V1)) @ ((cSUBSET @ V1) @ (cclosure @ V0)))))) @ (cstarlike @ V1)))))))
(TCONVEX_HULL_UNION_NONEMPTY_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (cconvex @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY)))))) @ ((c= @ ((chull @ cconvex) @ ((cUNION @ V0) @ V1))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((creal_le @ V4) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cvector_add @ ((c% @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V4)) @ V3)) @ ((c% @ V4) @ V5))))))))))))))))))
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(TINTERIOR_CLOSED_UNION_EMPTY_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c= @ (cinterior @ V0)) @ cEMPTY))) @ ((c= @ (cinterior @ ((cUNION @ V1) @ V0))) @ (cinterior @ V1))))))))
(TFRONTIER_MINIMAL_SEPARATING_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (c~ @ (cconnected @ ((cDIFF @ cUNIV) @ V1)))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cclosed @ V2)) @ ((cPSUBSET @ V2) @ V1))) @ (cconnected @ ((cDIFF @ cUNIV) @ V2)))))) @ ((cIN @ V0) @ (ccomponents @ ((cDIFF @ cUNIV) @ V1))))))) @ ((c= @ (cfrontier @ V0)) @ V1)))))))
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(TAR_FROM_UNION_AND_INTER_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cAR @ ((cUNION @ V1) @ V0))) @ (cAR @ ((cINTER @ V1) @ V0)))))) @ (cAR @ V1)))))))
(TANR_FROM_UNION_AND_INTER_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cANR @ ((cUNION @ V1) @ V0))) @ (cANR @ ((cINTER @ V1) @ V0)))))) @ (cANR @ V1)))))))
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(TSEPARATE_CLOSED_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (ccompact @ V1)) @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((creal_le @ V2) @ (cdistance @ ((c__comma__ @ V3) @ V4)))))))))))))))))
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(TSETDIST_CLOSED_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (ccompact @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c~ @ ((c= @ V1) @ cEMPTY)))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (cdistance @ ((c__comma__ @ V2) @ V3))) @ (csetdist @ ((c__comma__ @ V0) @ V1)))))))))))))))
(TSEPARATION_NORMAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ (copen @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V3)) @ ((c= @ ((cINTER @ V2) @ V3)) @ cEMPTY)))))))))))))))
(TCONNECTED_FROM_CLOSED_UNION_AND_INTER_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cconnected @ ((cUNION @ V0) @ V1))) @ (cconnected @ ((cINTER @ V0) @ V1)))))) @ (cconnected @ V1)))))))
(TENR_CLOSED_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cENR @ V0)) @ ((c/__caret__ @ (cENR @ V1)) @ (cENR @ ((cINTER @ V0) @ V1))))))) @ (cENR @ ((cUNION @ V0) @ V1))))))))
(TAR_FROM_UNION_AND_INTER_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cAR @ ((cUNION @ V0) @ V1))) @ (cAR @ ((cINTER @ V0) @ V1)))))) @ (cAR @ V1)))))))
(TAR_CLOSED_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cAR @ V0)) @ ((c/__caret__ @ (cAR @ V1)) @ (cAR @ ((cINTER @ V0) @ V1))))))) @ (cAR @ ((cUNION @ V0) @ V1))))))))
(TANR_FROM_UNION_AND_INTER_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cANR @ ((cUNION @ V0) @ V1))) @ (cANR @ ((cINTER @ V0) @ V1)))))) @ (cANR @ V1)))))))
(TANR_CLOSED_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cANR @ V0)) @ ((c/__caret__ @ (cANR @ V1)) @ (cANR @ ((cINTER @ V0) @ V1))))))) @ (cANR @ ((cUNION @ V0) @ V1))))))))
(TUNIFORMLY_CONTINUOUS_ON_DIST_CLOSEST_POINT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((cuniformly_continuous_on @ (^[V2]: (clift @ (cdistance @ ((c__comma__ @ V2) @ ((cclosest_point @ V0) @ V2)))))) @ V1)))))))
(TSETDIST_EQ_0_CLOSED_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (ccompact @ V1))) @ ((c= @ ((c= @ (csetdist @ ((c__comma__ @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ (c~ @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)))))))))))
(TCLOSED_COMPACT_DIFFERENCES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (ccompact @ V1))) @ (cclosed @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_sub @ V3) @ V4)))))))))))))))
(TCLOSED_COMPACT_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (ccompact @ V1))) @ (cclosed @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TCLOSURE_INTERIOR_UNION_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (cclosed @ V1))) @ ((c= @ (cclosure @ (cinterior @ ((cUNION @ V0) @ V1)))) @ ((cUNION @ (cclosure @ (cinterior @ V0))) @ (cclosure @ (cinterior @ V1))))))))))
(TCOBOUNDED_INTER_UNBOUNDED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ ((cDIFF @ cUNIV) @ V0))) @ (c~ @ (cbounded @ V1)))) @ (c~ @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY))))))))
(THAUSDIST_NONTRIVIAL_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V1)) @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c~ @ ((c= @ V0) @ cEMPTY)))))) @ ((c= @ (chausdist @ ((c__comma__ @ V1) @ V0))) @ ((creal_max @ (csup @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V0))))))))) @ (csup @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V1))))))))))))))))
(THAUSDIST_NONTRIVIAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V1)) @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c~ @ ((c= @ V0) @ cEMPTY)))))) @ ((c= @ (chausdist @ ((c__comma__ @ V1) @ V0))) @ (csup @ ((cUNION @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V0)))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V1))))))))))))))))
(THAUSDIST_COMPACT_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (ccompact @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY))))) @ ((cSUBSET @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((cIN @ V4) @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (chausdist @ ((c__comma__ @ V0) @ V1))))))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(THAUSDIST_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (cbounded @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c~ @ ((c= @ V1) @ cEMPTY)))))) @ ((c= @ (chausdist @ ((c__comma__ @ V0) @ V1))) @ (csup @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ (creal_abs @ ((creal_sub @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V0))) @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V1)))))))))))))))))
(TSETDIST_LE_HAUSDIST,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cbounded @ V1))) @ ((creal_le @ (csetdist @ ((c__comma__ @ V0) @ V1))) @ (chausdist @ ((c__comma__ @ V0) @ V1)))))))))
(THAUSDIST_CONVEX_HULLS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cbounded @ V1))) @ ((creal_le @ (chausdist @ ((c__comma__ @ ((chull @ cconvex) @ V0)) @ ((chull @ cconvex) @ V1)))) @ (chausdist @ ((c__comma__ @ V0) @ V1)))))))))
(TDIAMETER_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cbounded @ V1))) @ ((creal_le @ (cdiameter @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))) @ ((creal_add @ (cdiameter @ V0)) @ (cdiameter @ V1)))))))))
(THAUSDIST_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cbounded @ V1))) @ ((c= @ ((c= @ (chausdist @ ((c__comma__ @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c= @ (cclosure @ V0)) @ (cclosure @ V1)))))))))))
(TBOUNDED_DIFFS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cbounded @ V1))) @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_sub @ V3) @ V4)))))))))))))))
(TBOUNDED_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cbounded @ V1))) @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TAFFINE_DEPENDENT_MONO,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine_dependent @ V0)) @ ((cSUBSET @ V0) @ V1))) @ (caffine_dependent @ V1)))))))
(TFACE_OF_AFFINE_TRIVIAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V1)) @ ((cface_of @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c= @ V0) @ V1))))))))
(TAFFINE_HULL_AFFINE_INTER_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V1)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ (c~ @ ((c= @ ((cINTER @ V1) @ V0)) @ cEMPTY))))) @ ((c= @ ((chull @ caffine) @ ((cINTER @ V1) @ V0))) @ V1)))))))
(TMAXIMAL_AFFINE_INDEPENDENT_SUBSET_AFFINE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V0))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ (c~ @ (caffine_dependent @ V2))))) @ ((c= @ V2) @ V0)))))))) @ ((c= @ ((chull @ caffine) @ V0)) @ V1)))))))
(TAFFINE_HULL_AFFINE_INTER_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V1)) @ ((c/__caret__ @ (copen @ V0)) @ (c~ @ ((c= @ ((cINTER @ V1) @ V0)) @ cEMPTY))))) @ ((c= @ ((chull @ caffine) @ ((cINTER @ V1) @ V0))) @ V1)))))))
(TAFFINE_HULL_AFFINE_INTER_NONEMPTY_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V1)) @ (c~ @ ((c= @ ((cINTER @ V1) @ (cinterior @ V0))) @ cEMPTY)))) @ ((c= @ ((chull @ caffine) @ ((cINTER @ V1) @ V0))) @ V1)))))))
(TCARD_EQ_OPEN_IN_AFFINE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ (caff_dim @ V0)) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY)))))) @ ((c=_c @ V1) @ cUNIV)))))))
(TAFF_DIM_SUMS_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V0)) @ ((c/__caret__ @ (caffine @ V1)) @ (c~ @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY))))) @ ((c= @ (caff_dim @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))) @ ((cint_sub @ ((cint_add @ (caff_dim @ V0)) @ (caff_dim @ V1))) @ (caff_dim @ ((cINTER @ V0) @ V1))))))))))
(TOPEN_IN_CONNECTED_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ (ccomponents @ V0))) @ ((cIN @ V1) @ (ccomponents @ V0)))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)))))))
(TFACE_OF_CONVEX_HULLS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((cDISJOINT @ ((chull @ caffine) @ V0)) @ ((chull @ cconvex) @ ((cDIFF @ V1) @ V0)))))) @ ((cface_of @ ((chull @ cconvex) @ V0)) @ ((chull @ cconvex) @ V1))))))))
(TEXCHANGE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cindependent @ V1)) @ ((cSUBSET @ V1) @ (cspan @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cHAS_SIZE @ V2) @ (cCARD @ V0))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ ((cUNION @ V1) @ V0))) @ ((cSUBSET @ V1) @ (cspan @ V2)))))))))))))
(TENR_RETRACT_OF_ENR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cENR @ V0)) @ ((cretract_of @ V1) @ V0))) @ (cENR @ V1)))))))
(TENR_COMPONENT_ENR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cENR @ V0)) @ ((cIN @ V1) @ (ccomponents @ V0)))) @ (cENR @ V1)))))))
(TAR_RETRACT_OF_AR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cAR @ V0)) @ ((cretract_of @ V1) @ V0))) @ (cAR @ V1)))))))
(TAR_IMP_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cAR @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0))) @ ((cretract_of @ V0) @ V1)))))))
(TANR_IMP_NEIGHBOURHOOD_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cANR @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((cretract_of @ V1) @ V2))))))))))
(TANR_IMP_CLOSED_NEIGHBOURHOOD_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cANR @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V3)) @ ((cretract_of @ V1) @ V3)))))))))))))))
(TANR_RETRACT_OF_ANR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cANR @ V0)) @ ((cretract_of @ V1) @ V0))) @ (cANR @ V1)))))))
(TANR_COMPONENT_ANR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cANR @ V0)) @ ((cIN @ V1) @ (ccomponents @ V0)))) @ (cANR @ V1)))))))
(TELEMENTARY_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c? @ (^[V2]: ((cdivision_of @ V2) @ V0)))) @ (c? @ (^[V2]: ((cdivision_of @ V2) @ V1))))) @ (c? @ (^[V2]: ((cdivision_of @ V2) @ ((cUNION @ V0) @ V1))))))))))
(TCONVEX_HULL_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (caffine_dependent @ ((cUNION @ V0) @ V1)))) @ ((c= @ ((cINTER @ ((chull @ cconvex) @ V0)) @ ((chull @ cconvex) @ V1))) @ ((chull @ cconvex) @ ((cINTER @ V0) @ V1)))))))))
(TAFFINE_HULL_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (caffine_dependent @ ((cUNION @ V0) @ V1)))) @ ((c= @ ((cINTER @ ((chull @ caffine) @ V0)) @ ((chull @ caffine) @ V1))) @ ((chull @ caffine) @ ((cINTER @ V0) @ V1)))))))))
(TFACET_OF_CONVEX_HULL_AFFINE_INDEPENDENT_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (caffine_dependent @ V1))) @ ((c= @ ((cfacet_of @ V0) @ ((chull @ cconvex) @ V1))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cCARD @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c= @ V0) @ ((chull @ cconvex) @ ((cDELETE @ V1) @ V2))))))))))))))
(TFACET_OF_CONVEX_HULL_AFFINE_INDEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (caffine_dependent @ V1))) @ ((c= @ ((cfacet_of @ V0) @ ((chull @ cconvex) @ V1))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c= @ V0) @ ((chull @ cconvex) @ ((cDELETE @ V1) @ V2))))))))))))))
(TFACE_OF_CONVEX_HULL_AFFINE_INDEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ ((c= @ ((cface_of @ V1) @ ((chull @ cconvex) @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c= @ V1) @ ((chull @ cconvex) @ V2))))))))))))
(TEXPOSED_FACE_OF_POLYHEDRON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cpolyhedron @ V1)) @ ((c= @ ((cexposed_face_of @ V0) @ V1)) @ ((cface_of @ V0) @ V1))))))))
(TOPEN_INTER_CLOSURE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (copen @ V0)) @ ((cSUBSET @ ((cINTER @ V0) @ (cclosure @ V1))) @ (cclosure @ ((cINTER @ V0) @ V1)))))))))
(TINTERIOR_MAXIMAL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (copen @ V0)) @ ((c= @ ((cSUBSET @ V0) @ (cinterior @ V1))) @ ((cSUBSET @ V0) @ V1))))))))
(TOPEN_INTER_CLOSURE_EQ_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (copen @ V0)) @ ((c= @ ((c= @ ((cINTER @ V0) @ (cclosure @ V1))) @ cEMPTY)) @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY))))))))
(TMEASURE_NEGLIGIBLE_SYMDIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V1)) @ ((cDIFF @ V1) @ V0)))) @ ((c= @ (cmeasure @ V0)) @ (cmeasure @ V1))))))))
(TNEGLIGIBLE_SYMDIFF_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V1)) @ ((cDIFF @ V1) @ V0)))) @ ((c= @ (cnegligible @ V0)) @ (cnegligible @ V1))))))))
(TMEASURABLE_NEGLIGIBLE_SYMDIFF_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V1)) @ ((cDIFF @ V1) @ V0)))) @ ((c= @ (cmeasurable @ V0)) @ (cmeasurable @ V1))))))))
(TNEGLIGIBLE_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnegligible @ V0)) @ (cnegligible @ ((cDIFF @ V0) @ V1))))))))
(TFACE_OF_STILLCONVEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cconvex @ V1)) @ ((c= @ ((cface_of @ V0) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c/__caret__ @ (cconvex @ ((cDIFF @ V1) @ V0))) @ ((c= @ V0) @ ((cINTER @ ((chull @ caffine) @ V0)) @ V1)))))))))))
(TCONVEX_ON_SETDIST,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cconvex @ V0)) @ ((cconvex_on @ (^[V2]: (csetdist @ ((c__comma__ @ ((cINSERT @ V2) @ cEMPTY)) @ V0)))) @ V1)))))))
(TCLOSURE_MINIMAL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cclosed @ V1)) @ ((c= @ ((cSUBSET @ (cclosure @ V0)) @ V1)) @ ((cSUBSET @ V0) @ V1))))))))
(TCLOSED_SUBSET_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cclosed @ V0)) @ ((c= @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ ((cSUBSET @ V0) @ V1))))))))
(TFACE_OF_AFFINE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (caffine @ V1)) @ ((c= @ ((cface_of @ V0) @ V1)) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c= @ V0) @ V1)))))))))
(TCOUNTABLE_ENR_CONNECTED_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cENR @ V1)) @ (cCOUNTABLE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cconnected_component @ V1) @ V3)))))))))))))
(TCOUNTABLE_ANR_PATH_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cANR @ V1)) @ (cCOUNTABLE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cpath_component @ V1) @ V3)))))))))))))
(TCOUNTABLE_ANR_CONNECTED_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cANR @ V1)) @ (cCOUNTABLE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cconnected_component @ V1) @ V3)))))))))))))
(TDEFORMATION_RETRACT_IMP_HOMOTOPY_EQUIVALENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c? @ (^[V2]: ((c/__caret__ @ ((((chomotopic_with @ (^[V3]: cT)) @ ((c__comma__ @ V0) @ V0)) @ (^[V3]: V3)) @ V2)) @ ((cretraction @ ((c__comma__ @ V0) @ V1)) @ V2))))) @ ((chomotopy_equivalent @ V0) @ V1)))))))
(THEINE_BOREL_IMP_BOLZANO_WEIERSTRASS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (copen @ V3))))) @ ((cSUBSET @ V0) @ (cUNIONS @ V2)))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ V2)) @ ((c/__caret__ @ (cFINITE @ V3)) @ ((cSUBSET @ V0) @ (cUNIONS @ V3)))))))))) @ ((c==> @ ((c/__caret__ @ (cINFINITE @ V1)) @ ((cSUBSET @ V1) @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((climit_point_of @ V2) @ V1)))))))))))
(TDIM_ORTHOGONAL_SUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V1))) @ ((c= @ ((cdot @ V2) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ ((c= @ (cdim @ ((cUNION @ V0) @ V1))) @ ((c+ @ (cdim @ V0)) @ (cdim @ V1)))))))))
(TSETDIST_CLOSURE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csetdist @ ((c__comma__ @ (cclosure @ V0)) @ V1))) @ (csetdist @ ((c__comma__ @ V0) @ V1))))))))
(TSETDIST_CLOSURE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csetdist @ ((c__comma__ @ V0) @ (cclosure @ V1)))) @ (csetdist @ ((c__comma__ @ V0) @ V1))))))))
(TSETDIST_DIFFERENCES,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csetdist @ ((c__comma__ @ V0) @ V1))) @ (csetdist @ ((c__comma__ @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ cEMPTY)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_sub @ V3) @ V4))))))))))))))))
(THAUSDIST_CLOSURE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (chausdist @ ((c__comma__ @ (cclosure @ V0)) @ V1))) @ (chausdist @ ((c__comma__ @ V0) @ V1))))))))
(Thausdist,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (chausdist @ ((c__comma__ @ V1) @ V0))) @ ((cLET @ (^[V2]: (cLET_END @ (((cCOND @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((creal_le @ V4) @ V3)))))))) @ (csup @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((cUNION @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V0)))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V1)))))))))))))))
(THAUSDIST_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (chausdist @ ((c__comma__ @ V1) @ V0))) @ (chausdist @ ((c__comma__ @ V0) @ V1))))))))
(THAUSDIST_CLOSURE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (chausdist @ ((c__comma__ @ V0) @ (cclosure @ V1)))) @ (chausdist @ ((c__comma__ @ V0) @ V1))))))))
(TCONVEX_CONE_HULL_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ cconvex_cone) @ ((cUNION @ V0) @ V1))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ ((chull @ cconvex_cone) @ V0))) @ ((cIN @ V4) @ ((chull @ cconvex_cone) @ V1)))) @ ((cvector_add @ V3) @ V4))))))))))))))
(TCONVEX_HULL_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ cconvex) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ ((chull @ cconvex) @ V0))) @ ((cIN @ V4) @ ((chull @ cconvex) @ V1)))) @ ((cvector_add @ V3) @ V4))))))))))))))
(TUNION_FRONTIER,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cUNION @ (cfrontier @ V0)) @ (cfrontier @ V1))) @ ((cUNION @ (cfrontier @ ((cUNION @ V0) @ V1))) @ ((cUNION @ (cfrontier @ ((cINTER @ V0) @ V1))) @ ((cINTER @ (cfrontier @ V0)) @ (cfrontier @ V1))))))))))
(TSPAN_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cspan @ ((cUNION @ V0) @ V1))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ (cspan @ V0))) @ ((cIN @ V4) @ (cspan @ V1)))) @ ((cvector_add @ V3) @ V4))))))))))))))
(TINTERIOR_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinterior @ ((cINTER @ V0) @ V1))) @ ((cINTER @ (cinterior @ V0)) @ (cinterior @ V1))))))))
(TCLOSURE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cclosure @ ((cUNION @ V0) @ V1))) @ ((cUNION @ (cclosure @ V0)) @ (cclosure @ V1))))))))
(TSUMS_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((cIN @ V4) @ V0))) @ ((cvector_add @ V3) @ V4))))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4))))))))))))))
(TOPEN_IN_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (copen @ V2)) @ ((c= @ V0) @ ((cINTER @ V1) @ V2)))))))))))
(TOPEN_IN_CONTAINS_CBALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((cSUBSET @ ((cINTER @ (ccball @ ((c__comma__ @ V2) @ V3))) @ V0)) @ V1))))))))))))))
(TOPEN_IN_CONTAINS_BALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((cSUBSET @ ((cINTER @ (cball @ ((c__comma__ @ V2) @ V3))) @ V0)) @ V1))))))))))))))
(Topen_in,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V4) @ V2))) @ V3))) @ ((cIN @ V4) @ V1)))))))))))))))))
(TEXPOSED_FACE_OF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cexposed_face_of @ V0) @ V1)) @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V0) @ V1)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((creal_le @ ((cdot @ V2) @ V5)) @ V3)) @ V5))))))) @ ((c= @ V0) @ ((cINTER @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V2) @ V5)) @ V3)) @ V5))))))))))))))))))))))
(TEXPOSED_FACE_OF_PARALLEL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cexposed_face_of @ V0) @ V1)) @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((creal_le @ ((cdot @ V2) @ V5)) @ V3)) @ V5))))))) @ ((c/__caret__ @ ((c= @ V0) @ ((cINTER @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V2) @ V5)) @ V3)) @ V5)))))))) @ ((c/__caret__ @ ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c~ @ ((c= @ V0) @ V1)))) @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0)))))) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ ((chull @ caffine) @ V1))) @ (c~ @ ((c= @ V0) @ V1)))) @ ((cIN @ ((cvector_add @ V4) @ V2)) @ ((chull @ caffine) @ V1)))))))))))))))))))
(TCLOSED_IN_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (cclosed @ V2)) @ ((c= @ V0) @ ((cINTER @ V1) @ V2)))))))))))
(TCLOSED_IN_INTER_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((c= @ ((cINTER @ V0) @ (cclosure @ V1))) @ V1)))))))
(TCLOSED_IN_LIMPT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((climit_point_of @ V2) @ V1)) @ ((cIN @ V2) @ V0))) @ ((cIN @ V2) @ V1)))))))))))
(TIN_COMPONENTS_MAXIMAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V1) @ (ccomponents @ V0))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cconnected @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ (cconnected @ V2))))) @ ((c= @ V2) @ V1)))))))))))))
(TIN_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ (ccomponents @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c= @ V0) @ ((cconnected_component @ V1) @ V2)))))))))))
(TNOWHERE_DENSE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cinterior @ (cclosure @ ((cUNION @ V0) @ V1)))) @ cEMPTY)) @ ((c/__caret__ @ ((c= @ (cinterior @ (cclosure @ V0))) @ cEMPTY)) @ ((c= @ (cinterior @ (cclosure @ V1))) @ cEMPTY))))))))
(TNEGLIGIBLE_UNION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnegligible @ ((cUNION @ V0) @ V1))) @ ((c/__caret__ @ (cnegligible @ V0)) @ (cnegligible @ V1))))))))
(TDEFORMATION_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c/__caret__ @ ((((chomotopic_with @ (^[V3]: cT)) @ ((c__comma__ @ V0) @ V0)) @ (^[V3]: V3)) @ V2)) @ ((cretraction @ ((c__comma__ @ V0) @ V1)) @ V2))))) @ ((c/__caret__ @ ((cretract_of @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((((chomotopic_with @ (^[V3]: cT)) @ ((c__comma__ @ V0) @ V0)) @ (^[V3]: V3)) @ V2)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)))))))))))
(TOPEN_IN_TRANS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)))))))
(TCLOSED_IN_TRANS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1))))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)))))))
(THAS_MEASURE_NEGLIGIBLE_SYMDIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_measure @ V0) @ V2)) @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V1)) @ ((cDIFF @ V1) @ V0))))) @ ((chas_measure @ V1) @ V2)))))))))
(THAS_MEASURE_UNION_NEGLIGIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_measure @ V0) @ V2)) @ (cnegligible @ V1))) @ ((chas_measure @ ((cUNION @ V0) @ V1)) @ V2)))))))))
(THAS_MEASURE_DIFF_NEGLIGIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_measure @ V0) @ V2)) @ (cnegligible @ V1))) @ ((chas_measure @ ((cDIFF @ V0) @ V1)) @ V2)))))))))
(TREAL_HAUSDIST_LE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (cbounded @ V1)) @ (cbounded @ V0))))) @ ((c= @ ((creal_le @ (chausdist @ ((c__comma__ @ V1) @ V0))) @ V2)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V0))) @ V2))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V1))) @ V2))))))))))))))
(TREAL_SETDIST_LT_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((creal_lt @ (csetdist @ ((c__comma__ @ V0) @ V1))) @ V2)))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V3) @ V4))) @ V2)))))))))))))))
(TREAL_HAUSDIST_LE_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ V5) @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V2))))) @ ((cvector_add @ V4) @ V5)))))))))) @ ((cSUBSET @ V1) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V2))))) @ ((cvector_add @ V4) @ V5))))))))))))) @ ((creal_le @ (chausdist @ ((c__comma__ @ V0) @ V1))) @ V2)))))))))
(TREAL_HAUSDIST_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V1))) @ V2))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V3) @ cEMPTY)) @ V0))) @ V2)))))))) @ ((creal_le @ (chausdist @ ((c__comma__ @ V0) @ V1))) @ V2)))))))))
(THAS_MEASURE_UNION_NEGLIGIBLE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnegligible @ V0)) @ ((c= @ ((chas_measure @ ((cUNION @ V1) @ V0)) @ V2)) @ ((chas_measure @ V1) @ V2))))))))))
(THAS_MEASURE_DIFF_NEGLIGIBLE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnegligible @ V0)) @ ((c= @ ((chas_measure @ ((cDIFF @ V1) @ V0)) @ V2)) @ ((chas_measure @ V1) @ V2))))))))))
(TREAL_LE_SETDIST_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((creal_le @ V2) @ (csetdist @ ((c__comma__ @ V0) @ V1)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((creal_le @ V2) @ (cdistance @ ((c__comma__ @ V3) @ V4))))))))) @ ((c==> @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c= @ V1) @ cEMPTY))) @ ((creal_le @ V2) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))
(THAS_MEASURE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_measure @ V0) @ V2)) @ ((c/__caret__ @ ((chas_measure @ V1) @ V3)) @ ((cSUBSET @ V0) @ V1)))) @ ((creal_le @ V2) @ V3)))))))))))
(THAS_MEASURE_NEGLIGIBLE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_measure @ V0) @ V2)) @ ((c/__caret__ @ ((chas_measure @ V1) @ V3)) @ (cnegligible @ ((cINTER @ V0) @ V1))))) @ ((chas_measure @ ((cUNION @ V0) @ V1)) @ ((creal_add @ V2) @ V3))))))))))))
(TCLOSED_IN_UNION_COMPLEMENT_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((clocally @ cconnected) @ V0)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((cSUBSET @ V2) @ (ccomponents @ ((cDIFF @ V0) @ V1)))))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cUNION @ V1) @ (cUNIONS @ V2)))))))))))
(TLEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (c~ @ ((c= @ (V2 @ V4)) @ cEMPTY)))) @ V4))))))) @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cmeasure @ V0))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (cmeasurable @ (V2 @ V3)))))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cUNIONS @ ((cIMAGE @ V2) @ V1)))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (c~ @ ((c= @ V3) @ V4))))) @ ((cDISJOINT @ (V2 @ V3)) @ (V2 @ V4)))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cSUBSET @ ((cIMAGE @ (^[V4]: ((cvector_sub @ V4) @ V3))) @ (V2 @ V3))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))))))))))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V4))) @ (c~ @ ((cDISJOINT @ ((cIMAGE @ (^[V5]: ((cvector_sub @ V5) @ V3))) @ (V2 @ V3))) @ ((cIMAGE @ (^[V5]: ((cvector_sub @ V5) @ V4))) @ (V2 @ V4)))))))))))))))))))
(TCONNECTED_EQUIVALENCE_RELATION_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((V2 @ V5) @ V6)) @ ((V2 @ V6) @ V5))))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((V2 @ V5) @ V6)) @ ((V2 @ V6) @ V7))) @ ((V2 @ V5) @ V7))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((cIN @ V6) @ V5))) @ (c? @ (^[V7]: ((c/__caret__ @ ((cIN @ V7) @ V5)) @ (V1 @ V7)))))))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ (c? @ (^[V6]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V6)) @ ((c/__caret__ @ ((cIN @ V5) @ V6)) @ (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((cIN @ V7) @ V6)) @ ((c/__caret__ @ ((cIN @ V8) @ V6)) @ ((c/__caret__ @ (V1 @ V7)) @ (V1 @ V8))))) @ ((V2 @ V7) @ V8)))))))))))))))))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (V1 @ V3)) @ (V1 @ V4))))) @ ((V2 @ V3) @ V4))))))))))))))
(TRETRACT_FIXPOINT_PROPERTY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V1) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V0))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V3 @ V4)) @ V4))))))))) @ ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V1))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ V3)))))))))))))
(TSCHAUDER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0))))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ V3))))))))))))
(TSCHAUDER_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cAR @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (ccompact @ V1)))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ V3))))))))))))
(Tretraction,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cretraction @ ((c__comma__ @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ V3)))))))))))))))
(TBROUWER_SURJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (ccompact @ V1)) @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ V1))) @ ((cIN @ ((cvector_add @ V4) @ ((cvector_sub @ V5) @ (V2 @ V5)))) @ V1))))))))))) @ ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V4)) @ V3)))))))))))))))
(TLIM_UNION_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c--> @ V2) @ V3) @ ((cwithin @ (cat @ V4)) @ V0))) @ ((c/__caret__ @ (((c--> @ V2) @ V3) @ ((cwithin @ (cat @ V4)) @ V1))) @ ((c= @ ((cUNION @ V0) @ V1)) @ cUNIV)))) @ (((c--> @ V2) @ V3) @ (cat @ V4))))))))))))))
(TOUTSIDE_UNION_OUTSIDE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ ((cINTER @ V2) @ (coutside @ ((cUNION @ V1) @ V0)))) @ cEMPTY)) @ ((cSUBSET @ (coutside @ ((cUNION @ V1) @ V0))) @ (coutside @ ((cUNION @ V1) @ V2)))))))))))
(TENR_NEIGHBORHOOD_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V2) @ V0)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ (cENR @ V1)))) @ (cENR @ V2)))))))))
(TANR_NEIGHBORHOOD_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V2) @ V0)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ (cANR @ V1)))) @ (cANR @ V2)))))))))
(TRETRACT_OF_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V1) @ V0)) @ ((cretract_of @ V0) @ V2))) @ ((cretract_of @ V1) @ V2)))))))))
(TOPEN_IN_SUBSET_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((cSUBSET @ V1) @ V0)))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2)))))))))
(TOPEN_IN_INTER_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ (copen @ V2))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cINTER @ V1) @ V2))))))))))
(TCLOSED_IN_UNION_COMPLEMENT_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((clocally @ cconnected) @ V0)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((cIN @ V2) @ (ccomponents @ ((cDIFF @ V0) @ V1)))))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cUNION @ V1) @ V2))))))))))
(TSURA_BURA_CLOPEN_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((clocally @ ccompact) @ V0)) @ ((c/__caret__ @ ((cIN @ V1) @ (ccomponents @ V0))) @ ((c/__caret__ @ (ccompact @ V1)) @ ((c/__caret__ @ (copen @ V2)) @ ((cSUBSET @ V1) @ V2)))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((c/__caret__ @ (ccompact @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V3)) @ ((cSUBSET @ V3) @ V2))))))))))))))
(TSUBSET_OF_FACE_OF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cface_of @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c~ @ ((cDISJOINT @ V2) @ (crelative_interior @ V1)))))) @ ((cSUBSET @ V1) @ V2)))))))))
(TFACE_OF_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cface_of @ V1) @ V0)) @ ((c/__caret__ @ ((cface_of @ V2) @ V0)) @ (c~ @ ((cDISJOINT @ (crelative_interior @ V1)) @ (crelative_interior @ V2)))))) @ ((c= @ V1) @ V2)))))))))
(TEXPOSED_FACE_OF_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cexposed_face_of @ V0) @ V2)) @ ((cexposed_face_of @ V1) @ V2))) @ ((cexposed_face_of @ ((cINTER @ V0) @ V1)) @ V2)))))))))
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(TCONNECTED_SUBSET_CLOPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((c/__caret__ @ (cconnected @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c~ @ ((c= @ ((cINTER @ V1) @ V2)) @ cEMPTY))))))) @ ((cSUBSET @ V1) @ V2)))))))))
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(TCLOSED_MAP_OPEN_SUPERSET_PREIMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V5)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V3) @ V5)))))) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((cSUBSET @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ ((cIN @ (V3 @ V6)) @ V1))) @ V6)))))) @ V4))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V5)) @ ((cSUBSET @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V2)) @ ((cIN @ (V3 @ V7)) @ V5))) @ V7)))))) @ V4)))))))))))))))))
(TOPEN_IN_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cDELETE @ V1) @ V2))))))))))
(TPATH_COMPONENT_INTERMEDIATE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cpath_component @ V1) @ V2)) @ V0)) @ ((cSUBSET @ V0) @ V1))) @ ((c= @ ((cpath_component @ V0) @ V2)) @ ((cpath_component @ V1) @ V2))))))))))
(TCONNECTED_COMPONENT_INTERMEDIATE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cconnected_component @ V1) @ V2)) @ V0)) @ ((cSUBSET @ V0) @ V1))) @ ((c= @ ((cconnected_component @ V0) @ V2)) @ ((cconnected_component @ V1) @ V2))))))))))
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(THOMOTOPY_EQUIVALENT_RELATIVE_FRONTIER_PUNCTURED_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ (crelative_interior @ V0))) @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (crelative_frontier @ V0)) @ V1)) @ ((cSUBSET @ V1) @ ((chull @ caffine) @ V0)))))))) @ ((chomotopy_equivalent @ (crelative_frontier @ V0)) @ ((cDELETE @ V1) @ V2))))))))))
(TFACE_OF_CONVEX_HULL_INSERT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((cIN @ V2) @ ((chull @ caffine) @ V0))))) @ ((c= @ ((cface_of @ V1) @ ((chull @ cconvex) @ ((cINSERT @ V2) @ V0)))) @ ((c__caret__/ @ ((cface_of @ V1) @ ((chull @ cconvex) @ V0))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cface_of @ V3) @ ((chull @ cconvex) @ V0))) @ ((c= @ V1) @ ((chull @ cconvex) @ ((cINSERT @ V2) @ V3))))))))))))))))
(TSPAN_INDUCT_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V1 @ (cvec @ (cNUMERAL @ c_0)))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (V1 @ V5))) @ (V1 @ ((cvector_add @ ((c% @ V3) @ V4)) @ V5))))))))))) @ ((c==> @ ((cIN @ V2) @ (cspan @ V0))) @ (V1 @ V2))))))))))
(TCONVEX_LOCAL_GLOBAL_MINIMUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((creal_le @ (V3 @ V2)) @ (V3 @ V5)))))))))) @ ((c==> @ ((cIN @ V4) @ V1)) @ ((creal_le @ (V3 @ V2)) @ (V3 @ V4)))))))))))))))
(TCONNECTED_INDUCTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((cIN @ V6) @ V5))) @ (c? @ (^[V7]: ((c/__caret__ @ ((cIN @ V7) @ V5)) @ (V1 @ V7)))))))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ (c? @ (^[V6]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V6)) @ ((c/__caret__ @ ((cIN @ V5) @ V6)) @ (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((cIN @ V7) @ V6)) @ ((c/__caret__ @ ((cIN @ V8) @ V6)) @ ((c/__caret__ @ (V1 @ V7)) @ ((c/__caret__ @ (V1 @ V8)) @ (V3 @ V7)))))) @ (V3 @ V8)))))))))))))))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (V1 @ V2)) @ ((c/__caret__ @ (V1 @ V4)) @ (V3 @ V2)))))) @ (V3 @ V4))))))))))))))
(TSETDIST_LE_DIST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V1))) @ ((creal_le @ (csetdist @ ((c__comma__ @ V0) @ V1))) @ (cdistance @ ((c__comma__ @ V2) @ V3)))))))))))))
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(TORTHOGONAL_SUBSPACE_DECOMP_UNIQUE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((cIN @ V7) @ V1))) @ ((corthogonal @ V6) @ V7))))))) @ ((c/__caret__ @ ((cIN @ V2) @ (cspan @ V0))) @ ((c/__caret__ @ ((cIN @ V3) @ (cspan @ V0))) @ ((c/__caret__ @ ((cIN @ V4) @ (cspan @ V1))) @ ((c/__caret__ @ ((cIN @ V5) @ (cspan @ V1))) @ ((c= @ ((cvector_add @ V2) @ V4)) @ ((cvector_add @ V3) @ V5)))))))) @ ((c= @ V4) @ V5)))))))))))))))
(TURYSOHN_LOCAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((c= @ ((cINTER @ V1) @ V3)) @ cEMPTY)))) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((cIN @ (V5 @ V6)) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL))))))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V1)) @ ((c= @ (V5 @ V6)) @ V2))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V3)) @ ((c= @ (V5 @ V6)) @ V4)))))))))))))))))))))
(TCOVERING_SPACE_IMP_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccovering_space @ ((c__comma__ @ V2) @ V1)) @ V0)) @ ((ccontinuous_on @ V1) @ V2)))))))))
(TQUOTIENT_MAP_IMP_CONTINUOUS_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V2)) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V0)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((cIN @ (V1 @ V5)) @ V3))) @ V5))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3))))))) @ ((ccontinuous_on @ V1) @ V2)))))))))
(TQUOTIENT_MAP_IMP_CONTINUOUS_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V2)) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V0)) @ ((c= @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((cIN @ (V1 @ V5)) @ V3))) @ V5))))))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3))))))) @ ((ccontinuous_on @ V1) @ V2)))))))))
(TCONTINUOUS_FROM_CLOSED_GRAPH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V2)) @ V0)) @ (cclosed @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ V2)) @ ((cpastecart @ V4) @ (V1 @ V4))))))))))) @ ((ccontinuous_on @ V1) @ V2)))))))))
(THOMOTOPIC_WITH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V2)) @ ((c= @ (V5 @ V7)) @ (V6 @ V7)))))) @ ((c= @ (V4 @ V5)) @ (V4 @ V6)))))))) @ ((c= @ ((((chomotopic_with @ V4) @ ((c__comma__ @ V2) @ V0)) @ V1) @ V3)) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V2))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V5) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V2))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((c= @ (V5 @ ((cpastecart @ (cvec @ (cNUMERAL @ c_0))) @ V6))) @ (V1 @ V6)))))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((c= @ (V5 @ ((cpastecart @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V6))) @ (V3 @ V6)))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ (V4 @ (^[V7]: (V5 @ ((cpastecart @ V6) @ V7))))))))))))))))))))))))))
(TCOVERING_SPACE_LIFT_UNIQUE_IDENTITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V3) @ V1)) @ V0)) @ ((c/__caret__ @ (cpath_connected @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V3)) @ V3)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V3)) @ ((c= @ (V1 @ (V4 @ V6))) @ (V1 @ V6)))))) @ ((c/__caret__ @ ((cIN @ V2) @ V3)) @ ((c= @ (V4 @ V2)) @ V2)))))))) @ ((c==> @ ((cIN @ V5) @ V3)) @ ((c= @ (V4 @ V5)) @ V5))))))))))))))))
(THOMEOMORPHIC_PCROSS_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((chomeomorphic @ ((cPCROSS @ V1) @ V0)) @ ((cPCROSS @ V0) @ V1)))))))
(TISOMETRY_SUBSPACES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V1)) @ ((c/__caret__ @ (csubspace @ V0)) @ ((c= @ (cdim @ V1)) @ (cdim @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ (clinear @ V2)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V1)) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (cvector_norm @ (V2 @ V3))) @ (cvector_norm @ V3)))))))))))))))
(TSUBSPACE_ISOMORPHISM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V1)) @ ((c/__caret__ @ (csubspace @ V0)) @ ((c= @ (cdim @ V1)) @ (cdim @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ (clinear @ V2)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V1)) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))))))))))))
(TISOMETRY_SUBSET_SUBSPACE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V1)) @ ((c/__caret__ @ (csubspace @ V0)) @ ((c<= @ (cdim @ V1)) @ (cdim @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ (clinear @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (cvector_norm @ (V2 @ V3))) @ (cvector_norm @ V3)))))))))))))))
(TAR_IMP_ABSOLUTE_RETRACT_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cAR @ V0)) @ ((c/__caret__ @ ((chomeomorphic @ V0) @ V1)) @ (cclosed @ V1)))) @ ((cretract_of @ V1) @ cUNIV)))))))
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(TIMAGE_FSTCART_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIMAGE @ cfstcart) @ ((cPCROSS @ V1) @ V0))) @ (((cCOND @ ((c= @ V0) @ cEMPTY)) @ cEMPTY) @ V1)))))))
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(TCLOSED_MAP_FSTCART,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cPCROSS @ V1) @ V0))) @ V2))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ cfstcart) @ V2))))))))))
(TCLOSED_IN_COMPACT_PROJECTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cPCROSS @ V1) @ V0))) @ V2))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ ((cpastecart @ V5) @ V4)) @ V2))))) @ V4))))))))))))))
(TCOVERING_SPACE_LIFT_UNIQUE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V3)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V4)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V7) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V7) @ V4)) @ V1)) @ ((c/__caret__ @ (c! @ (^[V10]: ((c==> @ ((cIN @ V10) @ V4)) @ ((c= @ (V2 @ V10)) @ (V3 @ (V7 @ V10))))))) @ ((c/__caret__ @ ((ccontinuous_on @ V8) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V8) @ V4)) @ V1)) @ ((c/__caret__ @ (c! @ (^[V10]: ((c==> @ ((cIN @ V10) @ V4)) @ ((c= @ (V2 @ V10)) @ (V3 @ (V8 @ V10))))))) @ ((c/__caret__ @ ((cIN @ V6) @ (ccomponents @ V4))) @ ((c/__caret__ @ ((cIN @ V5) @ V6)) @ ((c/__caret__ @ ((c= @ (V7 @ V5)) @ (V8 @ V5))) @ ((cIN @ V9) @ V6)))))))))))))) @ ((c= @ (V7 @ V9)) @ (V8 @ V9))))))))))))))))))))))))
(TCOVERING_SPACE_LIFT_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V3)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V5)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V5)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V6) @ V5)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V6) @ V5)) @ V1)) @ ((c/__caret__ @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ V5)) @ ((c= @ (V2 @ V9)) @ (V3 @ (V6 @ V9))))))) @ ((c/__caret__ @ ((ccontinuous_on @ V7) @ V5)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V7) @ V5)) @ V1)) @ ((c/__caret__ @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ V5)) @ ((c= @ (V2 @ V9)) @ (V3 @ (V7 @ V9))))))) @ ((c/__caret__ @ (cconnected @ V5)) @ ((c/__caret__ @ ((cIN @ V4) @ V5)) @ ((c/__caret__ @ ((c= @ (V6 @ V4)) @ (V7 @ V4))) @ ((cIN @ V8) @ V5)))))))))))))) @ ((c= @ (V6 @ V8)) @ (V7 @ V8))))))))))))))))))))))
(TCOVERING_SPACE_LIFT_HOMOTOPY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V5)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V3))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V3))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V3)) @ ((c= @ (V4 @ ((cpastecart @ (cvec @ (cNUMERAL @ c_0))) @ V6))) @ (V5 @ (V2 @ V6))))))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V3)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V3)) @ V1))))))) @ (c? @ (^[V6]: ((c/__caret__ @ ((ccontinuous_on @ V6) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V3))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V6) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V3))) @ V1)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V3)) @ ((c= @ (V6 @ ((cpastecart @ (cvec @ (cNUMERAL @ c_0))) @ V7))) @ (V2 @ V7)))))) @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V3))) @ ((c= @ (V4 @ V7)) @ (V5 @ (V6 @ V7)))))))))))))))))))))))))
(TCOVERING_SPACE_LIFT_HOMOTOPY_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V5)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ ((cPCROSS @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ ((cPCROSS @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V3)) @ ((c= @ (V4 @ ((cpastecart @ V6) @ (cvec @ (cNUMERAL @ c_0))))) @ (V5 @ (V2 @ V6))))))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V3)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V3)) @ V1))))))) @ (c? @ (^[V6]: ((c/__caret__ @ ((ccontinuous_on @ V6) @ ((cPCROSS @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V6) @ ((cPCROSS @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ V1)) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V3)) @ ((c= @ (V6 @ ((cpastecart @ V7) @ (cvec @ (cNUMERAL @ c_0))))) @ (V2 @ V7)))))) @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ ((cPCROSS @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((c= @ (V4 @ V7)) @ (V5 @ (V6 @ V7)))))))))))))))))))))))))
(THOMOTOPY_EQUIVALENT_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chomotopy_equivalent @ V1) @ V0)) @ ((chomotopy_equivalent @ V0) @ V2))) @ ((chomotopy_equivalent @ V1) @ V2)))))))))
(THOMEOMORPHIC_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chomeomorphic @ V1) @ V0)) @ ((chomeomorphic @ V0) @ V2))) @ ((chomeomorphic @ V1) @ V2)))))))))
(THOMOTOPIC_COMPOSE_CONTINUOUS_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((((chomotopic_with @ (^[V6]: cT)) @ ((c__comma__ @ V0) @ V2)) @ V3) @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V5) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V5) @ V1)) @ V0)))) @ ((((chomotopic_with @ (^[V6]: cT)) @ ((c__comma__ @ V1) @ V2)) @ ((co @ V3) @ V5)) @ ((co @ V4) @ V5))))))))))))))))
(TNULLHOMOTOPIC_THROUGH_CONTRACTIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V1)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V2)) @ (ccontractible @ V0)))))) @ (c? @ (^[V5]: ((((chomotopic_with @ (^[V6]: cT)) @ ((c__comma__ @ V1) @ V2)) @ ((co @ V3) @ V4)) @ (^[V6]: V5))))))))))))))))
(THOMOTOPIC_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((((chomotopic_with @ (^[V7]: cT)) @ ((c__comma__ @ V1) @ V0)) @ V4) @ V6)) @ ((((chomotopic_with @ (^[V7]: cT)) @ ((c__comma__ @ V0) @ V2)) @ V3) @ V5))) @ ((((chomotopic_with @ (^[V7]: cT)) @ ((c__comma__ @ V1) @ V2)) @ ((co @ V3) @ V4)) @ ((co @ V5) @ V6))))))))))))))))))
(THOMOTOPIC_THROUGH_CONTRACTIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V1)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V6) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V6) @ V1)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V5) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V5) @ V0)) @ V2)) @ ((c/__caret__ @ (ccontractible @ V0)) @ (cpath_connected @ V2))))))))))) @ ((((chomotopic_with @ (^[V7]: cT)) @ ((c__comma__ @ V1) @ V2)) @ ((co @ V3) @ V4)) @ ((co @ V5) @ V6))))))))))))))))))
(THOMEOMORPHISM_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((chomeomorphism @ ((c__comma__ @ V1) @ V0)) @ ((c__comma__ @ V4) @ V5))) @ ((chomeomorphism @ ((c__comma__ @ V0) @ V2)) @ ((c__comma__ @ V3) @ V6)))) @ ((chomeomorphism @ ((c__comma__ @ V1) @ V2)) @ ((c__comma__ @ ((co @ V3) @ V4)) @ ((co @ V5) @ V6)))))))))))))))))))
(TCOVERING_SPACE_LIFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V3)) @ V0)) @ ((c/__caret__ @ (csimply_connected @ V2)) @ ((c/__caret__ @ ((clocally @ cpath_connected) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V2)) @ ((cSUBSET @ ((cIMAGE @ V4) @ V2)) @ V0)))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V5) @ V2)) @ V1)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((c= @ (V3 @ (V5 @ V6))) @ (V4 @ V6)))))))))))))))))))))
(THOMOTOPIC_COMPOSE_CONTINUOUS_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((((chomotopic_with @ (^[V6]: cT)) @ ((c__comma__ @ V1) @ V0)) @ V3) @ V5)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V4) @ V0)) @ V2)))) @ ((((chomotopic_with @ (^[V6]: cT)) @ ((c__comma__ @ V1) @ V2)) @ ((co @ V4) @ V3)) @ ((co @ V4) @ V5))))))))))))))))
(TQUOTIENT_MAP_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cSUBSET @ V6) @ V0)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V1)) @ ((cIN @ (V3 @ V8)) @ V6))) @ V8))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V6)))))) @ (c! @ (^[V6]: ((c==> @ ((cSUBSET @ V6) @ V4)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V0)) @ ((cIN @ (V2 @ V8)) @ V6))) @ V8))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V4)) @ V6)))))))) @ ((c==> @ ((cSUBSET @ V5) @ V4)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((cIN @ (((co @ V2) @ V3) @ V7)) @ V5))) @ V7))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V4)) @ V5)))))))))))))))))
(TBROUWER_FACTOR_THROUGH_AR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ (ccompact @ V1)) @ (cAR @ V0))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ (V3 @ V4))) @ V4))))))))))))))
(THOMEOMORPHISM_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((chomeomorphism @ ((c__comma__ @ V1) @ V0)) @ ((c__comma__ @ V3) @ V2))) @ ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))))))))))))
(TRETRACT_OF_HOMOTOPICALLY_TRIVIAL_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V2) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V4) @ V1)) @ V0))) @ (c? @ (^[V5]: ((((chomotopic_with @ (^[V6]: cT)) @ ((c__comma__ @ V1) @ V0)) @ V4) @ (^[V6]: V5))))))))) @ ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V2))) @ (c? @ (^[V4]: ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V1) @ V2)) @ V3) @ (^[V5]: V4)))))))))))))))
(TRETRACT_OF_HOMOTOPICALLY_TRIVIAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V2) @ V0)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V5) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V5) @ V1)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V6) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V6) @ V1)) @ V0))))) @ ((((chomotopic_with @ (^[V7]: cT)) @ ((c__comma__ @ V1) @ V0)) @ V5) @ V6)))))))) @ ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V4) @ V1)) @ V2))))) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V1) @ V2)) @ V3) @ V4))))))))))))))
(THOMOTOPIC_INTO_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V1)) @ V2)) @ ((c/__caret__ @ ((cretract_of @ V2) @ V0)) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V1) @ V0)) @ V3) @ V4))))) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V1) @ V2)) @ V3) @ V4)))))))))))))
(TOPEN_MAP_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V5)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V3) @ V5)))))) @ ((cSUBSET @ V2) @ V0))) @ ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cIN @ (V3 @ V6)) @ V2))) @ V6))))))) @ V4)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ ((cIMAGE @ V3) @ V4)))))))))))))))
(TCLOSED_MAP_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V5)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V3) @ V5)))))) @ ((cSUBSET @ V2) @ V0))) @ ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cIN @ (V3 @ V6)) @ V2))) @ V6))))))) @ V4)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ ((cIMAGE @ V3) @ V4)))))))))))))))
(TUPPER_HEMICONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cSUBSET @ (V2 @ V3)) @ V0))))) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cSUBSET @ (V2 @ V5)) @ V3))) @ V5)))))))))) @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (c~ @ ((c= @ ((cINTER @ (V2 @ V5)) @ V3)) @ cEMPTY)))) @ V5))))))))))))))))))
(TLOWER_HEMICONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cSUBSET @ (V2 @ V3)) @ V0))))) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cSUBSET @ (V2 @ V5)) @ V3))) @ V5)))))))))) @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (c~ @ ((c= @ ((cINTER @ (V2 @ V5)) @ V3)) @ cEMPTY)))) @ V5))))))))))))))))))
(TUPPER_LOWER_HEMICONTINUOUS_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((cSUBSET @ (V2 @ V5)) @ V0))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((cSUBSET @ (V2 @ V7)) @ V5))) @ V7)))))))))) @ (c! @ (^[V5]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((cSUBSET @ (V2 @ V7)) @ V5))) @ V7)))))))))))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((c/__caret__ @ (cbounded @ (V2 @ V3))) @ (c~ @ ((c= @ (V2 @ V3)) @ cEMPTY)))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V3) @ V6))) @ V5))) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ (V2 @ V3))) @ (c? @ (^[V8]: ((c/__caret__ @ ((cIN @ V8) @ (V2 @ V6))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V7) @ V8))) @ V4)))))))) @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ (V2 @ V6))) @ (c? @ (^[V8]: ((c/__caret__ @ ((cIN @ V8) @ (V2 @ V3))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V7) @ V8))) @ V4)))))))))))))))))))))))))))
(TCOVERING_SPACE_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccovering_space @ ((c__comma__ @ V1) @ V2)) @ V0)) @ ((c= @ (ccompact @ V1)) @ ((c/__caret__ @ (ccompact @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c= @ (V2 @ V5)) @ V3))) @ V5)))))))))))))))))))
(TCOVERING_SPACE_FINITE_SHEETS_EQ_PROPER_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccovering_space @ ((c__comma__ @ V1) @ V2)) @ V0)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c= @ (V2 @ V5)) @ V3))) @ V5)))))))))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (ccompact @ V3))) @ (ccompact @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5))))))))))))))))))
(TCONTINUOUS_ON_OPEN_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c= @ ((ccontinuous_on @ V2) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5))))))))))))))))))
(TCONTINUOUS_ON_CLOSED_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c= @ ((ccontinuous_on @ V2) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5))))))))))))))))))
(TPROPER_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (ccompact @ V3))) @ (ccompact @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5)))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V2) @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (ccompact @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c= @ (V2 @ V5)) @ V3))) @ V5)))))))))))))))))))
(TOPEN_MAP_IFF_LOWER_HEMICONTINUOUS_PREIMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V2) @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cSUBSET @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((c= @ (V2 @ V7)) @ V5))) @ V7)))))) @ V3))) @ V5))))))))))))))))))
(TOPEN_MAP_CLOSED_SUPERSET_PREIMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V2) @ V3)))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V0)) @ ((cSUBSET @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cIN @ (V2 @ V6)) @ V4))) @ V6)))))) @ V3)))) @ (c? @ (^[V5]: ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V5)) @ ((cSUBSET @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((cIN @ (V2 @ V7)) @ V5))) @ V7)))))) @ V3)))))))))))))))))))
(TCLOSED_MAP_IFF_UPPER_HEMICONTINUOUS_PREIMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V2) @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cSUBSET @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((c= @ (V2 @ V7)) @ V5))) @ V7)))))) @ V3))) @ V5))))))))))))))))))
(TCLOSED_MAP_OPEN_SUPERSET_PREIMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V2) @ V3)))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V0)) @ ((cSUBSET @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cIN @ (V2 @ V6)) @ V4))) @ V6)))))) @ V3)))) @ (c? @ (^[V5]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V5)) @ ((cSUBSET @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((cIN @ (V2 @ V7)) @ V5))) @ V7)))))) @ V3)))))))))))))))))))
(TCLOSED_MAP_OPEN_SUPERSET_PREIMAGE_POINT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V2) @ V3)))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cSUBSET @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((c= @ (V2 @ V6)) @ V4))) @ V6)))))) @ V3)))) @ (c? @ (^[V5]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((c/__caret__ @ ((cIN @ V4) @ V5)) @ ((cSUBSET @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((cIN @ (V2 @ V7)) @ V5))) @ V7)))))) @ V3)))))))))))))))))))
(TCONTINUOUS_CLOSED_GRAPH_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cPCROSS @ V1) @ V0))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ V1)) @ ((cpastecart @ V4) @ (V2 @ V4))))))))))))))))
(TEXTENSION_INTO_AR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c/__caret__ @ ((cretract_of @ V0) @ cUNIV)) @ (cclosed @ V1))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((ccontinuous_on @ V3) @ cUNIV)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ cUNIV)) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V3 @ V4)) @ (V2 @ V4)))))))))))))))))
(TNEIGHBOURHOOD_EXTENSION_INTO_ANR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c/__caret__ @ (cANR @ V0)) @ (cclosed @ V1))))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cSUBSET @ V1) @ V3)) @ ((c/__caret__ @ (copen @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V3)) @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((c= @ (V4 @ V5)) @ (V2 @ V5)))))))))))))))))))))
(TQUOTIENT_MAP_OPEN_MAP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V0)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3))))))) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V2) @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ ((cIMAGE @ V2) @ V3)))) @ V5))))))))))))))))))
(TQUOTIENT_MAP_CLOSED_MAP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V0)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3))))))) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V2) @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ ((cIMAGE @ V2) @ V3)))) @ V5))))))))))))))))))
(TCONTINUOUS_DISCONNECTED_RANGE_CONSTANT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconnected @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ ((cconnected_component @ V0) @ V3)) @ ((cINSERT @ V3) @ cEMPTY))))))))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V4)) @ V3))))))))))))))
(TCONTINUOUS_CLOSED_GRAPH_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0))) @ ((c= @ ((ccontinuous_on @ V2) @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cPCROSS @ V1) @ V0))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ V1)) @ ((cpastecart @ V4) @ (V2 @ V4)))))))))))))))))
(TNULLHOMOTOPIC_INTO_RELATIVE_FRONTIER_EXTENSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ (crelative_frontier @ V0))) @ ((c/__caret__ @ (cconvex @ V0)) @ (cbounded @ V0))))))) @ ((c= @ (c? @ (^[V3]: ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V1) @ (crelative_frontier @ V0))) @ V2) @ (^[V4]: V3))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((ccontinuous_on @ V3) @ cUNIV)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ cUNIV)) @ (crelative_frontier @ V0))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V3 @ V4)) @ (V2 @ V4))))))))))))))))))
(TNULLHOMOTOPIC_INTO_ANR_EXTENSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ (cANR @ V0)))))) @ ((c= @ (c? @ (^[V3]: ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V1) @ V0)) @ V2) @ (^[V4]: V3))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((ccontinuous_on @ V3) @ cUNIV)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ cUNIV)) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V3 @ V4)) @ (V2 @ V4))))))))))))))))))
(Tcovering_space,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccovering_space @ ((c__comma__ @ V1) @ V2)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V1)) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V3) @ V4)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ ((c= @ (cUNIONS @ V5)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((cIN @ (V2 @ V7)) @ V4))) @ V7))))))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V5)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V6))))) @ ((c/__caret__ @ ((cpairwise @ cDISJOINT) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V5)) @ (c? @ (^[V7]: ((chomeomorphism @ ((c__comma__ @ V6) @ V4)) @ ((c__comma__ @ V2) @ V7)))))))))))))))))))))))))))))
(TCOVERING_SPACE_LIFT_PATH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V2)) @ V0)) @ ((c/__caret__ @ (cpath @ V3)) @ ((cSUBSET @ (cpath_image @ V3)) @ V0)))) @ (c? @ (^[V4]: ((c/__caret__ @ (cpath @ V4)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V4)) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V2 @ (V4 @ V5))) @ (V3 @ V5)))))))))))))))))))
(TCOVERING_SPACE_SIMPLY_CONNECTED_LOOP_LIFT_IS_LOOP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V2)) @ V0)) @ ((c/__caret__ @ (csimply_connected @ V0)) @ ((c/__caret__ @ (cpath @ V3)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V3)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V3)) @ (cpathstart @ V3))) @ ((c/__caret__ @ (cpath @ V4)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V4)) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V2 @ (V4 @ V5))) @ (V3 @ V5))))))))))))) @ ((c= @ (cpathfinish @ V4)) @ (cpathstart @ V4))))))))))))))
(TCONTINUOUS_OPEN_IN_PREIMAGE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5))))))))))))))))
(TCONTINUOUS_CLOSED_IN_PREIMAGE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5))))))))))))))))
(TPROPER_MAP_FROM_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c/__caret__ @ (ccompact @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3))))) @ (ccompact @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5))))))))))))))))
(TCONNECTED_OPEN_MONOTONE_PREIMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V4)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V2) @ V4)))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ (cconnected @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((c= @ (V2 @ V6)) @ V4))) @ V6))))))))))))) @ ((c==> @ ((c/__caret__ @ (cconnected @ V3)) @ ((cSUBSET @ V3) @ V0))) @ (cconnected @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5)))))))))))))))))
(TCONNECTED_CLOSED_MONOTONE_PREIMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V4)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cIMAGE @ V2) @ V4)))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ (cconnected @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((c= @ (V2 @ V6)) @ V4))) @ V6))))))))))))) @ ((c==> @ ((c/__caret__ @ (cconnected @ V3)) @ ((cSUBSET @ V3) @ V0))) @ (cconnected @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5)))))))))))))))))
(TCONNECTED_MONOTONE_QUOTIENT_PREIMAGE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cSUBSET @ V4) @ V0)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cIN @ (V2 @ V6)) @ V4))) @ V6))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ (cconnected @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((c= @ (V2 @ V6)) @ V4))) @ V6)))))))))) @ ((c/__caret__ @ ((c__caret__/ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3))) @ (cconnected @ V3)))))) @ (cconnected @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ (V2 @ V5)) @ V3))) @ V5))))))))))))))))
(TQUOTIENT_MAP_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cSUBSET @ V5) @ V0)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((cIN @ (V2 @ V7)) @ V5))) @ V7))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)))))) @ ((c__caret__/ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3))))) @ ((c==> @ ((cSUBSET @ V4) @ V3)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cIN @ (V2 @ V6)) @ V3))) @ V6))))))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V1)) @ ((cIN @ (V2 @ V8)) @ V3))) @ V8))))))) @ ((cIN @ (V2 @ V6)) @ V4))) @ V6))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V3)) @ V4)))))))))))))))
(TCOVERING_SPACE_FINITE_EQ_COMPACT_FIBRE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((ccovering_space @ ((c__comma__ @ V1) @ V2)) @ V0)) @ ((c= @ (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c= @ (V2 @ V5)) @ V3))) @ V5))))))) @ (ccompact @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c= @ (V2 @ V5)) @ V3))) @ V5)))))))))))))))))
(TCOVERING_SPACE_COUNTABLE_SHEETS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((ccovering_space @ ((c__comma__ @ V1) @ V2)) @ V0)) @ (cCOUNTABLE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c= @ (V2 @ V5)) @ V3))) @ V5))))))))))))))))
(TCOVERING_SPACE_FINITE_SHEETS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V2)) @ V0)) @ (ccompact @ V1))) @ (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c= @ (V2 @ V5)) @ V3))) @ V5))))))))))))))))
(TCOVERING_SPACE_INJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V2)) @ V0)) @ ((c/__caret__ @ (cpath_connected @ V1)) @ (csimply_connected @ V0)))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))))))))))
(TAR_IMP_ABSOLUTE_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cAR @ V0)) @ ((c/__caret__ @ ((chomeomorphic @ V0) @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V1)))) @ ((cretract_of @ V1) @ V2)))))))))
(TANR_IMP_ABSOLUTE_NEIGHBOURHOOD_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cANR @ V0)) @ ((c/__caret__ @ ((chomeomorphic @ V0) @ V2)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2)))) @ (c? @ (^[V3]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cretract_of @ V2) @ V3))))))))))))
(TANR_IMP_ABSOLUTE_CLOSED_NEIGHBOURHOOD_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cANR @ V0)) @ ((c/__caret__ @ ((chomeomorphic @ V0) @ V2)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2)))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V4)) @ ((cretract_of @ V2) @ V4)))))))))))))))))
(TCOVERING_SPACE_LIFT_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V5)) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V4)) @ ((c/__caret__ @ (csimply_connected @ V4)) @ ((c/__caret__ @ ((clocally @ cpath_connected) @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V6) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V6) @ V4)) @ V0)) @ ((c= @ (V6 @ V2)) @ (V5 @ V3)))))))))) @ (c? @ (^[V7]: ((c/__caret__ @ ((ccontinuous_on @ V7) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V7) @ V4)) @ V1)) @ ((c/__caret__ @ ((c= @ (V7 @ V2)) @ V3)) @ (c! @ (^[V8]: ((c==> @ ((cIN @ V8) @ V4)) @ ((c= @ (V5 @ (V7 @ V8))) @ (V6 @ V8))))))))))))))))))))))))))
(TCOVERING_SPACE_LIFT_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V5)) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V4)) @ ((c/__caret__ @ (cpath_connected @ V4)) @ ((c/__caret__ @ ((clocally @ cpath_connected) @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V6) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V6) @ V4)) @ V0)) @ ((c/__caret__ @ ((c= @ (V6 @ V2)) @ (V5 @ V3))) @ (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ (cpath @ V7)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V7)) @ V4)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V7)) @ V2)) @ ((c= @ (cpathfinish @ V7)) @ V2))))) @ (c? @ (^[V8]: ((c/__caret__ @ (cpath @ V8)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V8)) @ V1)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V8)) @ V3)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V8)) @ V3)) @ (((chomotopic_paths @ V0) @ ((co @ V6) @ V7)) @ ((co @ V5) @ V8)))))))))))))))))))) @ (c? @ (^[V7]: ((c/__caret__ @ ((ccontinuous_on @ V7) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V7) @ V4)) @ V1)) @ ((c/__caret__ @ ((c= @ (V7 @ V2)) @ V3)) @ (c! @ (^[V8]: ((c==> @ ((cIN @ V8) @ V4)) @ ((c= @ (V5 @ (V7 @ V8))) @ (V6 @ V8))))))))))))))))))))))))))
(TCOVERING_SPACE_LIFT_STRONGER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V5)) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V4)) @ ((c/__caret__ @ (cpath_connected @ V4)) @ ((c/__caret__ @ ((clocally @ cpath_connected) @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V6) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V6) @ V4)) @ V0)) @ ((c/__caret__ @ ((c= @ (V6 @ V2)) @ (V5 @ V3))) @ (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ (cpath @ V7)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V7)) @ V4)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V7)) @ V2)) @ ((c= @ (cpathfinish @ V7)) @ V2))))) @ (c? @ (^[V8]: (((chomotopic_paths @ V0) @ ((co @ V6) @ V7)) @ (clinepath @ ((c__comma__ @ V8) @ V8))))))))))))))))) @ (c? @ (^[V7]: ((c/__caret__ @ ((ccontinuous_on @ V7) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V7) @ V4)) @ V1)) @ ((c/__caret__ @ ((c= @ (V7 @ V2)) @ V3)) @ (c! @ (^[V8]: ((c==> @ ((cIN @ V8) @ V4)) @ ((c= @ (V5 @ (V7 @ V8))) @ (V6 @ V8))))))))))))))))))))))))))
(TMUMFORD_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V0)) @ ((c/__caret__ @ ((clocally @ ccompact) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (ccompact @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c= @ (V3 @ V5)) @ V2))) @ V5))))))))))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V4)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((c/__caret__ @ ((cSUBSET @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((c= @ (V3 @ V7)) @ V2))) @ V7)))))) @ V4)) @ ((c/__caret__ @ ((cIN @ V2) @ V5)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V4)) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V6) @ V5)) @ (ccompact @ V6))) @ (ccompact @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V4)) @ ((cIN @ (V3 @ V8)) @ V6))) @ V8))))))))))))))))))))))))))))
(TUPPER_LOWER_HEMICONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((cSUBSET @ (V3 @ V5)) @ V0))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((cSUBSET @ (V3 @ V7)) @ V5))) @ V7)))))))))) @ (c! @ (^[V5]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((cSUBSET @ (V3 @ V7)) @ V5))) @ V7)))))))))))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (cbounded @ (V3 @ V2))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V2) @ V6))) @ V5))) @ ((creal_lt @ (chausdist @ ((c__comma__ @ (V3 @ V2)) @ (V3 @ V6)))) @ V4))))))))))))))))))))
(TCOVERING_SPACE_LIFT_PATH_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V3)) @ V0)) @ ((c/__caret__ @ (cpath @ V4)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V4)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V4)) @ (V3 @ V2))) @ ((cIN @ V2) @ V1)))))) @ (c? @ (^[V5]: ((c/__caret__ @ (cpath @ V5)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V5)) @ V1)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V5)) @ V2)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (V3 @ (V5 @ V6))) @ (V4 @ V6))))))))))))))))))))))
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(THOMEOMORPHISM_MOVING_POINTS_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (copen @ V4)) @ ((c/__caret__ @ (cconnected @ V4)) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ ((cIN @ (V2 @ V5)) @ V4)) @ ((cIN @ (V3 @ V5)) @ V4)))))) @ ((cpairwise @ (^[V5]: (^[V6]: ((c/__caret__ @ (c~ @ ((c= @ (V2 @ V5)) @ (V2 @ V6)))) @ (c~ @ ((c= @ (V3 @ V5)) @ (V3 @ V6))))))) @ V1)))))))) @ (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((chomeomorphism @ ((c__comma__ @ V0) @ V0)) @ ((c__comma__ @ V5) @ V6))) @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V1)) @ ((c= @ (V5 @ (V2 @ V7))) @ (V3 @ V7)))))) @ ((c/__caret__ @ ((cSUBSET @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ (c~ @ ((c/__caret__ @ ((c= @ (V5 @ V8)) @ V8)) @ ((c= @ (V6 @ V8)) @ V8)))) @ V8)))))) @ V4)) @ (cbounded @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ (c~ @ ((c/__caret__ @ ((c= @ (V5 @ V8)) @ V8)) @ ((c= @ (V6 @ V8)) @ V8)))) @ V8)))))))))))))))))))))))))
(THOMOTOPIC_LOOPS_SHIFTPATH_SELF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V2)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V2)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V2)) @ (cpathstart @ V2))) @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))))) @ (((chomotopic_loops @ V0) @ V2) @ ((cshiftpath @ V1) @ V2))))))))))
(THOMOTOPIC_JOIN_SUBPATHS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cpath @ V4)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V4)) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))))))) @ (((chomotopic_paths @ V0) @ ((c++ @ (((csubpath @ V2) @ V1) @ V4)) @ (((csubpath @ V1) @ V3) @ V4))) @ (((csubpath @ V2) @ V3) @ V4))))))))))))))
(TCONTINUOUS_AT_LIFT_SETDIST,(c! @ (^[V0]: (c! @ (^[V1]: ((ccontinuous @ (^[V2]: (clift @ (csetdist @ ((c__comma__ @ ((cINSERT @ V2) @ cEMPTY)) @ V0))))) @ (cat @ V1)))))))
(TCLOSED_IN_CONNECTED_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cconnected_component @ V0) @ V1)))))))
(TPATH_COMPONENT_SUBSET_CONNECTED_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ ((cpath_component @ V0) @ V1)) @ ((cconnected_component @ V0) @ V1)))))))
(TAFFINE_HULL_INSERT_SUBSET_SPAN,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ ((chull @ caffine) @ ((cINSERT @ V1) @ V0))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ (cspan @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ V0)) @ ((cvector_sub @ V5) @ V1))))))))) @ ((cvector_add @ V1) @ V3))))))))))))
(TOPEN_IN_PATH_COMPONENT_LOCALLY_PATH_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ cpath_connected) @ V0)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cpath_component @ V0) @ V1))))))))
(TLOCALLY_PATH_CONNECTED_PATH_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ cpath_connected) @ V0)) @ ((clocally @ cpath_connected) @ ((cpath_component @ V0) @ V1))))))))
(TLOCALLY_PATH_CONNECTED_CONNECTED_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ cpath_connected) @ V0)) @ ((clocally @ cpath_connected) @ ((cconnected_component @ V0) @ V1))))))))
(TCLOSED_IN_PATH_COMPONENT_LOCALLY_PATH_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ cpath_connected) @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cpath_component @ V0) @ V1))))))))
(TPATH_COMPONENT_EQ_CONNECTED_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ cpath_connected) @ V0)) @ ((c= @ ((cpath_component @ V0) @ V1)) @ ((cconnected_component @ V0) @ V1))))))))
(TOPEN_IN_CONNECTED_COMPONENT_LOCALLY_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ cconnected) @ V0)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ ((cconnected_component @ V0) @ V1))))))))
(TLOCALLY_CONNECTED_CONNECTED_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ cconnected) @ V0)) @ ((clocally @ cconnected) @ ((cconnected_component @ V0) @ V1))))))))
(TLOCALLY_COMPACT_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((clocally @ ccompact) @ V0)) @ ((clocally @ ccompact) @ ((cDELETE @ V0) @ V1))))))))
(TNETLIMIT_WITHIN_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ (cinterior @ V0))) @ ((c= @ (cnetlimit @ ((cwithin @ (cat @ V1)) @ V0))) @ V1)))))))
(TPATH_COMPONENT_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (((cpath_component @ V0) @ V1) @ V1)))))))
(TCONNECTED_COMPONENT_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (((cconnected_component @ V0) @ V1) @ V1)))))))
(TAFFINE_HULL_SPAN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c= @ ((chull @ caffine) @ V0)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ (cspan @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ ((cDELETE @ V0) @ V1))) @ ((cvector_sub @ V5) @ V1))))))))) @ ((cvector_add @ V1) @ V3)))))))))))))
(TDIFFS_AFFINE_HULL_SPAN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ ((chull @ caffine) @ V0))) @ ((cvector_sub @ V3) @ V1))))))) @ (cspan @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cvector_sub @ V3) @ V1))))))))))))))
(TCLOSEST_POINT_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ ((c= @ ((cclosest_point @ V0) @ V1)) @ V1)))))))
(TORTHONORMAL_BASIS_EXPAND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cIN @ V1) @ (cspan @ V0))))) @ ((c= @ ((cvsum @ V0) @ (^[V2]: ((c% @ ((cdot @ V2) @ V1)) @ V2)))) @ V1)))))))
(TBESSEL_INEQUALITY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((creal_le @ ((csum @ V0) @ (^[V2]: ((creal_pow @ ((cdot @ V2) @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TCARD_LT_IMP_DISCONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<_c @ V0) @ cUNIV)) @ ((cIN @ V1) @ V0))) @ ((c= @ ((cconnected_component @ V0) @ V1)) @ ((cINSERT @ V1) @ cEMPTY))))))))
(TPATH_CONNECTED_OPEN_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (copen @ V0)) @ (cconnected @ V0)))) @ (cpath_connected @ ((cDELETE @ V0) @ V1))))))))
(TCONNECTED_OPEN_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (copen @ V0)) @ (cconnected @ V0)))) @ (cconnected @ ((cDELETE @ V0) @ V1))))))))
(TAFFINE_INDEPENDENT_CARD_DIM_DIFFS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V0))) @ ((cIN @ V1) @ V0))) @ ((c= @ (cCARD @ V0)) @ ((c+ @ (cdim @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cvector_sub @ V3) @ V1)))))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TLIMPT_OF_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((cIN @ V1) @ V0))) @ ((c= @ ((climit_point_of @ V1) @ V0)) @ (c~ @ ((c= @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))))
(TTRIVIAL_LIMIT_WITHIN_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((cIN @ V1) @ V0))) @ ((c= @ (ctrivial_limit @ ((cwithin @ (cat @ V1)) @ V0))) @ ((c= @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))))
(TSUPPORTING_HYPERPLANE_RELATIVE_FRONTIER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ ((cIN @ V1) @ (cclosure @ V0))) @ (c~ @ ((cIN @ V1) @ (crelative_interior @ V0)))))) @ (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (cclosure @ V0))) @ ((creal_le @ ((cdot @ V2) @ V1)) @ ((cdot @ V2) @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (crelative_interior @ V0))) @ ((creal_lt @ ((cdot @ V2) @ V1)) @ ((cdot @ V2) @ V3)))))))))))))))
(TSUPPORTING_HYPERPLANE_RELATIVE_BOUNDARY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c~ @ ((cIN @ V1) @ (crelative_interior @ V0)))))) @ (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ ((cdot @ V2) @ V1)) @ ((cdot @ V2) @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (crelative_interior @ V0))) @ ((creal_lt @ ((cdot @ V2) @ V1)) @ ((cdot @ V2) @ V3)))))))))))))))
(TRELATIVE_BOUNDARY_RETRACT_OF_PUNCTURED_AFFINE_HULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (ccompact @ V0)) @ ((cIN @ V1) @ (crelative_interior @ V0))))) @ ((cretract_of @ ((cDIFF @ V0) @ (crelative_interior @ V0))) @ ((cDELETE @ ((chull @ caffine) @ V0)) @ V1))))))))
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(THAS_DERIVATIVE_MUL_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((chas_derivative @ ((co @ clift) @ V0)) @ ((co @ clift) @ V2)) @ ((cwithin @ (cat @ V4)) @ V5))) @ (((chas_derivative @ V3) @ V1) @ ((cwithin @ (cat @ V4)) @ V5)))) @ (((chas_derivative @ (^[V6]: ((c% @ (V0 @ V6)) @ (V3 @ V6)))) @ (^[V6]: ((cvector_add @ ((c% @ (V0 @ V4)) @ (V1 @ V6))) @ ((c% @ (V2 @ V6)) @ (V3 @ V4))))) @ ((cwithin @ (cat @ V4)) @ V5))))))))))))))))
(TUNIFORMLY_CONTINUOUS_ON_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cuniformly_continuous_on @ ((co @ clift) @ V0)) @ V2)) @ ((c/__caret__ @ ((cuniformly_continuous_on @ V1) @ V2)) @ ((c/__caret__ @ (cbounded @ ((cIMAGE @ ((co @ clift) @ V0)) @ V2))) @ (cbounded @ ((cIMAGE @ V1) @ V2)))))) @ ((cuniformly_continuous_on @ (^[V3]: ((c% @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TDIFFERENTIABLE_ON_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdifferentiable_on @ ((co @ clift) @ V0)) @ V2)) @ ((cdifferentiable_on @ V1) @ V2))) @ ((cdifferentiable_on @ (^[V3]: ((c% @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TDIFFERENTIABLE_MUL_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ ((co @ clift) @ V0)) @ (cat @ V2))) @ ((cdifferentiable @ V1) @ (cat @ V2)))) @ ((cdifferentiable @ (^[V3]: ((c% @ (V0 @ V3)) @ (V1 @ V3)))) @ (cat @ V2))))))))))
(TDIFFERENTIABLE_MUL_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ ((co @ clift) @ V0)) @ ((cwithin @ (cat @ V2)) @ V3))) @ ((cdifferentiable @ V1) @ ((cwithin @ (cat @ V2)) @ V3)))) @ ((cdifferentiable @ (^[V4]: ((c% @ (V0 @ V4)) @ (V1 @ V4)))) @ ((cwithin @ (cat @ V2)) @ V3))))))))))))
(TUNIFORMLY_CONTINUOUS_ON_VMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cuniformly_continuous_on @ ((co @ clift) @ V0)) @ V2)) @ ((cuniformly_continuous_on @ (^[V3]: ((c% @ (V0 @ V3)) @ V1))) @ V2)))))))))
(TBILINEAR_BOUNDED,(c! @ (^[V0]: ((c==> @ (cbilinear @ V0)) @ (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((creal_le @ (cvector_norm @ ((V0 @ V2) @ V3))) @ ((creal_mul @ V1) @ ((creal_mul @ (cvector_norm @ V2)) @ (cvector_norm @ V3))))))))))))))
(TBILINEAR_EQ_STDBASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbilinear @ V0)) @ ((c/__caret__ @ (cbilinear @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))))) @ ((c= @ ((V0 @ (cbasis @ V2)) @ (cbasis @ V3))) @ ((V1 @ (cbasis @ V2)) @ (cbasis @ V3))))))))))) @ ((c= @ V0) @ V1)))))))
(TBILINEAR_CONTINUOUS_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V1) @ V3)) @ ((c/__caret__ @ ((ccontinuous @ V2) @ V3)) @ (cbilinear @ V0)))) @ ((ccontinuous @ (^[V4]: ((V0 @ (V1 @ V4)) @ (V2 @ V4)))) @ V3)))))))))))
(TBABY_SARD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ (((chas_derivative @ V1) @ (V0 @ V3)) @ ((cwithin @ (cat @ V3)) @ V2))) @ ((c< @ (crank @ (cmatrix @ (V0 @ V3)))) @ (cdimindex @ cUNIV)))))))) @ (cnegligible @ ((cIMAGE @ V1) @ V2))))))))))
(THAS_ANTIDERIVATIVE_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: (c? @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ (((chas_derivative @ V3) @ (V4 @ V5)) @ ((cwithin @ (cat @ V5)) @ V1))) @ (c! @ (^[V6]: ((creal_le @ (cvector_norm @ ((cvector_sub @ ((V4 @ V5) @ V6)) @ ((V0 @ V5) @ V6)))) @ ((creal_mul @ V2) @ (cvector_norm @ V6)))))))))))))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (((chas_derivative @ V2) @ (V0 @ V3)) @ ((cwithin @ (cat @ V3)) @ V1)))))))))))))
(TDIFFERENTIABLE_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V1)) @ (((chas_derivative @ V2) @ (V0 @ V6)) @ ((cwithin @ (cat @ V6)) @ V1)))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V1)) @ ((creal_le @ (conorm @ (V0 @ V6))) @ V3))))))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ V5) @ V1))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ (V2 @ V4)) @ (V2 @ V5)))) @ ((creal_mul @ V3) @ (cvector_norm @ ((cvector_sub @ V4) @ V5)))))))))))))))))))
(TDOMINATED_CONVERGENCE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((cintegrable_on @ (V1 @ V4)) @ V3)))) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((creal_le @ (cvector_norm @ ((V1 @ V4) @ V5))) @ (cdrop @ (V0 @ V5))))))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ (((c--> @ (^[V5]: ((V1 @ V5) @ V4))) @ (V2 @ V4)) @ csequentially)))))))) @ ((cintegrable_on @ V2) @ V3)))))))))))
(TDOMINATED_CONVERGENCE_ABSOLUTELY_INTEGRABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((cabsolutely_integrable_on @ (V1 @ V4)) @ V3)))) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((creal_le @ (cvector_norm @ (V2 @ V5))) @ (cdrop @ (V0 @ V5))))))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ (((c--> @ (^[V5]: ((V1 @ V5) @ V4))) @ (V2 @ V4)) @ csequentially)))))))) @ ((cabsolutely_integrable_on @ V2) @ V3)))))))))))
(TDOMINATED_CONVERGENCE_INTEGRABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((cabsolutely_integrable_on @ (V1 @ V4)) @ V3)))) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((creal_le @ (cvector_norm @ (V2 @ V5))) @ (cdrop @ (V0 @ V5))))))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ (((c--> @ (^[V5]: ((V1 @ V5) @ V4))) @ (V2 @ V4)) @ csequentially)))))))) @ ((cintegrable_on @ V2) @ V3)))))))))))
(TDOMINATED_CONVERGENCE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((cintegrable_on @ (V1 @ V4)) @ V2)))) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V2)) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((creal_le @ (cvector_norm @ ((V1 @ V4) @ V5))) @ (cdrop @ (V0 @ V5))))))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ (((c--> @ (^[V5]: ((V1 @ V5) @ V4))) @ (V3 @ V4)) @ csequentially)))))))) @ (((c--> @ (^[V4]: ((cintegral @ V2) @ (V1 @ V4)))) @ ((cintegral @ V2) @ V3)) @ csequentially)))))))))))
(TABSOLUTELY_INTEGRABLE_ABSOLUTELY_INTEGRABLE_DROP_UBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ (cdrop @ (V1 @ V3))) @ (cdrop @ (V0 @ V3))))))) @ ((c/__caret__ @ ((cintegrable_on @ V1) @ V2)) @ ((cabsolutely_integrable_on @ V0) @ V2)))) @ ((cabsolutely_integrable_on @ V1) @ V2)))))))))
(TABSOLUTELY_INTEGRABLE_ABSOLUTELY_INTEGRABLE_DROP_LBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ (cdrop @ (V0 @ V3))) @ (cdrop @ (V1 @ V3))))))) @ ((c/__caret__ @ ((cabsolutely_integrable_on @ V0) @ V2)) @ ((cintegrable_on @ V1) @ V2)))) @ ((cabsolutely_integrable_on @ V1) @ V2)))))))))
(TMEASURABLE_ON_DROP_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V0) @ V2)) @ ((cmeasurable_on @ V1) @ V2))) @ ((cmeasurable_on @ (^[V3]: ((c% @ (cdrop @ (V0 @ V3))) @ (V1 @ V3)))) @ V2)))))))))
(TMEASURABLE_BOUNDED_BY_INTEGRABLE_IMP_INTEGRABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V2)) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ (cvector_norm @ (V1 @ V3))) @ (cdrop @ (V0 @ V3))))))))) @ ((cintegrable_on @ V1) @ V2)))))))))
(TMEASURABLE_BOUNDED_BY_INTEGRABLE_IMP_ABSOLUTELY_INTEGRABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V2)) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ (cvector_norm @ (V1 @ V3))) @ (cdrop @ (V0 @ V3))))))))) @ ((cabsolutely_integrable_on @ V1) @ V2)))))))))
(TABSOLUTELY_INTEGRABLE_INTEGRABLE_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ (cvector_norm @ (V1 @ V3))) @ (cdrop @ (V0 @ V3))))))) @ ((c/__caret__ @ ((cintegrable_on @ V1) @ V2)) @ ((cintegrable_on @ V0) @ V2)))) @ ((cabsolutely_integrable_on @ V1) @ V2)))))))))
(TINTEGRABLE_ON_ALL_INTERVALS_INTEGRABLE_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((cintegrable_on @ (^[V5]: (((cCOND @ ((cIN @ V5) @ V2)) @ (V1 @ V5)) @ (cvec @ (cNUMERAL @ c_0))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ (cvector_norm @ (V1 @ V3))) @ (cdrop @ (V0 @ V3))))))) @ ((cintegrable_on @ V0) @ V2)))) @ ((cintegrable_on @ V1) @ V2)))))))))
(TINTEGRAL_DROP_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V1)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (cdrop @ (V0 @ V3))) @ (cdrop @ (V2 @ V3))))))))) @ ((creal_le @ (cdrop @ ((cintegral @ V1) @ V0))) @ (cdrop @ ((cintegral @ V1) @ V2)))))))))))
(TABSOLUTELY_INTEGRABLE_ABSOLUTELY_INTEGRABLE_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ (cvector_norm @ (V1 @ V3))) @ (cvector_norm @ (V0 @ V3))))))) @ ((c/__caret__ @ ((cintegrable_on @ V1) @ V2)) @ ((cabsolutely_integrable_on @ V0) @ V2)))) @ ((cabsolutely_integrable_on @ V1) @ V2)))))))))
(TOPERATIVE_INTEGRAL,(c! @ (^[V0]: ((coperative @ (clifted @ cvector_add)) @ (^[V1]: (((cCOND @ ((cintegrable_on @ V0) @ V1)) @ (cSOME @ ((cintegral @ V1) @ V0))) @ cNONE))))))
(TMEASURABLE_ON_EMPTY,(c! @ (^[V0]: ((cmeasurable_on @ V0) @ cEMPTY))))
(TCONTINUOUS_ON_EMPTY,(c! @ (^[V0]: ((ccontinuous_on @ V0) @ cEMPTY))))
(TCONTINUOUS_IMP_MEASURABLE_ON,(c! @ (^[V0]: ((c==> @ ((ccontinuous_on @ V0) @ cUNIV)) @ ((cmeasurable_on @ V0) @ cUNIV)))))
(TBOUNDED_SETVARIATION_ABSOLUTELY_INTEGRABLE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ cUNIV)) @ ((chas_bounded_setvariation_on @ (^[V1]: ((cintegral @ V1) @ V0))) @ cUNIV))) @ ((cabsolutely_integrable_on @ V0) @ cUNIV)))))
(TISOMETRY_LINEAR,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c= @ (V0 @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0)))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cdistance @ ((c__comma__ @ (V0 @ V1)) @ (V0 @ V2)))) @ (cdistance @ ((c__comma__ @ V1) @ V2))))))))) @ (clinear @ V0)))))
(TLINEAR_BIJECTIVE_DIMINDEX_EQ,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))))) @ ((c= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))))))
(TLINEAR_BIJECTIVE_LEFT_RIGHT_INVERSE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c= @ (V1 @ (V0 @ V2))) @ V2)))) @ (c! @ (^[V2]: ((c= @ (V0 @ (V1 @ V2))) @ V2)))))))))))
(TLINEAR_SURJECTIVE_DIMINDEX_LE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1))))))) @ ((c<= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))))))
(TLINEAR_SURJECTIVE_RIGHT_INVERSE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c= @ ((co @ V0) @ V1)) @ cI))))))))
(TLINEAR_INJECTIVE_DIMINDEX_LE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))) @ ((c<= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))))))
(TLINEAR_INJECTIVE_BOUNDED_BELOW_POS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c! @ (^[V2]: ((creal_le @ ((creal_mul @ (cvector_norm @ V2)) @ V1)) @ (cvector_norm @ (V0 @ V2))))))))))))
(TLINEAR_INJECTIVE_LEFT_INVERSE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c= @ ((co @ V1) @ V0)) @ cI))))))))
(TONORM_NEG,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (conorm @ (^[V1]: (cvector_neg @ (V0 @ V1))))) @ (conorm @ V0))))))
(TDIM_IMAGE_KERNEL,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ ((c+ @ (cdim @ ((cIMAGE @ V0) @ cUNIV))) @ (cdim @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c= @ (V0 @ V2)) @ (cvec @ (cNUMERAL @ c_0)))) @ V2)))))))) @ (cdimindex @ cUNIV))))))
(TADJOINT_ADJOINT,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (cadjoint @ (cadjoint @ V0))) @ V0)))))
(TMATRIX_VECTOR_MUL,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ V0) @ (^[V1]: ((cmatrix_vector_mul @ (cmatrix @ V0)) @ V1)))))))
(TONORM_EQ_0,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ ((c= @ (conorm @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c! @ (^[V1]: ((c= @ (V0 @ V1)) @ (cvec @ (cNUMERAL @ c_0))))))))))
(TMATRIX_RIGHT_INVERTIBLE,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ (cmatrix @ V0)) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c= @ ((co @ V0) @ V1)) @ cI)))))))))
(TMATRIX_LEFT_INVERTIBLE,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V1) @ (cmatrix @ V0))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ ((c= @ ((co @ V1) @ V0)) @ cI)))))))))
(TADJOINT_INJECTIVE,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ ((cadjoint @ V0) @ V1)) @ ((cadjoint @ V0) @ V2))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1))))))))))
(TADJOINT_SURJECTIVE,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ ((cadjoint @ V0) @ V2)) @ V1)))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))))))
(TADJOINT_LINEAR,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ (clinear @ (cadjoint @ V0))))))
(TLINEAR_BOUNDED_POS,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c! @ (^[V2]: ((creal_le @ (cvector_norm @ (V0 @ V2))) @ ((creal_mul @ V1) @ (cvector_norm @ V2))))))))))))
(TLINEAR_BOUNDED,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ (c? @ (^[V1]: (c! @ (^[V2]: ((creal_le @ (cvector_norm @ (V0 @ V2))) @ ((creal_mul @ V1) @ (cvector_norm @ V2)))))))))))
(TONORM_conjunct1,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((creal_le @ (cvector_norm @ (V0 @ V2))) @ ((creal_mul @ V1) @ (cvector_norm @ V2)))))) @ ((creal_le @ (conorm @ V0)) @ V1))))))))
(TONORM_conjunct0,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ (c! @ (^[V1]: ((creal_le @ (cvector_norm @ (V0 @ V1))) @ ((creal_mul @ (conorm @ V0)) @ (cvector_norm @ V1)))))))))
(TADJOINT_CLAUSES_conjunct1,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ ((cadjoint @ V0) @ V2)) @ V1)) @ ((cdot @ V2) @ (V0 @ V1)))))))))))
(TADJOINT_CLAUSES_conjunct0,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ V1) @ ((cadjoint @ V0) @ V2))) @ ((cdot @ (V0 @ V1)) @ V2))))))))))
(TINTEGRABLE_SUBINTERVALS_IMP_MEASURABLE,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))) @ ((cmeasurable_on @ V0) @ cUNIV)))))
(TINTEGRABLE_CCONTINUOUS_EXPLICIT_SYMMETRIC,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (cnegligible @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((cIN @ V2) @ V1))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((creal_lt @ V5) @ V4))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((c% @ (creal_inv @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cvector_sub @ V2) @ ((c% @ V5) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cvector_add @ V2) @ ((c% @ V5) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ cNIL))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cvector_sub @ V2) @ ((c% @ V5) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cvector_add @ V2) @ ((c% @ V5) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ cNIL))) @ V0))) @ (V0 @ V2)))) @ V3)))))))))))))))))))
(TINTEGRABLE_CCONTINUOUS_EXPLICIT,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (cnegligible @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((cIN @ V2) @ V1))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((creal_lt @ V5) @ V4))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((c% @ (creal_inv @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ ((cvector_add @ V2) @ ((c% @ V5) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ cNIL))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ ((cvector_add @ V2) @ ((c% @ V5) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ cNIL))) @ V0))) @ (V0 @ V2)))) @ V3)))))))))))))))))))
(TABSOLUTELY_INTEGRABLE_LEBESGUE_POINTS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((cabsolutely_integrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (cnegligible @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((cIN @ V2) @ V1))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((creal_lt @ V5) @ V4))) @ ((creal_lt @ (cvector_norm @ ((c% @ (creal_inv @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cvector_sub @ V2) @ ((c% @ V5) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cvector_add @ V2) @ ((c% @ V5) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ cNIL))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cvector_sub @ V2) @ ((c% @ V5) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cvector_add @ V2) @ ((c% @ V5) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ cNIL))) @ (^[V6]: (clift @ (cvector_norm @ ((cvector_sub @ (V0 @ V6)) @ (V0 @ V2))))))))) @ V3)))))))))))))))))))
(TISOMETRY_IMP_AFFINITY,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cdistance @ ((c__comma__ @ (V0 @ V1)) @ (V0 @ V2)))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V2]: ((c= @ (V0 @ V2)) @ ((cvector_add @ (V0 @ (cvec @ (cNUMERAL @ c_0)))) @ (V1 @ V2))))))))))))
(Tonorm,(c! @ (^[V0]: ((c= @ (conorm @ V0)) @ (csup @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cvector_norm @ (V0 @ V2))))))))))))
(Tadjoint,(c! @ (^[V0]: ((c= @ (cadjoint @ V0)) @ (c__at__ @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cdot @ (V0 @ V2)) @ V3)) @ ((cdot @ V2) @ (V1 @ V3)))))))))))))
(Tmatrix,(c! @ (^[V0]: ((c= @ (cmatrix @ V0)) @ (clambda @ (^[V1]: (clambda @ (^[V2]: ((c$ @ (V0 @ (cbasis @ V2))) @ V1)))))))))
(TMEASURABLE_ON_SIMPLE_FUNCTION_LIMIT,(c! @ (^[V0]: ((c= @ ((cmeasurable_on @ V0) @ cUNIV)) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: ((cmeasurable_on @ (V1 @ V2)) @ cUNIV)))) @ ((c/__caret__ @ (c! @ (^[V2]: (cFINITE @ ((cIMAGE @ (V1 @ V2)) @ cUNIV))))) @ (c! @ (^[V2]: (((c--> @ (^[V3]: ((V1 @ V3) @ V2))) @ (V0 @ V2)) @ csequentially)))))))))))
(TMEASURABLE_ON_PREIMAGE_OPEN_HALFSPACE_COMPONENT_LT,(c! @ (^[V0]: ((c= @ ((cmeasurable_on @ V0) @ cUNIV)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((creal_lt @ ((c$ @ (V0 @ V4)) @ V2)) @ V1)) @ V4)))))))))))))))
(TMEASURABLE_ON_PREIMAGE_OPEN_HALFSPACE_COMPONENT_LE,(c! @ (^[V0]: ((c= @ ((cmeasurable_on @ V0) @ cUNIV)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((creal_le @ ((c$ @ (V0 @ V4)) @ V2)) @ V1)) @ V4)))))))))))))))
(TMEASURABLE_ON_PREIMAGE_OPEN_HALFSPACE_COMPONENT_GT,(c! @ (^[V0]: ((c= @ ((cmeasurable_on @ V0) @ cUNIV)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((creal_gt @ ((c$ @ (V0 @ V4)) @ V2)) @ V1)) @ V4)))))))))))))))
(TMEASURABLE_ON_PREIMAGE_OPEN_HALFSPACE_COMPONENT_GE,(c! @ (^[V0]: ((c= @ ((cmeasurable_on @ V0) @ cUNIV)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((creal_ge @ ((c$ @ (V0 @ V4)) @ V2)) @ V1)) @ V4)))))))))))))))
(TMEASURABLE_ON_COMPONENTWISE,(c! @ (^[V0]: ((c= @ ((cmeasurable_on @ V0) @ cUNIV)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((cmeasurable_on @ (^[V2]: (clift @ ((c$ @ (V0 @ V2)) @ V1)))) @ cUNIV))))))))
(TMEASURABLE_ON_PREIMAGE_OPEN,(c! @ (^[V0]: ((c= @ ((cmeasurable_on @ V0) @ cUNIV)) @ (c! @ (^[V1]: ((c==> @ (copen @ V1)) @ (clebesgue_measurable @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ (V0 @ V3)) @ V1)) @ V3)))))))))))))
(TMEASURABLE_ON_PREIMAGE_CLOSED,(c! @ (^[V0]: ((c= @ ((cmeasurable_on @ V0) @ cUNIV)) @ (c! @ (^[V1]: ((c==> @ (cclosed @ V1)) @ (clebesgue_measurable @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ (V0 @ V3)) @ V1)) @ V3)))))))))))))
(TMEASURABLE_ON_PREIMAGE_OPEN_INTERVAL,(c! @ (^[V0]: ((c= @ ((cmeasurable_on @ V0) @ cUNIV)) @ (c! @ (^[V1]: (c! @ (^[V2]: (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ (V0 @ V4)) @ (copen_interval @ ((c__comma__ @ V1) @ V2)))) @ V4))))))))))))))
(TMEASURABLE_ON_PREIMAGE_CLOSED_INTERVAL,(c! @ (^[V0]: ((c= @ ((cmeasurable_on @ V0) @ cUNIV)) @ (c! @ (^[V1]: (c! @ (^[V2]: (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ (V0 @ V4)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ V4))))))))))))))
(TABSOLUTELY_INTEGRABLE_BOUNDED_SETVARIATION_UNIV_EQ,(c! @ (^[V0]: ((c= @ ((cabsolutely_integrable_on @ V0) @ cUNIV)) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ cUNIV)) @ ((chas_bounded_setvariation_on @ (^[V1]: ((cintegral @ V1) @ V0))) @ cUNIV))))))
(Tlinear,(c! @ (^[V0]: ((c= @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (V0 @ ((cvector_add @ V1) @ V2))) @ ((cvector_add @ (V0 @ V1)) @ (V0 @ V2)))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (V0 @ ((c% @ V1) @ V2))) @ ((c% @ V1) @ (V0 @ V2))))))))))))
(TLINEAR_SUBSPACE_GRAPH,(c! @ (^[V0]: ((c= @ (clinear @ V0)) @ (csubspace @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ ((cpastecart @ V2) @ (V0 @ V2))))))))))))
(TLINEAR_MATRIX_EXISTS,(c! @ (^[V0]: ((c= @ (clinear @ V0)) @ (c? @ (^[V1]: ((c= @ V0) @ (^[V2]: ((cmatrix_vector_mul @ V1) @ V2)))))))))
(TLINEAR_COMPONENTWISE,(c! @ (^[V0]: ((c= @ (clinear @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ (clinear @ (^[V2]: (clift @ ((c$ @ (V0 @ V2)) @ V1)))))))))))
(TOPERATIVE_APPROXIMABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((coperative @ c/__caret__) @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ (V0 @ V4)) @ (V3 @ V4)))) @ V1))))) @ ((cintegrable_on @ V3) @ V2))))))))))))
(TNORM_BOUND_GENERALIZE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((c= @ (c! @ (^[V2]: ((c==> @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_le @ (cvector_norm @ (V0 @ V2))) @ V1))))) @ (c! @ (^[V2]: ((creal_le @ (cvector_norm @ (V0 @ V2))) @ ((creal_mul @ V1) @ (cvector_norm @ V2))))))))))))
(THAS_INTEGRAL_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((chas_integral @ V0) @ V2) @ V3)) @ (((chas_integral @ (^[V4]: ((c% @ V1) @ (V0 @ V4)))) @ ((c% @ V1) @ V2)) @ V3)))))))))))
(TPIECEWISE_DIFFERENTIABLE_AFFINE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cpiecewise_differentiable_on @ V0) @ ((cIMAGE @ (^[V4]: ((cvector_add @ ((c% @ V1) @ V4)) @ V2))) @ V3))) @ ((cpiecewise_differentiable_on @ ((co @ V0) @ (^[V4]: ((cvector_add @ ((c% @ V1) @ V4)) @ V2)))) @ V3)))))))))))
(THAS_INTEGRAL_COMPONENT_LBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V0) @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ (cdimindex @ cUNIV))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((creal_le @ V1) @ ((c$ @ (V0 @ V6)) @ V5))))))))) @ ((creal_le @ ((creal_mul @ V1) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ ((c$ @ V4) @ V5))))))))))))))))
(TINTEGRABLE_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (c~ @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((cintegrable_on @ (^[V5]: (V0 @ ((cvector_add @ ((c% @ V1) @ V5)) @ V2)))) @ ((cIMAGE @ (^[V5]: ((cvector_add @ ((c% @ (creal_inv @ V1)) @ V5)) @ (cvector_neg @ ((c% @ (creal_inv @ V1)) @ V2))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))))))))
(TINTEGRAL_COMPONENT_UBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ ((creal_le @ ((c$ @ (V0 @ V5)) @ V1)) @ V2)))))))) @ ((creal_le @ ((c$ @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ V0)) @ V1)) @ ((creal_mul @ V2) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))))
(TCONTINUOUS_ON_LIFT_COMPONENT_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous_on @ V0) @ V2)) @ ((ccontinuous_on @ (^[V3]: (clift @ ((c$ @ (V0 @ V3)) @ V1)))) @ V2)))))))))
(TLINEAR_VMUL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV))))) @ (clinear @ (^[V3]: ((c% @ ((c$ @ (V0 @ V3)) @ V1)) @ V2)))))))))))
(TDIFFERENTIABLE_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((cdifferentiable @ V0) @ V1)))))))
(THAS_INTEGRAL_COMBINE_TAGGED_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V1) @ V3)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ ((c__comma__ @ V4) @ V5)) @ V1)) @ (((chas_integral @ V0) @ (V2 @ V5)) @ V5)))))))) @ (((chas_integral @ V0) @ ((cvsum @ V1) @ (cGABS @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((cGEQ @ (V4 @ ((c__comma__ @ V5) @ V6))) @ (V2 @ V6)))))))))) @ V3)))))))))))
(TRSUM_DIFF_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ (V0 @ V6)) @ (V2 @ V6)))) @ V3)))))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ ((cvsum @ V1) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ ((c% @ (ccontent @ V8)) @ (V0 @ V7))))))))))) @ ((cvsum @ V1) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ ((c% @ (ccontent @ V8)) @ (V2 @ V7))))))))))))) @ ((creal_mul @ V3) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))))))))))))))))))
(TINTEGRABLE_STRETCH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ (cdimindex @ cUNIV)))) @ (c~ @ ((c= @ (V1 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ ((cintegrable_on @ (^[V4]: (V0 @ (clambda @ (^[V5]: ((creal_mul @ (V1 @ V5)) @ ((c$ @ V4) @ V5))))))) @ ((cIMAGE @ (^[V4]: (clambda @ (^[V5]: ((creal_mul @ (creal_inv @ (V1 @ V5))) @ ((c$ @ V4) @ V5)))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))
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(THAS_INTEGRAL_SPIKE_INTERIOR_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (copen_interval @ ((c__comma__ @ V3) @ V4)))) @ ((c= @ (V1 @ V5)) @ (V0 @ V5)))))) @ ((c= @ (((chas_integral @ V0) @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (((chas_integral @ V1) @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))))))))
(TFRECHET_DERIVATIVE_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_derivative @ V1) @ V0) @ (cat @ V2))) @ ((c= @ V0) @ ((cfrechet_derivative @ V1) @ (cat @ V2)))))))))))
(TDIFFERENTIABLE_AT_LIFT_DOT2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ V0) @ (cat @ V2))) @ ((cdifferentiable @ V1) @ (cat @ V2)))) @ ((cdifferentiable @ (^[V3]: (clift @ ((cdot @ (V0 @ V3)) @ (V1 @ V3))))) @ (cat @ V2))))))))))
(Thas_derivative_at,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_derivative @ V0) @ V1) @ (cat @ V2))) @ ((c/__caret__ @ (clinear @ V1)) @ (((c--> @ (^[V3]: ((c% @ (creal_inv @ (cvector_norm @ ((cvector_sub @ V3) @ V2)))) @ ((cvector_sub @ (V0 @ V3)) @ ((cvector_add @ (V0 @ V2)) @ (V1 @ ((cvector_sub @ V3) @ V2))))))) @ (cvec @ (cNUMERAL @ c_0))) @ (cat @ V2)))))))))))
(THAS_DERIVATIVE_AT_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_derivative @ V0) @ V1) @ (cat @ V2))) @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V5) @ V2))) @ V4)) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ ((cvector_sub @ (V0 @ V5)) @ (V0 @ V2))) @ (V1 @ ((cvector_sub @ V5) @ V2))))) @ ((creal_mul @ V3) @ (cvector_norm @ ((cvector_sub @ V5) @ V2))))))))))))))))))))))
(THAS_DERIVATIVE_COMPONENTWISE_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_derivative @ V0) @ V1) @ (cat @ V2))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (((chas_derivative @ (^[V4]: (clift @ ((c$ @ (V0 @ V4)) @ V3)))) @ (^[V4]: (clift @ ((c$ @ (V1 @ V4)) @ V3)))) @ (cat @ V2)))))))))))))
(TDIFFERENTIABLE_WITHIN_LIFT_DOT2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ V0) @ ((cwithin @ (cat @ V2)) @ V3))) @ ((cdifferentiable @ V1) @ ((cwithin @ (cat @ V2)) @ V3)))) @ ((cdifferentiable @ (^[V4]: (clift @ ((cdot @ (V0 @ V4)) @ (V1 @ V4))))) @ ((cwithin @ (cat @ V2)) @ V3))))))))))))
(Thas_derivative_within,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((chas_derivative @ V0) @ V1) @ ((cwithin @ (cat @ V2)) @ V3))) @ ((c/__caret__ @ (clinear @ V1)) @ (((c--> @ (^[V4]: ((c% @ (creal_inv @ (cvector_norm @ ((cvector_sub @ V4) @ V2)))) @ ((cvector_sub @ (V0 @ V4)) @ ((cvector_add @ (V0 @ V2)) @ (V1 @ ((cvector_sub @ V4) @ V2))))))) @ (cvec @ (cNUMERAL @ c_0))) @ ((cwithin @ (cat @ V2)) @ V3)))))))))))))
(THAS_DERIVATIVE_COMPONENTWISE_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((chas_derivative @ V0) @ V1) @ ((cwithin @ (cat @ V2)) @ V3))) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ (cdimindex @ cUNIV)))) @ (((chas_derivative @ (^[V5]: (clift @ ((c$ @ (V0 @ V5)) @ V4)))) @ (^[V5]: (clift @ ((c$ @ (V1 @ V5)) @ V4)))) @ ((cwithin @ (cat @ V2)) @ V3)))))))))))))))
(TINTEGRABLE_SPIKE_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((c==> @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (copen_interval @ ((c__comma__ @ V2) @ V3)))) @ ((c= @ (V1 @ V4)) @ (V0 @ V4)))))) @ ((cintegrable_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))
(TCONTINUOUS_AT_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V3]: ((c= @ (cvector_norm @ (V1 @ V3))) @ (cvector_norm @ V3)))))) @ ((c= @ ((ccontinuous @ V0) @ (cat @ (V1 @ V2)))) @ ((ccontinuous @ (^[V3]: (V0 @ (V1 @ V3)))) @ (cat @ V2)))))))))))
(TUNIFORMLY_CONTINUOUS_EXTENDS_TO_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cuniformly_continuous_on @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cuniformly_continuous_on @ V2) @ (cclosure @ V1))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ (V0 @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ (cclosure @ V1))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V3 @ V4)) @ (V0 @ V4))))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosure @ V1))) @ ((c= @ (V3 @ V4)) @ (V2 @ V4))))))))))))))))))
(TPIECEWISE_DIFFERENTIABLE_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpiecewise_differentiable_on @ V0) @ V1)) @ ((cpiecewise_differentiable_on @ (^[V2]: (cvector_neg @ (V0 @ V2)))) @ V1)))))))
(TMEASURABLE_ON_NORM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cmeasurable_on @ V0) @ V1)) @ ((cmeasurable_on @ (^[V2]: (clift @ (cvector_norm @ (V0 @ V2))))) @ V1)))))))
(TMEASURABLE_ON_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cmeasurable_on @ V0) @ V1)) @ ((cmeasurable_on @ (^[V2]: (cvector_neg @ (V0 @ V2)))) @ V1)))))))
(TINTEGRABLE_IMP_MEASURABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cintegrable_on @ V0) @ V1)) @ ((cmeasurable_on @ V0) @ V1)))))))
(TINTEGRABLE_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cintegrable_on @ V0) @ V1)) @ ((cintegrable_on @ (^[V2]: (cvector_neg @ (V0 @ V2)))) @ V1)))))))
(TDIFFERENTIABLE_IMP_CONTINUOUS_ON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdifferentiable_on @ V0) @ V1)) @ ((ccontinuous_on @ V0) @ V1)))))))
(TCLOSURE_IMAGE_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ccontinuous_on @ V0) @ (cclosure @ V1))) @ ((c= @ (cclosure @ ((cIMAGE @ V0) @ (cclosure @ V1)))) @ (cclosure @ ((cIMAGE @ V0) @ V1)))))))))
(TCONTINUOUS_ON_LIFT_NORM_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ccontinuous_on @ V0) @ V1)) @ ((ccontinuous_on @ (^[V2]: (clift @ (cvector_norm @ (V0 @ V2))))) @ V1)))))))
(TCONTINUOUS_ON_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ccontinuous_on @ V0) @ V1)) @ ((ccontinuous_on @ (^[V2]: (clambda @ (^[V3]: (creal_abs @ ((c$ @ (V0 @ V2)) @ V3)))))) @ V1)))))))
(TCARD_LE_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ccontinuous_on @ V0) @ V1)) @ ((c<=_c @ (ccomponents @ ((cIMAGE @ V0) @ V1))) @ (ccomponents @ V1))))))))
(TCARD_LE_PATH_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ccontinuous_on @ V0) @ V1)) @ ((c<=_c @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ ((cIMAGE @ V0) @ V1))) @ ((cpath_component @ ((cIMAGE @ V0) @ V1)) @ V3))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ ((cpath_component @ V1) @ V3)))))))))))))
(TCARD_LE_CONNECTED_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ccontinuous_on @ V0) @ V1)) @ ((c<=_c @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ ((cIMAGE @ V0) @ V1))) @ ((cconnected_component @ ((cIMAGE @ V0) @ V1)) @ V3))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ ((cconnected_component @ V1) @ V3)))))))))))))
(TABSOLUTELY_INTEGRABLE_BOUNDED_SETVARIATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cabsolutely_integrable_on @ V0) @ V1)) @ ((chas_bounded_setvariation_on @ (^[V2]: ((cintegral @ V2) @ V0))) @ V1)))))))
(TABSOLUTELY_INTEGRABLE_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cabsolutely_integrable_on @ V0) @ V1)) @ ((cabsolutely_integrable_on @ (^[V2]: (clambda @ (^[V3]: (creal_abs @ ((c$ @ (V0 @ V2)) @ V3)))))) @ V1)))))))
(TUNIFORMLY_CONTINUOUS_ON_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cuniformly_continuous_on @ V0) @ V1)) @ ((ccontinuous_on @ V0) @ (cclosure @ V1)))) @ ((cuniformly_continuous_on @ V0) @ (cclosure @ V1))))))))
(TBOUNDED_UNIFORMLY_CONTINUOUS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cuniformly_continuous_on @ V0) @ V1)) @ (cbounded @ V1))) @ (cbounded @ ((cIMAGE @ V0) @ V1))))))))
(TLOCALLY_PATH_CONNECTED_CONTINUOUS_IMAGE_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ cpath_connected) @ V1)) @ ((c/__caret__ @ (ccompact @ V1)) @ ((ccontinuous_on @ V0) @ V1)))) @ ((clocally @ cpath_connected) @ ((cIMAGE @ V0) @ V1))))))))
(TLOCALLY_CONNECTED_CONTINUOUS_IMAGE_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ cconnected) @ V1)) @ ((c/__caret__ @ (ccompact @ V1)) @ ((ccontinuous_on @ V0) @ V1)))) @ ((clocally @ cconnected) @ ((cIMAGE @ V0) @ V1))))))))
(TCONTINUOUS_ON_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((clocally @ cconnected) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (ccomponents @ V1))) @ ((ccontinuous_on @ V0) @ V2)))))) @ ((ccontinuous_on @ V0) @ V1)))))))
(TCLOSURE_IMAGE_BOUNDED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ (cclosure @ V1))) @ (cbounded @ V1))) @ ((c= @ (cclosure @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (cclosure @ V1)))))))))
(TLOCALLY_COMPACT_PROPER_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ ((cIMAGE @ V0) @ V1))) @ (ccompact @ V2))) @ (ccompact @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ (V0 @ V4)) @ V2))) @ V4)))))))))) @ ((clocally @ ccompact) @ V1)))) @ ((clocally @ ccompact) @ ((cIMAGE @ V0) @ V1))))))))
(TPATH_CONNECTED_CONTINUOUS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ (cpath_connected @ V1))) @ (cpath_connected @ ((cIMAGE @ V0) @ V1))))))))
(TCONTINUOUS_IMP_MEASURABLE_ON_LEBESGUE_MEASURABLE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ (clebesgue_measurable @ V1))) @ ((cmeasurable_on @ V0) @ V1)))))))
(TCONNECTED_CONTINUOUS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ (cconnected @ V1))) @ (cconnected @ ((cIMAGE @ V0) @ V1))))))))
(TCOMPACT_UNIFORMLY_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ (ccompact @ V1))) @ ((cuniformly_continuous_on @ V0) @ V1)))))))
(TCOMPACT_CONTINUOUS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ (ccompact @ V1))) @ (ccompact @ ((cIMAGE @ V0) @ V1))))))))
(TCONTINUOUS_IMP_MEASURABLE_ON_CLOSED_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ (cclosed @ V1))) @ ((cmeasurable_on @ V0) @ V1)))))))
(TLOCALLY_COMPACT_PROPER_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ ((cIMAGE @ V0) @ V1))) @ (ccompact @ V2))) @ (ccompact @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ (V0 @ V4)) @ V2))) @ V4))))))))))) @ ((c= @ ((clocally @ ccompact) @ V1)) @ ((clocally @ ccompact) @ ((cIMAGE @ V0) @ V1)))))))))
(TSPANNING_SURJECTIVE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ cUNIV) @ (cspan @ V1))) @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c= @ (V0 @ V3)) @ V2)))))))) @ ((cSUBSET @ cUNIV) @ (cspan @ ((cIMAGE @ V0) @ V1)))))))))
(TLEBESGUE_MEASURABLE_DIFFERENTIABLE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((cdifferentiable_on @ V0) @ V1)) @ (clebesgue_measurable @ V1)))) @ (clebesgue_measurable @ ((cIMAGE @ V0) @ V1))))))))
(TNEGLIGIBLE_DIFFERENTIABLE_IMAGE_NEGLIGIBLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (cnegligible @ V1)) @ ((cdifferentiable_on @ V0) @ V1)))) @ (cnegligible @ ((cIMAGE @ V0) @ V1))))))))
(TNEGLIGIBLE_LOCALLY_LIPSCHITZ_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (cnegligible @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (copen @ V3)) @ ((c/__caret__ @ ((cIN @ V2) @ V3)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ ((cINTER @ V1) @ V3))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ (V0 @ V5)) @ (V0 @ V2)))) @ ((creal_mul @ V4) @ (cvector_norm @ ((cvector_sub @ V5) @ V2))))))))))))))))))) @ (cnegligible @ ((cIMAGE @ V0) @ V1))))))))
(TNEGLIGIBLE_DIFFERENTIABLE_IMAGE_LOWDIM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c< @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))) @ ((cdifferentiable_on @ V0) @ V1))) @ (cnegligible @ ((cIMAGE @ V0) @ V1))))))))
(TPATH_CONNECTED_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath_connected @ V1)) @ (clinear @ V0))) @ (cpath_connected @ ((cIMAGE @ V0) @ V1))))))))
(TCONTINUOUS_ON_COMPONENTS_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (ccomponents @ V1))) @ ((ccontinuous_on @ V0) @ V2)))))) @ ((ccontinuous_on @ V0) @ V1)))))))
(TINTERIOR_BIJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c= @ (V0 @ V3)) @ V2)))))))) @ ((c= @ (cinterior @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (cinterior @ V1)))))))))
(TFRONTIER_BIJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c= @ (V0 @ V3)) @ V2)))))))) @ ((c= @ (cfrontier @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (cfrontier @ V1)))))))))
(TPOLYTOPE_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c= @ (V0 @ V3)) @ V2)))))))) @ ((c= @ (cpolytope @ ((cIMAGE @ V0) @ V1))) @ (cpolytope @ V1))))))))
(TPOLYHEDRON_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c= @ (V0 @ V3)) @ V2)))))))) @ ((c= @ (cpolyhedron @ ((cIMAGE @ V0) @ V1))) @ (cpolyhedron @ V1))))))))
(TOPEN_BIJECTIVE_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c= @ (V0 @ V3)) @ V2)))))))) @ ((c= @ (copen @ ((cIMAGE @ V0) @ V1))) @ (copen @ V1))))))))
(TDEPENDENT_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V2)) @ (V0 @ V3))))) @ ((c= @ V2) @ V3))))))) @ (cdependent @ V1)))) @ (cdependent @ ((cIMAGE @ V0) @ V1))))))))
(TAFFINE_DEPENDENT_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V2)) @ (V0 @ V3))))) @ ((c= @ V2) @ V3))))))) @ (caffine_dependent @ V1)))) @ (caffine_dependent @ ((cIMAGE @ V0) @ V1))))))))
(TDIM_IMAGE_KERNEL_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (csubspace @ V1))) @ ((c= @ ((c+ @ (cdim @ ((cIMAGE @ V0) @ V1))) @ (cdim @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))) @ V3)))))))) @ (cdim @ V1))))))))
(TPOLYTOPE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (cpolytope @ V1))) @ (cpolytope @ ((cIMAGE @ V0) @ V1))))))))
(TPOLYHEDRON_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (cpolyhedron @ V1))) @ (cpolyhedron @ ((cIMAGE @ V0) @ V1))))))))
(TRELATIVE_INTERIOR_LINEAR_IMAGE_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (cconvex @ V1))) @ ((c= @ (crelative_interior @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (crelative_interior @ V1)))))))))
(TCLOSURE_BOUNDED_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (cbounded @ V1))) @ ((c= @ (cclosure @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (cclosure @ V1)))))))))
(TLINEAR_IMAGE_SUBSET_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c= @ (V0 @ V3)) @ V2))))))) @ ((cSUBSET @ ((cIMAGE @ V0) @ (cinterior @ V1))) @ (cinterior @ ((cIMAGE @ V0) @ V1)))))))))
(TOPEN_SURJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c= @ (V0 @ V3)) @ V2))))))) @ ((c==> @ (copen @ V1)) @ (copen @ ((cIMAGE @ V0) @ V1)))))))))
(TDIAMETER_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: ((c= @ (cvector_norm @ (V0 @ V2))) @ (cvector_norm @ V2)))))) @ ((c= @ (cdiameter @ ((cIMAGE @ V0) @ V1))) @ (cdiameter @ V1))))))))
(THOMOTOPY_EQUIVALENT_INJECTIVE_LINEAR_IMAGE_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((chomotopy_equivalent @ ((cIMAGE @ V0) @ V1)) @ V1)))))))
(THOMEOMORPHIC_INJECTIVE_LINEAR_IMAGE_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((chomeomorphic @ ((cIMAGE @ V0) @ V1)) @ V1)))))))
(TLINEAR_INTERIOR_IMAGE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((cSUBSET @ (cinterior @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (cinterior @ V1)))))))))
(TCOMPLETE_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c==> @ (ccomplete @ V1)) @ (ccomplete @ ((cIMAGE @ V0) @ V1)))))))))
(TCLOSED_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c==> @ (cclosed @ V1)) @ (cclosed @ ((cIMAGE @ V0) @ V1)))))))))
(TDIM_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cdim @ ((cIMAGE @ V0) @ V1))) @ (cdim @ V1))))))))
(TAFF_DIM_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (caff_dim @ ((cIMAGE @ V0) @ V1))) @ (caff_dim @ V1))))))))
(TFACES_OF_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cface_of @ V3) @ ((cIMAGE @ V0) @ V1))) @ V3)))))) @ ((cIMAGE @ (cIMAGE @ V0)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cface_of @ V3) @ V1)) @ V3)))))))))))))
(TRELATIVE_INTERIOR_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (crelative_interior @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (crelative_interior @ V1)))))))))
(TRELATIVE_FRONTIER_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (crelative_frontier @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (crelative_frontier @ V1)))))))))
(TCLOSURE_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cclosure @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (cclosure @ V1)))))))))
(TEXTREME_POINTS_OF_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cextreme_point_of @ V3) @ ((cIMAGE @ V0) @ V1))) @ V3)))))) @ ((cIMAGE @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cextreme_point_of @ V3) @ V1)) @ V3)))))))))))))
(TLOCALLY_PATH_CONNECTED_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ ((clocally @ cpath_connected) @ ((cIMAGE @ V0) @ V1))) @ ((clocally @ cpath_connected) @ V1))))))))
(TLOCALLY_CONNECTED_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ ((clocally @ cconnected) @ ((cIMAGE @ V0) @ V1))) @ ((clocally @ cconnected) @ V1))))))))
(TLOCALLY_COMPACT_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ ((clocally @ ccompact) @ ((cIMAGE @ V0) @ V1))) @ ((clocally @ ccompact) @ V1))))))))
(TSIMPLY_CONNECTED_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (csimply_connected @ ((cIMAGE @ V0) @ V1))) @ (csimply_connected @ V1))))))))
(TINDEPENDENT_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cindependent @ ((cIMAGE @ V0) @ V1))) @ (cindependent @ V1))))))))
(TDEPENDENT_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cdependent @ ((cIMAGE @ V0) @ V1))) @ (cdependent @ V1))))))))
(TCONVEX_CONE_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cconvex_cone @ ((cIMAGE @ V0) @ V1))) @ (cconvex_cone @ V1))))))))
(TCONTRACTIBLE_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (ccontractible @ ((cIMAGE @ V0) @ V1))) @ (ccontractible @ V1))))))))
(TCOMPLETE_INJECTIVE_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (ccomplete @ ((cIMAGE @ V0) @ V1))) @ (ccomplete @ V1))))))))
(TCLOSED_INJECTIVE_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cclosed @ ((cIMAGE @ V0) @ V1))) @ (cclosed @ V1))))))))
(TAFFINE_DEPENDENT_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (caffine_dependent @ ((cIMAGE @ V0) @ V1))) @ (caffine_dependent @ V1))))))))
(TENR_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cENR @ ((cIMAGE @ V0) @ V1))) @ (cENR @ V1))))))))
(TAR_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cAR @ ((cIMAGE @ V0) @ V1))) @ (cAR @ V1))))))))
(TANR_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cANR @ ((cIMAGE @ V0) @ V1))) @ (cANR @ V1))))))))
(TINDEPENDENT_INJECTIVE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cindependent @ V1)) @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))))) @ (cindependent @ ((cIMAGE @ V0) @ V1))))))))
(TINDEPENDENT_INJECTIVE_IMAGE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cindependent @ V1)) @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ (cspan @ V1))) @ ((c/__caret__ @ ((cIN @ V3) @ (cspan @ V1))) @ ((c= @ (V0 @ V2)) @ (V0 @ V3))))) @ ((c= @ V2) @ V3))))))))) @ (cindependent @ ((cIMAGE @ V0) @ V1))))))))
(TCOPLANAR_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccoplanar @ V1)) @ (clinear @ V0))) @ (ccoplanar @ ((cIMAGE @ V0) @ V1))))))))
(TCONVEX_CONE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex_cone @ V1)) @ (clinear @ V0))) @ (cconvex_cone @ ((cIMAGE @ V0) @ V1))))))))
(TCONNECTED_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconnected @ V1)) @ (clinear @ V0))) @ (cconnected @ ((cIMAGE @ V0) @ V1))))))))
(TCOMPACT_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V1)) @ (clinear @ V0))) @ (ccompact @ ((cIMAGE @ V0) @ V1))))))))
(TCLOSED_BOUNDEDPREIM_CONTINUOUS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ (c! @ (^[V2]: (cbounded @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((creal_le @ (cvector_norm @ (V0 @ V4))) @ V2))) @ V4))))))))))) @ (cclosed @ ((cIMAGE @ V0) @ V1))))))))
(TBOUNDED_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V1)) @ (clinear @ V0))) @ (cbounded @ ((cIMAGE @ V0) @ V1))))))))
(TCONTINUOUS_ON_COMPONENTS_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ (ccomponents @ V1))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (ccomponents @ V1))) @ ((ccontinuous_on @ V0) @ V2)))))) @ ((ccontinuous_on @ V0) @ V1)))))))
(TLOCALLY_PATH_CONNECTED_QUOTIENT_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V2) @ ((cIMAGE @ V0) @ V1))) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ (V0 @ V4)) @ V2))) @ V4))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V0) @ V1))) @ V2)))))) @ ((clocally @ cpath_connected) @ V1))) @ ((clocally @ cpath_connected) @ ((cIMAGE @ V0) @ V1))))))))
(TLOCALLY_CONNECTED_QUOTIENT_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V2) @ ((cIMAGE @ V0) @ V1))) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ (V0 @ V4)) @ V2))) @ V4))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V0) @ V1))) @ V2)))))) @ ((clocally @ cconnected) @ V1))) @ ((clocally @ cconnected) @ ((cIMAGE @ V0) @ V1))))))))
(TINTERIOR_IMAGE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((ccontinuous @ V0) @ (cat @ V2))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((cSUBSET @ (cinterior @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (cinterior @ V1)))))))))
(TNONNEGATIVE_ABSOLUTELY_INTEGRABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV))))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ (V0 @ V2)) @ V3)))))))) @ ((cintegrable_on @ V0) @ V1))) @ ((cabsolutely_integrable_on @ V0) @ V1)))))))
(TCONTINUOUS_ON_NO_LIMPT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (c? @ (^[V2]: ((climit_point_of @ V2) @ V1))))) @ ((ccontinuous_on @ V0) @ V1)))))))
(TLINEAR_UNIFORMLY_CONTINUOUS_ON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((cuniformly_continuous_on @ V0) @ V1)))))))
(TAFF_DIM_LINEAR_IMAGE_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((cint_le @ (caff_dim @ ((cIMAGE @ V0) @ V1))) @ (caff_dim @ V1))))))))
(TDIFFERENTIABLE_ON_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((cdifferentiable_on @ V0) @ V1)))))))
(TLINEAR_CONTINUOUS_ON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((ccontinuous_on @ V0) @ V1)))))))
(TCLOSURE_LINEAR_IMAGE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((cSUBSET @ ((cIMAGE @ V0) @ (cclosure @ V1))) @ (cclosure @ ((cIMAGE @ V0) @ V1)))))))))
(TCONVEX_CONE_HULL_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((c= @ ((chull @ cconvex_cone) @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ ((chull @ cconvex_cone) @ V1)))))))))
(TSPAN_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((c= @ (cspan @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ (cspan @ V1)))))))))
(TDIM_LINEAR_IMAGE_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((c<= @ (cdim @ ((cIMAGE @ V0) @ V1))) @ (cdim @ V1))))))))
(TCONTINUOUS_ON_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ ((ccontinuous_on @ V0) @ V1)))))))
(TCAUCHY_CONTINUOUS_IMP_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccauchy @ V2)) @ (c! @ (^[V3]: ((cIN @ (V2 @ V3)) @ V1))))) @ (ccauchy @ ((co @ V0) @ V2)))))) @ ((ccontinuous_on @ V0) @ V1)))))))
(TCONTINUOUS_ON_COMPONENTS_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (ccomponents @ V1))) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2)) @ ((ccontinuous_on @ V0) @ V2)))))) @ ((ccontinuous_on @ V0) @ V1)))))))
(THAS_INTEGRAL_IS_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c= @ (V0 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))))) @ (((chas_integral @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ V1)))))))
(TCONTRACTION_IMP_CONTINUOUS_ON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((cIN @ V3) @ V1))) @ ((creal_le @ (cdistance @ ((c__comma__ @ (V0 @ V2)) @ (V0 @ V3)))) @ (cdistance @ ((c__comma__ @ V2) @ V3))))))))) @ ((ccontinuous_on @ V0) @ V1)))))))
(TISOMETRY_ON_IMP_CONTINUOUS_ON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((cIN @ V3) @ V1))) @ ((c= @ (cdistance @ ((c__comma__ @ (V0 @ V2)) @ (V0 @ V3)))) @ (cdistance @ ((c__comma__ @ V2) @ V3))))))))) @ ((ccontinuous_on @ V0) @ V1)))))))
(TMEASURABLE_ON_NEG_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmeasurable_on @ (^[V2]: (cvector_neg @ (V0 @ V2)))) @ V1)) @ ((cmeasurable_on @ V0) @ V1)))))))
(TINTEGRABLE_COMPONENTWISE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cintegrable_on @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((cintegrable_on @ (^[V3]: (clift @ ((c$ @ (V0 @ V3)) @ V2)))) @ V1))))))))))
(TCONTINUOUS_ON_COMPONENTWISE_LIFT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous_on @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((ccontinuous_on @ (^[V3]: (clift @ ((c$ @ (V0 @ V3)) @ V2)))) @ V1))))))))))
(TABSOLUTELY_INTEGRABLE_MEASURABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cabsolutely_integrable_on @ V0) @ V1)) @ ((c/__caret__ @ ((cmeasurable_on @ V0) @ V1)) @ ((cintegrable_on @ (^[V2]: (clift @ (cvector_norm @ (V0 @ V2))))) @ V1))))))))
(TABSOLUTELY_INTEGRABLE_ABS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cabsolutely_integrable_on @ V0) @ V1)) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V1)) @ ((cintegrable_on @ (^[V2]: (clambda @ (^[V3]: (creal_abs @ ((c$ @ (V0 @ V2)) @ V3)))))) @ V1))))))))
(TABSOLUTELY_INTEGRABLE_COMPONENTWISE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cabsolutely_integrable_on @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((cabsolutely_integrable_on @ (^[V3]: (clift @ ((c$ @ (V0 @ V3)) @ V2)))) @ V1))))))))))
(TCOVERING_SPACE_IMP_SURJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccovering_space @ ((c__comma__ @ V1) @ V0)) @ V2)) @ ((c= @ ((cIMAGE @ V0) @ V1)) @ V2)))))))))
(TCOVERING_SPACE_LOCALLY_PATH_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V0)) @ V2)) @ ((clocally @ cpath_connected) @ V1))) @ ((clocally @ cpath_connected) @ V2)))))))))
(TCOVERING_SPACE_LOCALLY_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V0)) @ V2)) @ ((clocally @ cconnected) @ V1))) @ ((clocally @ cconnected) @ V2)))))))))
(TCOVERING_SPACE_LOCALLY_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V1) @ V0)) @ V2)) @ ((clocally @ ccompact) @ V1))) @ ((clocally @ ccompact) @ V2)))))))))
(TOPEN_MAP_IMP_QUOTIENT_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ V3))))))) @ ((c==> @ ((cSUBSET @ V2) @ ((cIMAGE @ V0) @ V1))) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ (V0 @ V4)) @ V2))) @ V4))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V0) @ V1))) @ V2)))))))))))
(TCLOSED_MAP_IMP_QUOTIENT_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ V3))))))) @ ((c==> @ ((cSUBSET @ V2) @ ((cIMAGE @ V0) @ V1))) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ (V0 @ V4)) @ V2))) @ V4))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V0) @ V1))) @ V2)))))))))))
(TBORSUK_HOMOTOPY_EXTENSION_HOMOTOPIC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((c/__caret__ @ ((c__caret__/ @ ((c/__caret__ @ (cANR @ V3)) @ (cANR @ V1))) @ (cANR @ V2))) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V0) @ V1)) @ V2)) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V3) @ V2)) @ V0) @ V4)))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((((chomotopic_with @ (^[V6]: cT)) @ ((c__comma__ @ V1) @ V2)) @ V0) @ V5)) @ ((c/__caret__ @ ((ccontinuous_on @ V5) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V5) @ V1)) @ V2)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V3)) @ ((c= @ (V5 @ V6)) @ (V4 @ V6))))))))))))))))))))))
(TBORSUK_HOMOTOPY_EXTENSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((c/__caret__ @ ((c__caret__/ @ ((c/__caret__ @ (cANR @ V3)) @ (cANR @ V1))) @ (cANR @ V2))) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V0) @ V1)) @ V2)) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V3) @ V2)) @ V0) @ V4)))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V5) @ V1)) @ V2)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V3)) @ ((c= @ (V5 @ V6)) @ (V4 @ V6)))))))))))))))))))))
(TINTEGRAL_NORM_BOUND_INTEGRAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V1)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (cvector_norm @ (V0 @ V3))) @ (cdrop @ (V2 @ V3))))))))) @ ((creal_le @ (cvector_norm @ ((cintegral @ V1) @ V0))) @ (cdrop @ ((cintegral @ V1) @ V2)))))))))))
(TINTEGRAL_NORM_BOUND_INTEGRAL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V1)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((creal_le @ (cvector_norm @ (V0 @ V4))) @ ((c$ @ (V2 @ V4)) @ V3)))))))))) @ ((creal_le @ (cvector_norm @ ((cintegral @ V1) @ V0))) @ ((c$ @ ((cintegral @ V1) @ V2)) @ V3))))))))))))
(TINTEGRAL_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V1)) @ ((cintegrable_on @ V2) @ V1))) @ ((c= @ ((cintegral @ V1) @ (^[V3]: ((cvector_sub @ (V0 @ V3)) @ (V2 @ V3))))) @ ((cvector_sub @ ((cintegral @ V1) @ V0)) @ ((cintegral @ V1) @ V2)))))))))))
(TINTEGRAL_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V1)) @ ((cintegrable_on @ V2) @ V1))) @ ((c= @ ((cintegral @ V1) @ (^[V3]: ((cvector_add @ (V0 @ V3)) @ (V2 @ V3))))) @ ((cvector_add @ ((cintegral @ V1) @ V0)) @ ((cintegral @ V1) @ V2)))))))))))
(TINTEGRAL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3)))))) @ ((c= @ ((cintegral @ V1) @ V0)) @ ((cintegral @ V1) @ V2))))))))))
(TINTEGRAL_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V1)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((creal_le @ ((c$ @ (V0 @ V4)) @ V3)) @ ((c$ @ (V2 @ V4)) @ V3)))))))))) @ ((creal_le @ ((c$ @ ((cintegral @ V1) @ V0)) @ V3)) @ ((c$ @ ((cintegral @ V1) @ V2)) @ V3))))))))))))
(TCONTINUOUS_ON_UNION_LOCAL_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V1) @ V2))) @ V1)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V1) @ V2))) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ ((ccontinuous_on @ V0) @ V2))))) @ ((ccontinuous_on @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TMEASURABLE_ON_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V0) @ V1)) @ ((cmeasurable_on @ V0) @ V2))) @ ((cmeasurable_on @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TMEASURABLE_ON_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V0) @ V1)) @ ((cmeasurable_on @ V0) @ V2))) @ ((cmeasurable_on @ V0) @ ((cINTER @ V1) @ V2))))))))))
(TMEASURABLE_ON_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V0) @ V1)) @ ((cmeasurable_on @ V0) @ V2))) @ ((cmeasurable_on @ V0) @ ((cDIFF @ V1) @ V2))))))))))
(TCONTINUOUS_ON_UNION_LOCAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V1) @ V2))) @ V1)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V1) @ V2))) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ ((ccontinuous_on @ V0) @ V2))))) @ ((ccontinuous_on @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TRETRACT_OF_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4))))))) @ (c! @ (^[V3]: (c? @ (^[V4]: ((c= @ (V0 @ V4)) @ V3)))))))) @ ((c= @ ((cretract_of @ ((cIMAGE @ V0) @ V1)) @ ((cIMAGE @ V0) @ V2))) @ ((cretract_of @ V1) @ V2))))))))))
(TEXPOSED_FACE_OF_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4))))))) @ (c! @ (^[V3]: (c? @ (^[V4]: ((c= @ (V0 @ V4)) @ V3)))))))) @ ((c= @ ((cexposed_face_of @ ((cIMAGE @ V0) @ V1)) @ ((cIMAGE @ V0) @ V2))) @ ((cexposed_face_of @ V1) @ V2))))))))))
(TSETDIST_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: ((c= @ (cvector_norm @ (V0 @ V3))) @ (cvector_norm @ V3)))))) @ ((c= @ (csetdist @ ((c__comma__ @ ((cIMAGE @ V0) @ V1)) @ ((cIMAGE @ V0) @ V2)))) @ (csetdist @ ((c__comma__ @ V1) @ V2)))))))))))
(THAUSDIST_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: ((c= @ (cvector_norm @ (V0 @ V3))) @ (cvector_norm @ V3)))))) @ ((c= @ (chausdist @ ((c__comma__ @ ((cIMAGE @ V0) @ V1)) @ ((cIMAGE @ V0) @ V2)))) @ (chausdist @ ((c__comma__ @ V1) @ V2)))))))))))
(TOPEN_IN_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ V2))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2))))))))))
(TFACET_OF_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((cfacet_of @ ((cIMAGE @ V0) @ V1)) @ ((cIMAGE @ V0) @ V2))) @ ((cfacet_of @ V1) @ V2))))))))))
(TFACE_OF_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((cface_of @ ((cIMAGE @ V0) @ V1)) @ ((cIMAGE @ V0) @ V2))) @ ((cface_of @ V1) @ V2))))))))))
(TEDGE_OF_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((cedge_of @ ((cIMAGE @ V0) @ V1)) @ ((cIMAGE @ V0) @ V2))) @ ((cedge_of @ V1) @ V2))))))))))
(TCLOSED_IN_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ V2))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2))))))))))
(TINTEGRABLE_RESTRICT_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cintegrable_on @ (^[V3]: (((cCOND @ ((cIN @ V3) @ V1)) @ (V0 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))) @ V2)) @ ((cintegrable_on @ V0) @ ((cINTER @ V1) @ V2))))))))))
(THOMOTOPY_EQUIVALENT_INJECTIVE_LINEAR_IMAGE_LEFT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((chomotopy_equivalent @ ((cIMAGE @ V0) @ V1)) @ V2)) @ ((chomotopy_equivalent @ V1) @ V2))))))))))
(THOMEOMORPHIC_INJECTIVE_LINEAR_IMAGE_LEFT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((chomeomorphic @ ((cIMAGE @ V0) @ V1)) @ V2)) @ ((chomeomorphic @ V1) @ V2))))))))))
(THAS_INTEGRAL_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V0) @ V2) @ V1)) @ (((chas_integral @ V0) @ V3) @ V1))) @ ((c= @ V2) @ V3)))))))))))
(THOMOTOPY_EQUIVALENT_INJECTIVE_LINEAR_IMAGE_RIGHT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((chomotopy_equivalent @ V1) @ ((cIMAGE @ V0) @ V2))) @ ((chomotopy_equivalent @ V1) @ V2))))))))))
(THOMEOMORPHIC_INJECTIVE_LINEAR_IMAGE_RIGHT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((chomeomorphic @ V1) @ ((cIMAGE @ V0) @ V2))) @ ((chomeomorphic @ V1) @ V2))))))))))
(THAS_INTEGRAL_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c/__caret__ @ (((chas_integral @ V0) @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ ((creal_le @ (cvector_norm @ (V0 @ V5))) @ V2))))))) @ ((creal_le @ (cvector_norm @ V1)) @ ((creal_mul @ V2) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))))
(THAS_INTEGRAL_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V0) @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ (c~ @ ((c= @ V2) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ (((chas_integral @ (^[V6]: (V0 @ ((cvector_add @ ((c% @ V2) @ V6)) @ V3)))) @ ((c% @ (creal_inv @ ((creal_pow @ (creal_abs @ V2)) @ (cdimindex @ cUNIV)))) @ V1)) @ ((cIMAGE @ (^[V6]: ((cvector_add @ ((c% @ (creal_inv @ V2)) @ V6)) @ (cvector_neg @ ((c% @ (creal_inv @ V2)) @ V3))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))))))))))))))))
(THAS_INTEGRAL_COMPONENT_UBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V0) @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ ((creal_le @ ((c$ @ (V0 @ V6)) @ V2)) @ V3)))))))) @ ((creal_le @ ((c$ @ V1) @ V2)) @ ((creal_mul @ V3) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))))))))))))))))))
(THAS_INTEGRAL_STRETCH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V0) @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV)))) @ (c~ @ ((c= @ (V2 @ V5)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ (((chas_integral @ (^[V5]: (V0 @ (clambda @ (^[V6]: ((creal_mul @ (V2 @ V6)) @ ((c$ @ V5) @ V6))))))) @ ((c% @ (creal_inv @ (creal_abs @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ V2)))) @ V1)) @ ((cIMAGE @ (^[V5]: (clambda @ (^[V6]: ((creal_mul @ (creal_inv @ (V2 @ V6))) @ ((c$ @ V5) @ V6)))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))))))))
(THAS_DERIVATIVE_LIFT_DOT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((chas_derivative @ V0) @ V2) @ V3)) @ (((chas_derivative @ (^[V4]: (clift @ ((cdot @ V1) @ (V0 @ V4))))) @ (^[V4]: (clift @ ((cdot @ V1) @ (V2 @ V4))))) @ V3)))))))))))
(THAS_INTEGRAL_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnegligible @ (cfrontier @ V2))) @ ((c= @ (((chas_integral @ V0) @ V1) @ (cinterior @ V2))) @ (((chas_integral @ V0) @ V1) @ V2))))))))))
(THAS_INTEGRAL_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnegligible @ (cfrontier @ V2))) @ ((c= @ (((chas_integral @ V0) @ V1) @ (cclosure @ V2))) @ (((chas_integral @ V0) @ V1) @ V2))))))))))
(THAS_INTEGRAL_RESTRICT_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_integral @ (^[V3]: (((cCOND @ ((cIN @ V3) @ V2)) @ (V0 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))) @ V1) @ cUNIV)) @ (((chas_integral @ V0) @ V1) @ V2)))))))))
(THAS_INTEGRAL_COMPONENTWISE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_integral @ V0) @ V1) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (((chas_integral @ (^[V4]: (clift @ ((c$ @ (V0 @ V4)) @ V3)))) @ (clift @ ((c$ @ V1) @ V3))) @ V2))))))))))))
(THAS_INTEGRAL_RESTRICT_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((chas_integral @ (^[V4]: (((cCOND @ ((cIN @ V4) @ V2)) @ (V0 @ V4)) @ (cvec @ (cNUMERAL @ c_0))))) @ V1) @ V3)) @ (((chas_integral @ V0) @ V1) @ ((cINTER @ V2) @ V3))))))))))))
(TLIM_LIFT_DOT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((c--> @ V0) @ V2) @ V3)) @ (((c--> @ ((co @ clift) @ (^[V4]: ((cdot @ V1) @ (V0 @ V4))))) @ (clift @ ((cdot @ V1) @ V2))) @ V3)))))))))))
(THAS_INTEGRAL_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V0) @ V1) @ V3)) @ ((c/__caret__ @ (((chas_integral @ V0) @ V2) @ V4)) @ (cnegligible @ ((cINTER @ V3) @ V4))))) @ (((chas_integral @ V0) @ ((cvector_add @ V1) @ V2)) @ ((cUNION @ V3) @ V4))))))))))))))
(THAS_INTEGRAL_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V0) @ V1) @ V3)) @ ((c/__caret__ @ (((chas_integral @ V0) @ V2) @ V4)) @ (cnegligible @ ((cDIFF @ V4) @ V3))))) @ (((chas_integral @ V0) @ ((cvector_sub @ V1) @ V2)) @ ((cDIFF @ V3) @ V4))))))))))))))
(THAS_INTEGRAL_REFLECT_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((chas_integral @ V0) @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V2)) @ cNIL)))) @ (((chas_integral @ (^[V4]: (V0 @ (cvector_neg @ V4)))) @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvector_neg @ V2)) @ (cvector_neg @ V3))) @ cNIL)))))))))))))
(THAS_INTEGRAL_REFLECT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((chas_integral @ (^[V4]: (V0 @ (cvector_neg @ V4)))) @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvector_neg @ V3)) @ (cvector_neg @ V2))) @ cNIL)))) @ (((chas_integral @ V0) @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(THAS_INTEGRAL_FACTOR_CONTENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((chas_integral @ V0) @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ (cgauge @ V5)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((cfine @ V5) @ V6))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ ((cvsum @ V6) @ (cGABS @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((cGEQ @ (V7 @ ((c__comma__ @ V8) @ V9))) @ ((c% @ (ccontent @ V9)) @ (V0 @ V8))))))))))) @ V1))) @ ((creal_mul @ V4) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))))))))))))
(TCONTINUOUS_ON_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((ccontinuous_on @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))
(TDIFFERENTIABLE_IMP_CONTINUOUS_AT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdifferentiable @ V0) @ (cat @ V1))) @ ((ccontinuous @ V0) @ (cat @ V1))))))))
(TLINEAR_CONTINUOUS_AT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((ccontinuous @ V0) @ (cat @ V1))))))))
(TMATRIX_WORKS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((c= @ ((cmatrix_vector_mul @ (cmatrix @ V0)) @ V1)) @ (V0 @ V1))))))))
(TDIFFERENTIABLE_COMPONENTWISE_AT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdifferentiable @ V0) @ (cat @ V1))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((cdifferentiable @ (^[V3]: (clift @ ((c$ @ (V0 @ V3)) @ V2)))) @ (cat @ V1)))))))))))
(TSPHERE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: (c? @ (^[V4]: ((c= @ (V0 @ V4)) @ V3)))))) @ (c! @ (^[V3]: ((c= @ (cvector_norm @ (V0 @ V3))) @ (cvector_norm @ V3))))))) @ ((c= @ (csphere @ ((c__comma__ @ (V0 @ V1)) @ V2))) @ ((cIMAGE @ V0) @ (csphere @ ((c__comma__ @ V1) @ V2))))))))))))
(TCBALL_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: (c? @ (^[V4]: ((c= @ (V0 @ V4)) @ V3)))))) @ (c! @ (^[V3]: ((c= @ (cvector_norm @ (V0 @ V3))) @ (cvector_norm @ V3))))))) @ ((c= @ (ccball @ ((c__comma__ @ (V0 @ V1)) @ V2))) @ ((cIMAGE @ V0) @ (ccball @ ((c__comma__ @ V1) @ V2))))))))))))
(TBALL_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: (c? @ (^[V4]: ((c= @ (V0 @ V4)) @ V3)))))) @ (c! @ (^[V3]: ((c= @ (cvector_norm @ (V0 @ V3))) @ (cvector_norm @ V3))))))) @ ((c= @ (cball @ ((c__comma__ @ (V0 @ V1)) @ V2))) @ ((cIMAGE @ V0) @ (cball @ ((c__comma__ @ V1) @ V2))))))))))))
(TMEM_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((cMEM @ (V0 @ V1)) @ ((cMAP @ V0) @ V2))) @ ((cMEM @ V1) @ V2))))))))))
(THAS_FRECHET_DERIVATIVE_UNIQUE_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_derivative @ V0) @ V2) @ (cat @ V1))) @ ((c= @ ((cfrechet_derivative @ V0) @ (cat @ V1))) @ V2)))))))))
(TFRECHET_DERIVATIVE_UNIQUE_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chas_derivative @ V0) @ V2) @ (cat @ V1))) @ (((chas_derivative @ V0) @ V3) @ (cat @ V1)))) @ ((c= @ V2) @ V3)))))))))))
(TMEASURABLE_ON_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cmeasurable_on @ V0) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V1) @ V3))) @ V2))) @ ((cmeasurable_on @ (^[V3]: (V0 @ ((cvector_add @ V1) @ V3)))) @ V2)))))))))
(TDIFFERENTIABLE_IMP_CONTINUOUS_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cdifferentiable @ V0) @ ((cwithin @ (cat @ V1)) @ V2))) @ ((ccontinuous @ V0) @ ((cwithin @ (cat @ V1)) @ V2))))))))))
(TCONTINUOUS_AT_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous @ V0) @ (cat @ V1))) @ ((ccontinuous @ V0) @ ((cwithin @ (cat @ V1)) @ V2))))))))))
(TLIMPT_INJECTIVE_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((climit_point_of @ (V0 @ V1)) @ ((cIMAGE @ V0) @ V2))) @ ((climit_point_of @ V1) @ V2))))))))))
(TEXTREME_POINT_OF_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((cextreme_point_of @ (V0 @ V1)) @ ((cIMAGE @ V0) @ V2))) @ ((cextreme_point_of @ V1) @ V2))))))))))
(TLINEAR_CONTINUOUS_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (clinear @ V0)) @ ((ccontinuous @ V0) @ ((cwithin @ (cat @ V1)) @ V2))))))))))
(TMEASURABLE_ON_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmeasurable_on @ (^[V3]: (V0 @ ((cvector_add @ V1) @ V3)))) @ V2)) @ ((cmeasurable_on @ V0) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V1) @ V3))) @ V2))))))))))
(TDIFFERENTIABLE_COMPONENTWISE_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdifferentiable @ V0) @ ((cwithin @ (cat @ V1)) @ V2))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((cdifferentiable @ (^[V4]: (clift @ ((c$ @ (V0 @ V4)) @ V3)))) @ ((cwithin @ (cat @ V1)) @ V2)))))))))))))
(TFRECHET_DERIVATIVE_UNIQUE_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_derivative @ V0) @ V3) @ ((cwithin @ (cat @ V1)) @ V2))) @ ((c/__caret__ @ (((chas_derivative @ V0) @ V4) @ ((cwithin @ (cat @ V1)) @ V2))) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ (cdimindex @ cUNIV))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V6)))) @ (c? @ (^[V7]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (creal_abs @ V7))) @ ((c/__caret__ @ ((creal_lt @ (creal_abs @ V7)) @ V6)) @ ((cIN @ ((cvector_add @ V1) @ ((c% @ V7) @ (cbasis @ V5)))) @ V2))))))))))))) @ ((c= @ V3) @ V4)))))))))))))
(TLIM_AT_ZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c--> @ V0) @ V2) @ (cat @ V1))) @ (((c--> @ (^[V3]: (V0 @ ((cvector_add @ V1) @ V3)))) @ V2) @ (cat @ (cvec @ (cNUMERAL @ c_0))))))))))))
(TINDEFINITE_INTEGRAL_UNIFORMLY_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cuniformly_continuous_on @ (^[V3]: ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cfstcart @ V3)) @ (csndcart @ V3))) @ cNIL))) @ V0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cpastecart @ V1) @ V1)) @ ((cpastecart @ V2) @ V2))) @ cNIL)))))))))))
(TEQUIINTEGRABLE_OPEN_INTERVAL_RESTRICTIONS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cequiintegrable_on @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ cUNIV)) @ ((cIN @ V5) @ cUNIV))) @ (^[V6]: (((cCOND @ ((cIN @ V6) @ (copen_interval @ ((c__comma__ @ V4) @ V5)))) @ (V0 @ V6)) @ (cvec @ (cNUMERAL @ c_0)))))))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TEQUIINTEGRABLE_CLOSED_INTERVAL_RESTRICTIONS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cequiintegrable_on @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ cUNIV)) @ ((cIN @ V5) @ cUNIV))) @ (^[V6]: (((cCOND @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ (V0 @ V6)) @ (cvec @ (cNUMERAL @ c_0)))))))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TINDEFINITE_INTEGRAL_CONTINUOUS_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((ccontinuous_on @ (^[V3]: ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V2)) @ cNIL))) @ V0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TINDEFINITE_INTEGRAL_CONTINUOUS_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((ccontinuous_on @ (^[V3]: ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V3)) @ cNIL))) @ V0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TINTEGRABLE_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TABSOLUTELY_INTEGRABLE_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cabsolutely_integrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(THAS_INTEGRAL_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (((chas_integral @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TBOUNDED_SETVARIATION_ABSOLUTELY_INTEGRABLE_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((chas_bounded_setvariation_on @ (^[V3]: ((cintegral @ V3) @ V0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))) @ ((cabsolutely_integrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TPRESERVES_NORM_INJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: ((c= @ (cvector_norm @ (V0 @ V3))) @ (cvector_norm @ V3)))))) @ ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))))
(TPRESERVES_NORM_PRESERVES_DOT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: ((c= @ (cvector_norm @ (V0 @ V3))) @ (cvector_norm @ V3)))))) @ ((c= @ ((cdot @ (V0 @ V1)) @ (V0 @ V2))) @ ((cdot @ V1) @ V2))))))))))
(TREFLECT_ALONG_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: ((c= @ (cvector_norm @ (V0 @ V3))) @ (cvector_norm @ V3)))))) @ ((c= @ ((creflect_along @ (V0 @ V1)) @ (V0 @ V2))) @ (V0 @ ((creflect_along @ V1) @ V2)))))))))))
(TORTHOGONAL_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: ((c= @ (cvector_norm @ (V0 @ V3))) @ (cvector_norm @ V3)))))) @ ((c= @ ((corthogonal @ (V0 @ V1)) @ (V0 @ V2))) @ ((corthogonal @ V1) @ V2))))))))))
(TOPEN_SEGMENT_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ (copen_segment @ ((c__comma__ @ (V0 @ V1)) @ (V0 @ V2)))) @ ((cIMAGE @ V0) @ (copen_segment @ ((c__comma__ @ V1) @ V2))))))))))))
(TINTEGRABLE_UNIFORM_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ (V0 @ V5)) @ (V4 @ V5)))) @ V3))))) @ ((cintegrable_on @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TINTEGRABLE_ON_LITTLE_SUBINTERVALS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL)))) @ ((c/__caret__ @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL))) @ (cball @ ((c__comma__ @ V3) @ V4)))) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL))))))))))))))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TINTEGRABLE_REFLECT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cintegrable_on @ (^[V3]: (V0 @ (cvector_neg @ V3)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvector_neg @ V2)) @ (cvector_neg @ V1))) @ cNIL)))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TEQUIINTEGRABLE_ON_SING,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cequiintegrable_on @ ((cINSERT @ V0) @ cEMPTY)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TCONTINUOUS_AT_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccontinuous @ V0) @ (cat @ ((cvector_add @ V1) @ V2)))) @ ((ccontinuous @ (^[V3]: (V0 @ ((cvector_add @ V1) @ V3)))) @ (cat @ V2))))))))))
(TABSOLUTELY_INTEGRABLE_BOUNDED_SETVARIATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cabsolutely_integrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((chas_bounded_setvariation_on @ (^[V3]: ((cintegral @ V3) @ V0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))
(TINTEGRABLE_SPLIT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV))))) @ ((cintegrable_on @ V0) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((c$ @ V6) @ V3)) @ V4)) @ V6)))))))))))))))))))
(TINTEGRABLE_SPLIT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV))))) @ ((cintegrable_on @ V0) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_ge @ ((c$ @ V6) @ V3)) @ V4)) @ V6)))))))))))))))))))
(TBOUNDED_EQUIINTEGRAL_OVER_THIN_TAGGED_PARTIAL_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cequiintegrable_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V0) @ V3)) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V3)) @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))) @ ((creal_le @ (cvector_norm @ (V5 @ V6))) @ (cvector_norm @ (V0 @ V6))))))))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4))))) @ (c? @ (^[V5]: ((c/__caret__ @ (cgauge @ V5)) @ (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V7)) @ ((c/__caret__ @ ((c<= @ V7) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((ctagged_partial_division_of @ V8) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cfine @ V5) @ V8)) @ ((c/__caret__ @ ((cIN @ V9) @ V3)) @ (c! @ (^[V10]: (c! @ (^[V11]: ((c==> @ ((cIN @ ((c__comma__ @ V10) @ V11)) @ V8)) @ (c~ @ ((c= @ ((cINTER @ V11) @ (cGSPEC @ (^[V12]: (c? @ (^[V13]: (((cSETSPEC @ V12) @ ((c= @ ((c$ @ V13) @ V7)) @ ((c$ @ V6) @ V7))) @ V13))))))) @ cEMPTY)))))))))))))) @ ((creal_lt @ ((csum @ V8) @ (cGABS @ (^[V10]: (c! @ (^[V11]: (c! @ (^[V12]: ((cGEQ @ (V10 @ ((c__comma__ @ V11) @ V12))) @ (cvector_norm @ ((cintegral @ V12) @ V9))))))))))) @ V4)))))))))))))))))))))))))
(TFRECHET_DERIVATIVE_WITHIN_CLOSED_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV)))) @ ((creal_lt @ ((c$ @ V2) @ V5)) @ ((c$ @ V3) @ V5)))))) @ ((c/__caret__ @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (((chas_derivative @ V0) @ V4) @ ((cwithin @ (cat @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))) @ ((c= @ ((cfrechet_derivative @ V0) @ ((cwithin @ (cat @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ V4)))))))))))))
(TFRECHET_DERIVATIVE_UNIQUE_WITHIN_OPEN_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ (copen_interval @ ((c__comma__ @ V2) @ V3)))) @ ((c/__caret__ @ (((chas_derivative @ V0) @ V4) @ ((cwithin @ (cat @ V1)) @ (copen_interval @ ((c__comma__ @ V2) @ V3))))) @ (((chas_derivative @ V0) @ V5) @ ((cwithin @ (cat @ V1)) @ (copen_interval @ ((c__comma__ @ V2) @ V3))))))) @ ((c= @ V4) @ V5)))))))))))))))
(TFRECHET_DERIVATIVE_UNIQUE_WITHIN_CLOSED_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V6)) @ ((c<= @ V6) @ (cdimindex @ cUNIV)))) @ ((creal_lt @ ((c$ @ V2) @ V6)) @ ((c$ @ V3) @ V6)))))) @ ((c/__caret__ @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((c/__caret__ @ (((chas_derivative @ V0) @ V4) @ ((cwithin @ (cat @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ (((chas_derivative @ V0) @ V5) @ ((cwithin @ (cat @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))) @ ((c= @ V4) @ V5)))))))))))))))
(TCONTINUOUS_AT_COMPOSE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V2) @ (cat @ V3))) @ ((c/__caret__ @ ((ccontinuous @ V0) @ (cat @ (V2 @ V3)))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c= @ (V2 @ (V0 @ V4))) @ V4)))) @ ((c= @ (V0 @ (V2 @ V3))) @ V3))))) @ ((c= @ ((ccontinuous @ V1) @ (cat @ (V2 @ V3)))) @ ((ccontinuous @ (^[V4]: (V1 @ (V2 @ V4)))) @ (cat @ V3)))))))))))))
(TMEASURABLE_ON_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmeasurable_on @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V1)) @ (V0 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))) @ cUNIV)) @ ((cmeasurable_on @ V0) @ V1)))))))
(TABSOLUTELY_INTEGRABLE_RESTRICT_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cabsolutely_integrable_on @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V1)) @ (V0 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))) @ cUNIV)) @ ((cabsolutely_integrable_on @ V0) @ V1)))))))
(TINTEGRABLE_RESTRICT_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cintegrable_on @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V1)) @ (V0 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))) @ cUNIV)) @ ((cintegrable_on @ V0) @ V1)))))))
(TCONTINUOUS_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccontinuous @ V0) @ ((cwithin @ (cat @ V1)) @ V2))) @ (((c--> @ V0) @ (V0 @ V1)) @ ((cwithin @ (cat @ V1)) @ V2))))))))))
(TCONTINUOUS_ON_LIFT_DET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))))) @ ((ccontinuous_on @ (^[V4]: (clift @ ((c$ @ ((c$ @ (V0 @ V4)) @ V2)) @ V3)))) @ V1))))))) @ ((ccontinuous_on @ (^[V2]: (clift @ (cdet @ (V0 @ V2))))) @ V1)))))))
(TLOCALLY_COMPACT_HOMEOMORPHISM_PROJECTION_CLOSED,(c! @ (^[V0]: ((c==> @ ((clocally @ ccompact) @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cclosed @ V1)) @ ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ cfstcart)))))))))))
(THOMEOMORPHIC_CLOSED_IN_CONVEX,(c! @ (^[V0]: ((c==> @ ((cint_lt @ (caff_dim @ V0)) @ (cint_of_num @ (cdimindex @ cUNIV)))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2)) @ ((chomeomorphic @ V0) @ V2))))))))))))
(TLOCALLY_COMPACT_HOMEOMORPHIC_CLOSED,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((clocally @ ccompact) @ V0)) @ ((c< @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV)))) @ (c? @ (^[V1]: ((c/__caret__ @ (cclosed @ V1)) @ ((chomeomorphic @ V0) @ V1))))))))
(Tcontent,(c! @ (^[V0]: ((c= @ (ccontent @ V0)) @ (((cCOND @ ((c= @ V0) @ cEMPTY)) @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V1]: ((creal_sub @ ((c$ @ (cinterval_upperbound @ V0)) @ V1)) @ ((c$ @ (cinterval_lowerbound @ V0)) @ V1)))))))))
(Tindicator,(c! @ (^[V0]: ((c= @ (cindicator @ V0)) @ (^[V1]: (((cCOND @ ((cIN @ V1) @ V0)) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))))))
(Tinterval_upperbound,(c! @ (^[V0]: ((c= @ (cinterval_upperbound @ V0)) @ (clambda @ (^[V1]: (csup @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ ((c$ @ V4) @ V1)) @ V3))))) @ V3))))))))))))
(Tinterval_lowerbound,(c! @ (^[V0]: ((c= @ (cinterval_lowerbound @ V0)) @ (clambda @ (^[V1]: (cinf @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ ((c$ @ V4) @ V1)) @ V3))))) @ V3))))))))))))
(THOMOTOPY_EQUIVALENT_EMPTY_conjunct0,(c! @ (^[V0]: ((c= @ ((chomotopy_equivalent @ V0) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TCONTINUOUS_CARD_LT_RANGE_CONSTANT_EQ,(c! @ (^[V0]: ((c= @ (cconnected @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c<_c @ ((cIMAGE @ V1) @ V0)) @ cUNIV))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2)))))))))))))
(TCONTINUOUS_FINITE_RANGE_CONSTANT_EQ,(c! @ (^[V0]: ((c= @ (cconnected @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (cFINITE @ ((cIMAGE @ V1) @ V0)))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2)))))))))))))
(TCONTINUOUS_COUNTABLE_RANGE_CONSTANT_EQ,(c! @ (^[V0]: ((c= @ (cconnected @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (cCOUNTABLE @ ((cIMAGE @ V1) @ V0)))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2)))))))))))))
(TCONTINUOUS_DISCRETE_RANGE_CONSTANT_EQ,(c! @ (^[V0]: ((c= @ (cconnected @ V0)) @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (c~ @ ((c= @ (V1 @ V4)) @ (V1 @ V2))))) @ ((creal_le @ V3) @ (cvector_norm @ ((cvector_sub @ (V1 @ V4)) @ (V1 @ V2))))))))))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2)))))))))))))
(TCONTINUOUS_DISCONNECTED_RANGE_CONSTANT_EQ,(c! @ (^[V0]: ((c= @ (cconnected @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c= @ ((cconnected_component @ V2) @ V3)) @ ((cINSERT @ V3) @ cEMPTY)))))))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V4)) @ V3)))))))))))))))
(TSUM_CONTENT_AREA_OVER_THIN_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V4) @ V3)) @ V1)) @ ((c/__caret__ @ ((creal_le @ V1) @ ((c$ @ V5) @ V3))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ (c~ @ ((c= @ ((cINTER @ V6) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c= @ ((c$ @ V8) @ V3)) @ V1)) @ V8))))))) @ cEMPTY)))))))))))) @ ((creal_le @ ((creal_mul @ ((creal_sub @ ((c$ @ V5) @ V3)) @ ((c$ @ V4) @ V3))) @ ((csum @ V2) @ (^[V6]: ((creal_div @ (ccontent @ V6)) @ ((creal_sub @ ((c$ @ (cinterval_upperbound @ V6)) @ V3)) @ ((c$ @ (cinterval_lowerbound @ V6)) @ V3))))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))))))))))))))))))
(TCONTINUOUS_GE_ON_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ ((co @ clift) @ V2)) @ (cclosure @ V0))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ V1) @ (V2 @ V4))))))) @ ((c==> @ ((cIN @ V3) @ (cclosure @ V0))) @ ((creal_le @ V1) @ (V2 @ V3)))))))))))))
(TLUZIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ ((cmeasurable_on @ V2) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)))) @ (c? @ (^[V3]: ((c/__caret__ @ (ccompact @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (cmeasure @ ((cDIFF @ V0) @ V3))) @ V1)) @ ((ccontinuous_on @ V2) @ V3))))))))))))))
(THOMOTOPIC_NON_ANTIPODAL_SPHEREMAPS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ (csphere @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ (csphere @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ (c~ @ ((c= @ (V2 @ V4)) @ (cvector_neg @ (V3 @ V4)))))))))))) @ ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ (csphere @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))) @ V2) @ V3)))))))))))
(TVSUM_OVER_TAGGED_PARTIAL_DIVISION_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ctagged_partial_division_of @ V1) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ cEMPTY))) @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (V2 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (cvec @ (cNUMERAL @ c_0)))))))))) @ ((c= @ ((cvsum @ V1) @ (cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ (V2 @ V5)))))))))) @ ((cvsum @ ((cIMAGE @ cSND) @ V1)) @ V2))))))))))
(TVSUM_OVER_TAGGED_DIVISION_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V1) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ cEMPTY))) @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (V2 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ (cvec @ (cNUMERAL @ c_0)))))))))) @ ((c= @ ((cvsum @ V1) @ (cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ (V2 @ V5)))))))))) @ ((cvsum @ ((cIMAGE @ cSND) @ V1)) @ V2))))))))))
(TMEASURABLE_ON_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((cmeasurable_on @ (V1 @ V4)) @ V3)))) @ ((c/__caret__ @ (cnegligible @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ V3) @ V0))) @ (((c--> @ (^[V5]: ((V1 @ V5) @ V4))) @ (V2 @ V4)) @ csequentially))))))) @ ((cmeasurable_on @ V2) @ V3)))))))))))
(TSET_VARIATION_POS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cset_variation @ V0) @ V1))))))))
(THAS_BOUNDED_SETVARIATION_ON_IMP_BOUNDED_ON_SUBINTERVALS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ (cbounded @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ V0)) @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))))
(THAS_BOUNDED_SETVARIATION_WORKS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V3) @ V4)) @ ((cSUBSET @ V4) @ V0))) @ ((creal_le @ ((csum @ V3) @ (^[V5]: (cvector_norm @ (V1 @ V5))))) @ V2))))))) @ ((creal_le @ ((cset_variation @ V0) @ V1)) @ V2))))))))))
(THAS_BOUNDED_SETVARIATION_WORKS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V2) @ V3)) @ ((cSUBSET @ V3) @ V0))) @ ((creal_le @ ((csum @ V2) @ (^[V4]: (cvector_norm @ (V1 @ V4))))) @ ((cset_variation @ V0) @ V1)))))))))))))
(THAS_BOUNDED_SETVARIATION_WORKS_ON_ELEMENTARY_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ (c? @ (^[V2]: ((cdivision_of @ V2) @ V0))))) @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cdivision_of @ V3) @ V0)) @ ((creal_le @ ((csum @ V3) @ (^[V4]: (cvector_norm @ (V1 @ V4))))) @ V2))))) @ ((creal_le @ ((cset_variation @ V0) @ V1)) @ V2))))))))))
(THAS_BOUNDED_SETVARIATION_WORKS_ON_ELEMENTARY_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ (c? @ (^[V2]: ((cdivision_of @ V2) @ V0))))) @ (c! @ (^[V2]: ((c==> @ ((cdivision_of @ V2) @ V0)) @ ((creal_le @ ((csum @ V2) @ (^[V3]: (cvector_norm @ (V1 @ V3))))) @ ((cset_variation @ V0) @ V1)))))))))))
(TSET_VARIATION_ON_NULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (cvec @ (cNUMERAL @ c_0))))))))) @ ((c/__caret__ @ ((c= @ (ccontent @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (cbounded @ V0)))) @ ((c= @ ((cset_variation @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TSET_VARIATION_ON_ELEMENTARY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c? @ (^[V2]: ((cdivision_of @ V2) @ V0)))) @ ((c= @ ((cset_variation @ V0) @ V1)) @ (csup @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cdivision_of @ V3) @ V0)) @ ((csum @ V3) @ (^[V4]: (cvector_norm @ (V1 @ V4)))))))))))))))))
(THAS_BOUNDED_SETVARIATION_ON_ELEMENTARY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c? @ (^[V2]: ((cdivision_of @ V2) @ V0)))) @ ((c= @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cdivision_of @ V3) @ V0)) @ ((creal_le @ ((csum @ V3) @ (^[V4]: (cvector_norm @ (V1 @ V4))))) @ V2)))))))))))))
(TSET_VARIATION_REFLECT2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cset_variation @ ((cIMAGE @ cvector_neg) @ V0)) @ (^[V2]: (V1 @ ((cIMAGE @ cvector_neg) @ V2))))) @ ((cset_variation @ V0) @ V1)))))))
(Tset_variation,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cset_variation @ V0) @ V1)) @ (csup @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c/__caret__ @ ((cdivision_of @ V3) @ V4)) @ ((cSUBSET @ V4) @ V0))))) @ ((csum @ V3) @ (^[V4]: (cvector_norm @ (V1 @ V4))))))))))))))))
(THAS_BOUNDED_SETVARIATION_ON,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V3) @ V4)) @ ((cSUBSET @ V4) @ V0))) @ ((creal_le @ ((csum @ V3) @ (^[V5]: (cvector_norm @ (V1 @ V5))))) @ V2)))))))))))))))
(Thas_bounded_setvariation_on,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V3) @ V4)) @ ((cSUBSET @ V4) @ V0))) @ ((creal_le @ ((csum @ V3) @ (^[V5]: (cvector_norm @ (V1 @ V5))))) @ V2))))))))))))))
(TSET_VARIATION_UBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V3) @ V4)) @ ((cSUBSET @ V4) @ V0))) @ ((creal_le @ ((csum @ V3) @ (^[V5]: (cvector_norm @ (V1 @ V5))))) @ V2)))))))) @ ((creal_le @ ((cset_variation @ V0) @ V1)) @ V2)))))))))
(TSET_VARIATION_ELEMENTARY_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c? @ (^[V3]: ((cdivision_of @ V3) @ V0)))) @ ((c= @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V3) @ V4)) @ ((cSUBSET @ V4) @ V0))) @ ((creal_le @ ((csum @ V3) @ (^[V5]: (cvector_norm @ (V1 @ V5))))) @ V2))))))) @ (c! @ (^[V3]: ((c==> @ ((cdivision_of @ V3) @ V0)) @ ((creal_le @ ((csum @ V3) @ (^[V4]: (cvector_norm @ (V1 @ V4))))) @ V2)))))))))))))
(THAS_BOUNDED_SETVARIATION_ON_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V1) @ V0)) @ ((cSUBSET @ V2) @ V0))) @ ((chas_bounded_setvariation_on @ V1) @ V2)))))))))
(TINTEGRAL_COMBINE_DIVISION_TOPDOWN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V0)) @ ((cdivision_of @ V1) @ V0))) @ ((c= @ ((cintegral @ V0) @ V2)) @ ((cvsum @ V1) @ (^[V3]: ((cintegral @ V3) @ V2))))))))))))
(TINTEGRAL_COMBINE_DIVISION_BOTTOMUP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V1) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cintegrable_on @ V2) @ V3)))))) @ ((c= @ ((cintegral @ V0) @ V2)) @ ((cvsum @ V1) @ (^[V3]: ((cintegral @ V3) @ V2))))))))))))
(THAS_INTEGRAL_COMBINE_DIVISION_TOPDOWN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V0)) @ ((c/__caret__ @ ((cdivision_of @ V1) @ V3)) @ ((cSUBSET @ V3) @ V0)))) @ (((chas_integral @ V2) @ ((cvsum @ V1) @ (^[V4]: ((cintegral @ V4) @ V2)))) @ V3)))))))))))
(TSET_VARIATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V3) @ V2)) @ ((c/__caret__ @ ((cdivision_of @ V1) @ V0)) @ ((cSUBSET @ V0) @ V2)))) @ ((creal_le @ ((csum @ V1) @ (^[V4]: (cvector_norm @ (V3 @ V4))))) @ ((cset_variation @ V2) @ V3))))))))))))
(TSUBADDITIVE_CONTENT_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdivision_of @ V1) @ V0)) @ ((cSUBSET @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ ((creal_le @ ((csum @ V1) @ ccontent)) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))
(TOPEN_OPEN_LEFT_PROJECTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (copen @ V1))) @ (copen @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((cIN @ ((cpastecart @ V3) @ V4)) @ V1))))) @ V3))))))))))))
(TCLOSED_COMPACT_PROJECTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ (cclosed @ V1))) @ (cclosed @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ ((cpastecart @ V4) @ V3)) @ V1))))) @ V3))))))))))))
(THOMOTOPY_EQUIVALENT_HOMOTOPIC_TRIVIALITY_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chomotopy_equivalent @ V0) @ V2)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V0))) @ (c? @ (^[V4]: ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V1) @ V0)) @ V3) @ (^[V5]: V4)))))))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V2))) @ (c? @ (^[V4]: ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V1) @ V2)) @ V3) @ (^[V5]: V4))))))))))))))))
(THOMOTOPY_EQUIVALENT_HOMOTOPIC_TRIVIALITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chomotopy_equivalent @ V0) @ V2)) @ ((c= @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V4) @ V1)) @ V0))))) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V1) @ V0)) @ V3) @ V4))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V4) @ V1)) @ V2))))) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V1) @ V2)) @ V3) @ V4)))))))))))))))
(TSPAN_PCROSS_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ (cspan @ ((cPCROSS @ V0) @ V1))) @ ((cPCROSS @ (cspan @ V0)) @ (cspan @ V1))))))))
(THOMOTOPY_EQUIVALENT_PATH_CONNECTEDNESS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomotopy_equivalent @ V0) @ V1)) @ ((c= @ (cpath_connected @ V0)) @ (cpath_connected @ V1))))))))
(THOMOTOPY_EQUIVALENT_CONTRACTIBILITY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomotopy_equivalent @ V0) @ V1)) @ ((c= @ (ccontractible @ V0)) @ (ccontractible @ V1))))))))
(THOMOTOPY_EQUIVALENT_CONNECTEDNESS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomotopy_equivalent @ V0) @ V1)) @ ((c= @ (cconnected @ V0)) @ (cconnected @ V1))))))))
(THOMEOMORPHIC_IMP_HOMOTOPY_EQUIVALENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomeomorphic @ V0) @ V1)) @ ((chomotopy_equivalent @ V0) @ V1)))))))
(THOMEOMORPHIC_IMP_CARD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomeomorphic @ V0) @ V1)) @ ((c=_c @ V0) @ V1)))))))
(THOMEOMORPHIC_COMPACT_ARNESS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomeomorphic @ V0) @ V1)) @ ((c= @ ((c/__caret__ @ (ccompact @ V0)) @ ((cretract_of @ V0) @ cUNIV))) @ ((c/__caret__ @ (ccompact @ V1)) @ ((cretract_of @ V1) @ cUNIV)))))))))
(THOMEOMORPHIC_SIMPLY_CONNECTED_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomeomorphic @ V0) @ V1)) @ ((c= @ (csimply_connected @ V0)) @ (csimply_connected @ V1))))))))
(THOMEOMORPHIC_CONTRACTIBLE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomeomorphic @ V0) @ V1)) @ ((c= @ (ccontractible @ V0)) @ (ccontractible @ V1))))))))
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(TSTARLIKE_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cstarlike @ V0)) @ (cstarlike @ V1))) @ (cstarlike @ ((cPCROSS @ V0) @ V1))))))))
(TSIMPLY_CONNECTED_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csimply_connected @ V0)) @ (csimply_connected @ V1))) @ (csimply_connected @ ((cPCROSS @ V0) @ V1))))))))
(TPOLYTOPE_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolytope @ V0)) @ (cpolytope @ V1))) @ (cpolytope @ ((cPCROSS @ V0) @ V1))))))))
(TPATH_CONNECTED_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath_connected @ V0)) @ (cpath_connected @ V1))) @ (cpath_connected @ ((cPCROSS @ V0) @ V1))))))))
(TOPEN_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ (copen @ V1))) @ (copen @ ((cPCROSS @ V0) @ V1))))))))
(TIS_INTERVAL_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cis_interval @ V0)) @ (cis_interval @ V1))) @ (cis_interval @ ((cPCROSS @ V0) @ V1))))))))
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(THOMEOMORPHIC_CONVEX_COMPACT_SETS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (ccompact @ V1)) @ ((c= @ (caff_dim @ V0)) @ (caff_dim @ V1))))))) @ ((chomeomorphic @ V0) @ V1)))))))
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(TCONVEX_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (cconvex @ V1))) @ (cconvex @ ((cPCROSS @ V0) @ V1))))))))
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(TCOMPACT_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ (ccompact @ V1))) @ (ccompact @ ((cPCROSS @ V0) @ V1))))))))
(TCLOSED_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (cclosed @ V1))) @ (cclosed @ ((cPCROSS @ V0) @ V1))))))))
(TBOUNDED_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cbounded @ V0)) @ (cbounded @ V1))) @ (cbounded @ ((cPCROSS @ V0) @ V1))))))))
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(TENR_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cENR @ V0)) @ (cENR @ V1))) @ (cENR @ ((cPCROSS @ V0) @ V1))))))))
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(TANR_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cANR @ V0)) @ (cANR @ V1))) @ (cANR @ ((cPCROSS @ V0) @ V1))))))))
(TCONVEX_HULL_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ cconvex) @ ((cPCROSS @ V0) @ V1))) @ ((cPCROSS @ ((chull @ cconvex) @ V0)) @ ((chull @ cconvex) @ V1))))))))
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(TIMAGE_SNDCART_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIMAGE @ csndcart) @ ((cPCROSS @ V0) @ V1))) @ (((cCOND @ ((c= @ V0) @ cEMPTY)) @ cEMPTY) @ V1)))))))
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(TSUBSPACE_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csubspace @ ((cPCROSS @ V0) @ V1))) @ ((c/__caret__ @ (csubspace @ V0)) @ (csubspace @ V1))))))))
(TSTARLIKE_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cstarlike @ ((cPCROSS @ V0) @ V1))) @ ((c/__caret__ @ (cstarlike @ V0)) @ (cstarlike @ V1))))))))
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(TOPEN_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (copen @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (copen @ V0)) @ (copen @ V1))))))))))
(TIS_INTERVAL_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cis_interval @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cis_interval @ V0)) @ (cis_interval @ V1))))))))))
(TCONVEX_CONE_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cconvex_cone @ ((cPCROSS @ V0) @ V1))) @ ((c/__caret__ @ (cconvex_cone @ V0)) @ (cconvex_cone @ V1))))))))
(TCONVEX_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cconvex @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cconvex @ V0)) @ (cconvex @ V1))))))))))
(TCONTRACTIBLE_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccontractible @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (ccontractible @ V0)) @ (ccontractible @ V1))))))))))
(TCONNECTED_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cconnected @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cconnected @ V0)) @ (cconnected @ V1))))))))))
(TCONIC_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cconic @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cconic @ V0)) @ (cconic @ V1))))))))))
(TCOMPACT_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccompact @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (ccompact @ V0)) @ (ccompact @ V1))))))))))
(TCLOSED_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cclosed @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cclosed @ V0)) @ (cclosed @ V1))))))))))
(TBOUNDED_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cbounded @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cbounded @ V0)) @ (cbounded @ V1))))))))))
(TAFFINE_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (caffine @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (caffine @ V0)) @ (caffine @ V1))))))))))
(TENR_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cENR @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cENR @ V0)) @ (cENR @ V1))))))))))
(TAR_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cAR @ ((cPCROSS @ V0) @ V1))) @ ((c/__caret__ @ (cAR @ V0)) @ ((c/__caret__ @ (cAR @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c~ @ ((c= @ V1) @ cEMPTY)))))))))))
(TANR_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cANR @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cANR @ V0)) @ (cANR @ V1))))))))))
(THOMOTOPIC_TRIVIALITY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V1))))) @ ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ V3))))))) @ ((c/__caret__ @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ (cpath_connected @ V1))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1))) @ (c? @ (^[V3]: ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ (^[V4]: V3))))))))))))))
(THOMOTOPIC_WITH_REFL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((chomotopic_with @ V2) @ ((c__comma__ @ V0) @ V1)) @ V3) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V1)) @ (V2 @ V3)))))))))))))
(TCLOSED_MAP_SNDCART,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cPCROSS @ V0) @ V1))) @ V2))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ csndcart) @ V2))))))))))
(TFACE_OF_PCROSS_DECOMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cface_of @ V2) @ ((cPCROSS @ V0) @ V1))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cface_of @ V3) @ V0)) @ ((c/__caret__ @ ((cface_of @ V4) @ V1)) @ ((c= @ V2) @ ((cPCROSS @ V3) @ V4))))))))))))))))
(THOMOTOPIC_PATHS_CONTINUOUS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chomotopic_paths @ V0) @ V2) @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V1)))) @ (((chomotopic_paths @ V1) @ ((co @ V3) @ V2)) @ ((co @ V3) @ V4))))))))))))))
(THOMOTOPIC_LOOPS_CONTINUOUS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chomotopic_loops @ V0) @ V2) @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V1)))) @ (((chomotopic_loops @ V1) @ ((co @ V3) @ V2)) @ ((co @ V3) @ V4))))))))))))))
(THOMEOMORPHIC_PCROSS_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((chomeomorphic @ ((cPCROSS @ V0) @ ((cPCROSS @ V1) @ V2))) @ ((cPCROSS @ ((cPCROSS @ V0) @ V1)) @ V2)))))))))
(THOMOTOPY_EQUIVALENT_COHOMOTOPIC_TRIVIALITY_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chomotopy_equivalent @ V0) @ V1)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V2))) @ (c? @ (^[V4]: ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V0) @ V2)) @ V3) @ (^[V5]: V4)))))))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V2))) @ (c? @ (^[V4]: ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V1) @ V2)) @ V3) @ (^[V5]: V4))))))))))))))))
(THOMOTOPY_EQUIVALENT_COHOMOTOPIC_TRIVIALITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chomotopy_equivalent @ V0) @ V1)) @ ((c= @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V4) @ V0)) @ V2))))) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V0) @ V2)) @ V3) @ V4))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V4) @ V1)) @ V2))))) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V1) @ V2)) @ V3) @ V4)))))))))))))))
(THOMEOMORPHIC_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chomeomorphic @ V0) @ V2)) @ ((chomeomorphic @ V1) @ V3))) @ ((chomeomorphic @ ((cPCROSS @ V0) @ V1)) @ ((cPCROSS @ V2) @ V3))))))))))))
(TABSOLUTE_RETRACT_HOMEOMORPHIC_CONVEX_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chomeomorphic @ V1) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ ((c/__caret__ @ (cconvex @ V0)) @ (ccompact @ V0)))))) @ ((cretract_of @ V1) @ V2)))))))))
(TPROPER_MAP_SNDCART,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ (ccompact @ V2)))) @ (ccompact @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ ((cPCROSS @ V0) @ V1))) @ ((cIN @ (csndcart @ V4)) @ V2))) @ V4))))))))))))))
(TENR_IMP_ABSOLUTE_NEIGHBOURHOOD_RETRACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cENR @ V0)) @ ((c/__caret__ @ ((chomeomorphic @ V0) @ V2)) @ ((cSUBSET @ V2) @ V1)))) @ (c? @ (^[V3]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3)) @ ((cretract_of @ V2) @ V3))))))))))))
(TINESSENTIAL_ON_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((clocally @ cconnected) @ V0)) @ ((c/__caret__ @ (cpath_connected @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (ccomponents @ V0))) @ (c? @ (^[V4]: ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V3) @ V1)) @ V2) @ (^[V5]: V4)))))))))) @ (c? @ (^[V3]: ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ (^[V4]: V3))))))))))))
(TCOVERING_SPACE_HOMEOMORPHISM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V0) @ V2)) @ V1)) @ ((c/__caret__ @ (cpath_connected @ V0)) @ (csimply_connected @ V1)))) @ (c? @ (^[V3]: ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))))))))))))
(TCOVERING_SPACE_FINITE_SHEETS_EQ_CLOSED_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V0) @ V2)) @ V1)) @ ((c/__caret__ @ (cconnected @ V1)) @ (c~ @ (c? @ (^[V3]: ((c= @ V1) @ ((cINSERT @ V3) @ cEMPTY)))))))) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c= @ (V2 @ V5)) @ V3))) @ V5)))))))))) @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3))))))))))))))
(TCOVERING_SPACE_FINITE_SHEETS_EQ_CLOSED_MAP_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V0) @ V2)) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((climit_point_of @ V3) @ V1)))))) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c= @ (V2 @ V5)) @ V3))) @ V5)))))))))) @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3))))))))))))))
(TNULLHOMOTOPIC_INTO_CONTRACTIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (ccontractible @ V1)))) @ (c? @ (^[V3]: ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ (^[V4]: V3))))))))))))
(TNULLHOMOTOPIC_FROM_CONTRACTIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (ccontractible @ V0)))) @ (c? @ (^[V3]: ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ (^[V4]: V3))))))))))))
(THOMEOMORPHISM_INJECTIVE_OPEN_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3))))))))) @ (c? @ (^[V3]: ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))))))))))))
(THOMEOMORPHISM_INJECTIVE_CLOSED_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3))))))))) @ (c? @ (^[V3]: ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))))))))))))
(THOMEOMORPHISM_INJECTIVE_OPEN_MAP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))))) @ ((c= @ (c? @ (^[V3]: ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))))) @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3))))))))))))))
(THOMEOMORPHISM_INJECTIVE_CLOSED_MAP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))))) @ ((c= @ (c? @ (^[V3]: ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))))) @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3))))))))))))))
(TINJECTIVE_MAP_OPEN_IFF_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))))) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3))))))))))))))
(TINESSENTIAL_ON_COMPONENTS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c__caret__/ @ ((clocally @ cconnected) @ V0)) @ ((c/__caret__ @ (ccompact @ V0)) @ (cANR @ V1)))) @ (cpath_connected @ V1))) @ ((c= @ (c? @ (^[V3]: ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ (^[V4]: V3))))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (ccomponents @ V0))) @ (c? @ (^[V4]: ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V3) @ V1)) @ V2) @ (^[V5]: V4))))))))))))))))))
(TISOMETRY_IMP_EMBEDDING,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V0))) @ ((c= @ (cdistance @ ((c__comma__ @ (V2 @ V3)) @ (V2 @ V4)))) @ (cdistance @ ((c__comma__ @ V3) @ V4)))))))))) @ (c? @ (^[V3]: ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))))))))))))
(THOMOTOPIC_WITH_IMP_PROPERTY_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((chomotopic_with @ V3) @ ((c__comma__ @ V0) @ V1)) @ V4) @ V2)) @ (V3 @ V4)))))))))))))
(THOMOTOPIC_WITH_IMP_PROPERTY_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((chomotopic_with @ V3) @ ((c__comma__ @ V0) @ V1)) @ V2) @ V4)) @ (V3 @ V4)))))))))))))
(THOMEOMORPHISM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V3 @ (V2 @ V4))) @ V4))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ (V3 @ V4))) @ V4)))))))))))))))))))
(THOMOTOPIC_ON_COMPONENTS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c__caret__/ @ ((clocally @ cconnected) @ V0)) @ ((c/__caret__ @ (ccompact @ V0)) @ (cANR @ V1)))) @ ((c= @ ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V1)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (ccomponents @ V0))) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V4) @ V1)) @ V2) @ V3)))))))))))))))))))
(THOMOTOPIC_ON_COMPONENTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((clocally @ cconnected) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (ccomponents @ V0))) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V4) @ V1)) @ V2) @ V3)))))) @ ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ V3)))))))))))
(THOMOTOPIC_WITH_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ (V2 @ V4)) @ (V3 @ V4))) @ cNIL))) @ V1))))))) @ ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ V3)))))))))))
(THOMOTOPIC_FROM_CONTRACTIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V1)) @ ((c/__caret__ @ (ccontractible @ V0)) @ (cpath_connected @ V1))))))) @ ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ V3)))))))))))
(THOMOTOPIC_INTO_CONTRACTIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ V1)) @ (ccontractible @ V1)))))) @ ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ V2) @ V3)))))))))))
(Thomotopic_with,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((((chomotopic_with @ V4) @ ((c__comma__ @ V0) @ V1)) @ V2) @ V3)) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V0))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V5) @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))) @ V0))) @ V1)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c= @ (V5 @ ((cpastecart @ (cvec @ (cNUMERAL @ c_0))) @ V6))) @ (V2 @ V6))))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c= @ (V5 @ ((cpastecart @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V6))) @ (V3 @ V6))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ (V4 @ (^[V7]: (V5 @ ((cpastecart @ V6) @ V7)))))))))))))))))))))))))
(TCOVERING_SPACE_OPEN_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V0) @ V2)) @ V1)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3))))))))))))
(TCOVERING_SPACE_CLOSED_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccovering_space @ ((c__comma__ @ V0) @ V2)) @ V1)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ (cFINITE @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c= @ (V2 @ V6)) @ V4))) @ V6)))))))))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3))))))))))))
(TCONTINUOUS_IMP_CLOSED_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (ccompact @ V0)))) @ ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3)))))))))))))
(TOPEN_MAP_IMP_CLOSED_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V4)))))) @ (c! @ (^[V4]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((cIN @ (V2 @ V6)) @ ((cIMAGE @ V2) @ V4)))) @ V6)))))))))))) @ ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3)))))))))))))
(TCLOSED_MAP_IMP_OPEN_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V4)))))) @ (c! @ (^[V4]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((cIN @ (V2 @ V6)) @ ((cIMAGE @ V2) @ V4)))) @ V6)))))))))))) @ ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3)))))))))))))
(TISOMETRY_IMP_OPEN_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ V0))) @ ((c= @ (cdistance @ ((c__comma__ @ (V2 @ V4)) @ (V2 @ V5)))) @ (cdistance @ ((c__comma__ @ V4) @ V5))))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V3)))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cIMAGE @ V2) @ V3))))))))))))
(TPROPER_MAP_FSTCART,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ (ccompact @ V2)))) @ (ccompact @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ ((cPCROSS @ V0) @ V1))) @ ((cIN @ (cfstcart @ V4)) @ V2))) @ V4))))))))))))))
(TRETRACT_OF_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V0) @ V2)) @ ((cretract_of @ V1) @ V3))) @ ((cretract_of @ ((cPCROSS @ V0) @ V1)) @ ((cPCROSS @ V2) @ V3))))))))))))
(TOPEN_IN_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cPCROSS @ V0) @ V1))) @ ((cPCROSS @ V2) @ V3))))))))))))
(TFACE_OF_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cface_of @ V0) @ V2)) @ ((cface_of @ V1) @ V3))) @ ((cface_of @ ((cPCROSS @ V0) @ V1)) @ ((cPCROSS @ V2) @ V3))))))))))))
(TCLOSED_IN_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V3))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cPCROSS @ V0) @ V1))) @ ((cPCROSS @ V2) @ V3))))))))))))
(TBILINEAR_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ (cbilinear @ V4)) @ ((c/__caret__ @ (cbilinear @ V5)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ (cspan @ V0))) @ ((c/__caret__ @ ((cSUBSET @ V3) @ (cspan @ V1))) @ (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((cIN @ V8) @ V0)) @ ((cIN @ V9) @ V1))) @ ((c= @ ((V4 @ V8) @ V9)) @ ((V5 @ V8) @ V9)))))))))))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ ((cIN @ V7) @ V3))) @ ((c= @ ((V4 @ V6) @ V7)) @ ((V5 @ V6) @ V7)))))))))))))))))))))
(TRETRACT_OF_IMP_EXTENSIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V2) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V2)) @ V1)))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V0)) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c= @ (V4 @ V5)) @ (V3 @ V5)))))))))))))))))))
(TEXTENSION_FROM_CLOPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V2)) @ V1)) @ ((c==> @ ((c= @ V1) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V0)) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c= @ (V4 @ V5)) @ (V3 @ V5)))))))))))))))))))
(TEXTENSION_INTO_AR_LOCAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V2)) @ V1)) @ ((c/__caret__ @ ((cretract_of @ V1) @ cUNIV)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ cUNIV)) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c= @ (V4 @ V5)) @ (V3 @ V5)))))))))))))))))))
(TEXTENSION_FROM_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c__caret__/ @ ((clocally @ cconnected) @ V0)) @ ((c/__caret__ @ (ccompact @ V0)) @ (cANR @ V1)))) @ ((c/__caret__ @ ((cIN @ V2) @ (ccomponents @ V0))) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V2)) @ V1))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V0)) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c= @ (V4 @ V5)) @ (V3 @ V5)))))))))))))))))))
(TDUGUNDJI,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((cSUBSET @ ((cIMAGE @ V3) @ V2)) @ V1)))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V0)) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c= @ (V4 @ V5)) @ (V3 @ V5)))))))))))))))))))
(TAR_IMP_ABSOLUTE_EXTENSOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cAR @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V2)) @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V0)) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c= @ (V4 @ V5)) @ (V3 @ V5)))))))))))))))))))
(TANR_IMP_ABSOLUTE_NEIGHBOURHOOD_EXTENSOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cANR @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V2)) @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2))))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((cSUBSET @ V2) @ V4)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V5) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V5) @ V4)) @ V1)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((c= @ (V5 @ V6)) @ (V3 @ V6)))))))))))))))))))))))
(TANR_IMP_ABSOLUTE_CLOSED_NEIGHBOURHOOD_EXTENSOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cANR @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V2)) @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2))))) @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V4)) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V5)) @ ((c/__caret__ @ ((ccontinuous_on @ V6) @ V5)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V6) @ V5)) @ V1)) @ (c! @ (^[V7]: ((c==> @ ((cIN @ V7) @ V2)) @ ((c= @ (V6 @ V7)) @ (V3 @ V7)))))))))))))))))))))))))))
(THOMOTOPIC_CONSTANT_MAPS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ V0) @ V1)) @ (^[V4]: V2)) @ (^[V4]: V3))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ (((cpath_component @ V1) @ V2) @ V3))))))))))))
(TCONTINUOUS_LE_ON_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ ((co @ clift) @ V1)) @ (cclosure @ V0))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ (V1 @ V4)) @ V3)))))) @ ((c==> @ ((cIN @ V2) @ (cclosure @ V0))) @ ((creal_le @ (V1 @ V2)) @ V3))))))))))))
(TINTEGRAL_DROP_POS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ (V1 @ V2)))))))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ ((cintegral @ V0) @ V1)))))))))
(THAS_INTEGRAL_DROP_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V1) @ V3) @ V0)) @ ((c/__caret__ @ (((chas_integral @ V2) @ V4) @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((creal_le @ (cdrop @ (V1 @ V5))) @ (cdrop @ (V2 @ V5))))))))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))))))))))))))
(THAS_INTEGRAL_DROP_POS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V1) @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ (V1 @ V3)))))))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ V2))))))))))
(THAS_INTEGRAL_DROP_NEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V1) @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (cdrop @ (V1 @ V3))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((creal_le @ (cdrop @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))
(TINTEGRAL_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cintegrable_on @ V1) @ V0)) @ ((c= @ ((cintegral @ V0) @ (^[V2]: (cvector_neg @ (V1 @ V2))))) @ (cvector_neg @ ((cintegral @ V0) @ V1)))))))))
(TABSOLUTELY_INTEGRABLE_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cabsolutely_integrable_on @ V1) @ V0)) @ ((creal_le @ (cvector_norm @ ((cintegral @ V0) @ V1))) @ (cdrop @ ((cintegral @ V0) @ (^[V2]: (clift @ (cvector_norm @ (V1 @ V2)))))))))))))
(TMEASURABLE_ON_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ cUNIV)) @ (clebesgue_measurable @ V0))) @ ((cmeasurable_on @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V0)) @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))) @ cUNIV)))))))
(THAS_DERIVATIVE_ZERO_CONNECTED_CONSTANT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (cconnected @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (((chas_derivative @ V1) @ (^[V3]: (cvec @ (cNUMERAL @ c_0)))) @ (cat @ V2)))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2))))))))))))
(TLINEAR_INJECTIVE_0_SUBSPACE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ (csubspace @ V0))) @ ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0)))))))))))))
(THAS_DERIVATIVE_ZERO_CONSTANT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (((chas_derivative @ V1) @ (^[V3]: (cvec @ (cNUMERAL @ c_0)))) @ ((cwithin @ (cat @ V2)) @ V0))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2))))))))))))
(TCONTINUOUS_CARD_LT_RANGE_CONSTANT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c<_c @ ((cIMAGE @ V1) @ V0)) @ cUNIV)))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2))))))))))))
(TCONTINUOUS_FINITE_RANGE_CONSTANT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (cFINITE @ ((cIMAGE @ V1) @ V0))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2))))))))))))
(TCONTINUOUS_COUNTABLE_RANGE_CONSTANT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (cCOUNTABLE @ ((cIMAGE @ V1) @ V0))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2))))))))))))
(TCONTINUOUS_DISCRETE_RANGE_CONSTANT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (c~ @ ((c= @ (V1 @ V4)) @ (V1 @ V2))))) @ ((creal_le @ V3) @ (cvector_norm @ ((cvector_sub @ (V1 @ V4)) @ (V1 @ V2)))))))))))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2))))))))))))
(TBROUWER_COMPACTNESS_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (c~ @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0)))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V2) @ (cvector_norm @ (V1 @ V3)))))))))))))))
(TCONTINUOUS_CLOSED_GRAPH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((ccontinuous_on @ V1) @ V0))) @ (cclosed @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ ((cpastecart @ V3) @ (V1 @ V3))))))))))))))
(TINJECTIVE_IMP_ISOMETRIC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ (csubspace @ V0)) @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0)))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_ge @ (cvector_norm @ (V1 @ V3))) @ ((creal_mul @ V2) @ (cvector_norm @ V3)))))))))))))))
(TCONTINUOUS_ON_EQ_CONTINUOUS_AT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (copen @ V0)) @ ((c= @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((ccontinuous @ V1) @ (cat @ V2))))))))))))
(TLUZIN_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (ccompact @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (cmeasure @ ((cDIFF @ V0) @ V3))) @ V2)) @ ((ccontinuous_on @ V1) @ V3))))))))))))))))
(TLUZIN_EQ_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (ccompact @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (cmeasure @ ((cDIFF @ V0) @ V3))) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ cUNIV)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((c= @ (V4 @ V5)) @ (V1 @ V5)))))))))))))))))))))))
(TMEASURABLE_ON_MEASURABLE_PREIMAGE_OPEN_HALFSPACE_COMPONENT_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (cmeasurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_lt @ ((c$ @ (V1 @ V5)) @ V3)) @ V2))) @ V5))))))))))))))))))
(TMEASURABLE_ON_MEASURABLE_PREIMAGE_OPEN_HALFSPACE_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (cmeasurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_le @ ((c$ @ (V1 @ V5)) @ V3)) @ V2))) @ V5))))))))))))))))))
(TMEASURABLE_ON_MEASURABLE_PREIMAGE_OPEN_HALFSPACE_COMPONENT_GT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (cmeasurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_gt @ ((c$ @ (V1 @ V5)) @ V3)) @ V2))) @ V5))))))))))))))))))
(TMEASURABLE_ON_MEASURABLE_PREIMAGE_OPEN_HALFSPACE_COMPONENT_GE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (cmeasurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_ge @ ((c$ @ (V1 @ V5)) @ V3)) @ V2))) @ V5))))))))))))))))))
(TMEASURABLE_ON_MEASURABLE_PREIMAGE_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ (copen @ V2)) @ (cmeasurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))))
(TMEASURABLE_ON_MEASURABLE_PREIMAGE_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ (cclosed @ V2)) @ (cmeasurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))))
(TMEASURABLE_ON_MEASURABLE_PREIMAGE_OPEN_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: (cmeasurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ (copen_interval @ ((c__comma__ @ V2) @ V3))))) @ V5)))))))))))))))))
(TMEASURABLE_ON_MEASURABLE_PREIMAGE_CLOSED_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: (cmeasurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ V5)))))))))))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_PREIMAGE_OPEN_HALFSPACE_COMPONENT_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clebesgue_measurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (clebesgue_measurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_lt @ ((c$ @ (V1 @ V5)) @ V3)) @ V2))) @ V5))))))))))))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_PREIMAGE_OPEN_HALFSPACE_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clebesgue_measurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (clebesgue_measurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_le @ ((c$ @ (V1 @ V5)) @ V3)) @ V2))) @ V5))))))))))))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_PREIMAGE_OPEN_HALFSPACE_COMPONENT_GT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clebesgue_measurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (clebesgue_measurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_gt @ ((c$ @ (V1 @ V5)) @ V3)) @ V2))) @ V5))))))))))))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_PREIMAGE_OPEN_HALFSPACE_COMPONENT_GE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clebesgue_measurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ (clebesgue_measurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_ge @ ((c$ @ (V1 @ V5)) @ V3)) @ V2))) @ V5))))))))))))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_PREIMAGE_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clebesgue_measurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ (copen @ V2)) @ (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_PREIMAGE_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clebesgue_measurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ (cclosed @ V2)) @ (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_PREIMAGE_OPEN_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clebesgue_measurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: (clebesgue_measurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ (copen_interval @ ((c__comma__ @ V2) @ V3))))) @ V5)))))))))))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_PREIMAGE_CLOSED_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clebesgue_measurable @ V0)) @ ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: (clebesgue_measurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ V5)))))))))))))))))
(TLINEAR_INDEPENDENT_EXTEND_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cindependent @ V0)) @ ((c==> @ (cFINITE @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cspan @ V0))) @ ((cIN @ V4) @ (cspan @ V0)))) @ ((c= @ (V2 @ ((cvector_add @ V3) @ V4))) @ ((cvector_add @ (V2 @ V3)) @ (V2 @ V4))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V3) @ (cspan @ V0))) @ ((c= @ (V2 @ ((c% @ V4) @ V3))) @ ((c% @ V4) @ (V2 @ V3))))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V2 @ V3)) @ (V1 @ V3))))))))))))))))
(TLINEAR_INDEPENDENT_EXTEND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cindependent @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (clinear @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V2 @ V3)) @ (V1 @ V3))))))))))))))
(TCAUCHY_CONTINUOUS_EXTENDS_TO_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccauchy @ V2)) @ (c! @ (^[V3]: ((cIN @ (V2 @ V3)) @ V0))))) @ (ccauchy @ ((co @ V1) @ V2)))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((ccontinuous_on @ V2) @ (cclosure @ V0))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V2 @ V3)) @ (V1 @ V3))))))))))))))
(TINTEGRAL_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((c= @ ((cintegral @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))))))))
(THAS_INTEGRAL_NEGLIGIBLE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV))))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ (V1 @ V2)) @ V3)))))))) @ ((c= @ (((chas_integral @ V1) @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ (cnegligible @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ (V1 @ V3)) @ (cvec @ (cNUMERAL @ c_0)))))) @ V3)))))))))))))
(TCOMPACT_CONTINUOUS_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))) @ ((c= @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V2)) @ ((cSUBSET @ V2) @ V0))) @ (ccompact @ ((cIMAGE @ V1) @ V2))))))))))))
(TINTEGRAL_RESTRICT_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cintegral @ cUNIV) @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V0)) @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((cintegral @ V0) @ V1)))))))
(Tmeasurable_on,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmeasurable_on @ V1) @ V0)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (cnegligible @ V2)) @ ((c/__caret__ @ (c! @ (^[V4]: ((ccontinuous_on @ (V3 @ V4)) @ cUNIV)))) @ (c! @ (^[V4]: ((c==> @ (c~ @ ((cIN @ V4) @ V2))) @ (((c--> @ (^[V5]: ((V3 @ V5) @ V4))) @ (((cCOND @ ((cIN @ V4) @ V0)) @ (V1 @ V4)) @ (cvec @ (cNUMERAL @ c_0)))) @ csequentially))))))))))))))))
(TINTEGRABLE_ALT_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cintegrable_on @ V1) @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((cintegrable_on @ (^[V4]: (((cCOND @ ((cIN @ V4) @ V0)) @ (V1 @ V4)) @ (cvec @ (cNUMERAL @ c_0))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V3))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V7)) @ cNIL))))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))) @ (^[V8]: (((cCOND @ ((cIN @ V8) @ V0)) @ (V1 @ V8)) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V7)) @ cNIL))) @ (^[V8]: (((cCOND @ ((cIN @ V8) @ V0)) @ (V1 @ V8)) @ (cvec @ (cNUMERAL @ c_0)))))))) @ V2)))))))))))))))))))))))
(TINTEGRABLE_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cintegrable_on @ V1) @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((cintegrable_on @ (^[V4]: (((cCOND @ ((cIN @ V4) @ V0)) @ (V1 @ V4)) @ (cvec @ (cNUMERAL @ c_0))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V3))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V3))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V7)) @ cNIL))))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))) @ (^[V8]: (((cCOND @ ((cIN @ V8) @ V0)) @ (V1 @ V8)) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V6) @ V7)) @ cNIL))) @ (^[V8]: (((cCOND @ ((cIN @ V8) @ V0)) @ (V1 @ V8)) @ (cvec @ (cNUMERAL @ c_0)))))))) @ V2)))))))))))))))))))))))
(TCONTINUOUS_ON_CLOSURE_SEQUENTIALLY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous_on @ V1) @ (cclosure @ V0))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosure @ V0))) @ ((c/__caret__ @ (c! @ (^[V4]: ((cIN @ (V2 @ V4)) @ V0)))) @ (((c--> @ V2) @ V3) @ csequentially)))) @ (((c--> @ ((co @ V1) @ V2)) @ (V1 @ V3)) @ csequentially))))))))))))
(TCONTINUOUS_ON_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous_on @ V1) @ (cclosure @ V0))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ (cclosure @ V0))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V5) @ V2))) @ V4))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V1 @ V5)) @ (V1 @ V2)))) @ V3))))))))))))))))))
(TCONTINUOUS_ON_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V1) @ V0))) @ V2)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4)))))))))))))))
(TCONTINUOUS_ON_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V1) @ V0))) @ V2)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4)))))))))))))))
(TCONTINUOUS_OPEN_IN_PREIMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ (copen @ V2)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4)))))))))))))))
(TCONTINUOUS_CLOSED_IN_PREIMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ (cclosed @ V2)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4)))))))))))))))
(TMEASURABLE_ON_MEASURABLE_PREIMAGE_OPEN_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V0)) @ (cmeasurable @ V0))) @ (c! @ (^[V2]: ((c==> @ (copen @ V2)) @ (cmeasurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4)))))))))))))))
(TMEASURABLE_ON_MEASURABLE_PREIMAGE_CLOSED_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V0)) @ (cmeasurable @ V0))) @ (c! @ (^[V2]: ((c==> @ (cclosed @ V2)) @ (cmeasurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4)))))))))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_PREIMAGE_OPEN_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V0)) @ (clebesgue_measurable @ V0))) @ (c! @ (^[V2]: ((c==> @ (copen @ V2)) @ (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4)))))))))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_PREIMAGE_CLOSED_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V0)) @ (clebesgue_measurable @ V0))) @ (c! @ (^[V2]: ((c==> @ (cclosed @ V2)) @ (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4)))))))))))))))
(TABSOLUTELY_INTEGRABLE_APPROXIMATE_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ ((cabsolutely_integrable_on @ V1) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cabsolutely_integrable_on @ V3) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ cUNIV)) @ ((c/__caret__ @ (cbounded @ ((cIMAGE @ V3) @ cUNIV))) @ ((creal_lt @ (cvector_norm @ ((cintegral @ V0) @ (^[V4]: (clift @ (cvector_norm @ ((cvector_sub @ (V1 @ V4)) @ (V3 @ V4)))))))) @ V2))))))))))))))
(TINTEGRAL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cintegrable_on @ V1) @ V0)) @ ((c= @ ((c$ @ ((cintegral @ V0) @ V1)) @ V2)) @ (cdrop @ ((cintegral @ V0) @ (^[V3]: (clift @ ((c$ @ (V1 @ V3)) @ V2))))))))))))))
(TLIFT_INTEGRAL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cintegrable_on @ V1) @ V0)) @ ((c= @ (clift @ ((c$ @ ((cintegral @ V0) @ V1)) @ V2))) @ ((cintegral @ V0) @ (^[V3]: (clift @ ((c$ @ (V1 @ V3)) @ V2)))))))))))))
(TINTEGRAL_COMPONENT_POS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((cintegrable_on @ V1) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ (V1 @ V3)) @ V2))))))))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ ((cintegral @ V0) @ V1)) @ V2))))))))))
(TUNIFORMLY_CONTINUOUS_IMP_CAUCHY_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cuniformly_continuous_on @ V1) @ V0)) @ ((c==> @ ((c/__caret__ @ (ccauchy @ V2)) @ (c! @ (^[V3]: ((cIN @ (V2 @ V3)) @ V0))))) @ (ccauchy @ ((co @ V1) @ V2)))))))))))
(TCONTINUOUS_CLOSED_IMP_CAUCHY_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (cclosed @ V0))) @ ((c==> @ ((c/__caret__ @ (ccauchy @ V2)) @ (c! @ (^[V3]: ((cIN @ (V2 @ V3)) @ V0))))) @ (ccauchy @ ((co @ V1) @ V2)))))))))))
(TPROPER_MAP_FROM_COMPOSITION_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ V0)) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V3)) @ V2)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V6) @ V2)) @ (ccompact @ V6))) @ (ccompact @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V0)) @ ((cIN @ (((co @ V4) @ V1) @ V8)) @ V6))) @ V8)))))))))))))) @ ((c==> @ ((c/__caret__ @ ((cSUBSET @ V5) @ V2)) @ (ccompact @ V5))) @ (ccompact @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V3)) @ ((cIN @ (V4 @ V7)) @ V5))) @ V7)))))))))))))))))))))
(THAS_DERIVATIVE_INVERSE_DIEUDONNE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (copen @ ((cIMAGE @ V4) @ V0))) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ ((cIMAGE @ V4) @ V0))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((c= @ (V2 @ (V4 @ V6))) @ V6))))))))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ (((chas_derivative @ V4) @ V1) @ (cat @ V5))) @ ((c/__caret__ @ (clinear @ V3)) @ ((c= @ ((co @ V3) @ V1)) @ cI))))) @ (((chas_derivative @ V2) @ V3) @ (cat @ (V4 @ V5))))))))))))))))))
(THAS_DERIVATIVE_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ ((cIN @ (V4 @ V5)) @ (cinterior @ ((cIMAGE @ V4) @ V0)))) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((c= @ (V2 @ (V4 @ V6))) @ V6))))) @ ((c/__caret__ @ (((chas_derivative @ V4) @ V1) @ (cat @ V5))) @ ((c/__caret__ @ (clinear @ V3)) @ ((c= @ ((co @ V3) @ V1)) @ cI))))))))) @ (((chas_derivative @ V2) @ V3) @ (cat @ (V4 @ V5)))))))))))))))))
(TCONTINUOUS_ON_INVERSE_OPEN_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ V0)) @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ (V1 @ V4))) @ V4))))) @ (c! @ (^[V4]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V3)) @ ((cIMAGE @ V1) @ V4))))))))) @ ((ccontinuous_on @ V2) @ V3)))))))))))
(TCONTINUOUS_ON_INVERSE_CLOSED_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ V0)) @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ (V1 @ V4))) @ V4))))) @ (c! @ (^[V4]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V3)) @ ((cIMAGE @ V1) @ V4))))))))) @ ((ccontinuous_on @ V2) @ V3)))))))))))
(TQUASICOMPACT_OPEN_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V2)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V2)) @ ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ V3))) @ V5))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V2)) @ ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ V3))) @ V5))))))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3))))))))))))))
(TQUOTIENT_MAP_OPEN_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V2)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V2)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ V3))) @ V5))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3)))))) @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V2)) @ ((c= @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ V3))) @ V5))))))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3))))))))))))))
(TMEASURABLE_MEASURABLE_PREIMAGE_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V0)) @ ((c/__caret__ @ (cmeasurable @ V0)) @ (copen @ V2)))) @ (cmeasurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TMEASURABLE_MEASURABLE_PREIMAGE_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V0)) @ ((c/__caret__ @ (cmeasurable @ V0)) @ (cclosed @ V2)))) @ (cmeasurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TLEBESGUE_MEASURABLE_LEBESGUE_MEASURABLE_PREIMAGE_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V0)) @ ((c/__caret__ @ (clebesgue_measurable @ V0)) @ (copen @ V2)))) @ (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TLEBESGUE_MEASURABLE_LEBESGUE_MEASURABLE_PREIMAGE_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V0)) @ ((c/__caret__ @ (clebesgue_measurable @ V0)) @ (cclosed @ V2)))) @ (clebesgue_measurable @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TCONTINUOUS_ON_IMP_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V1) @ V0))) @ V2))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TCONTINUOUS_ON_IMP_CLOSED_IN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cIMAGE @ V1) @ V0))) @ V2))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TCONTINUOUS_OPEN_PREIMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ (copen @ V0)) @ (copen @ V2)))) @ (copen @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TCONTINUOUS_CLOSED_PREIMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ (cclosed @ V0)) @ (cclosed @ V2)))) @ (cclosed @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(THOMEOMORPHISM_FROM_COMPOSITION_INJECTIVE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V2)) @ V3)) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ ((c= @ (V4 @ V5)) @ (V4 @ V6))))) @ ((c= @ V5) @ V6))))))) @ (c? @ (^[V5]: ((chomeomorphism @ ((c__comma__ @ V0) @ V3)) @ ((c__comma__ @ ((co @ V4) @ V1)) @ V5)))))))))) @ (c? @ (^[V5]: ((chomeomorphism @ ((c__comma__ @ V2) @ V3)) @ ((c__comma__ @ V4) @ V5))))))))))))))))
(THOMEOMORPHISM_FROM_COMPOSITION_SURJECTIVE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ V0)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V2)) @ V3)) @ (c? @ (^[V5]: ((chomeomorphism @ ((c__comma__ @ V0) @ V3)) @ ((c__comma__ @ ((co @ V4) @ V1)) @ V5))))))))) @ (c? @ (^[V5]: ((chomeomorphism @ ((c__comma__ @ V2) @ V3)) @ ((c__comma__ @ V4) @ V5))))))))))))))))
(TOPEN_MAP_FROM_COMPOSITION_SURJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ V0)) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V2)) @ V3)) @ (c! @ (^[V6]: ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V6)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V3)) @ ((cIMAGE @ ((co @ V4) @ V1)) @ V6))))))))) @ ((c==> @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V5)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V3)) @ ((cIMAGE @ V4) @ V5)))))))))))))))))
(TCLOSED_MAP_FROM_COMPOSITION_SURJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ V0)) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V2)) @ V3)) @ (c! @ (^[V6]: ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V6)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V3)) @ ((cIMAGE @ ((co @ V4) @ V1)) @ V6))))))))) @ ((c==> @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V5)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V3)) @ ((cIMAGE @ V4) @ V5)))))))))))))))))
(TQUOTIENT_MAP_FROM_COMPOSITION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V2)) @ V4)) @ (c! @ (^[V6]: ((c==> @ ((cSUBSET @ V6) @ V4)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V0)) @ ((cIN @ (((co @ V3) @ V1) @ V8)) @ V6))) @ V8))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V4)) @ V6)))))))))) @ ((c==> @ ((cSUBSET @ V5) @ V4)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V2)) @ ((cIN @ (V3 @ V7)) @ V5))) @ V7))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V4)) @ V5)))))))))))))))))
(TCOVERING_SPACE_QUOTIENT_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((ccovering_space @ ((c__comma__ @ V0) @ V1)) @ V2)) @ ((c==> @ ((cSUBSET @ V3) @ V2)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ V3))) @ V5))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3)))))))))))))
(TCONTINUOUS_IMP_QUOTIENT_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ V0)) @ V2)) @ (ccompact @ V0)))) @ ((c==> @ ((cSUBSET @ V3) @ V2)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ V3))) @ V5))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3)))))))))))))
(THAS_INTEGRAL_NORM_BOUND_INTEGRAL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (((chas_integral @ V1) @ V3) @ V0)) @ ((c/__caret__ @ (((chas_integral @ V2) @ V4) @ V0)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((creal_le @ (cvector_norm @ (V1 @ V6))) @ ((c$ @ (V2 @ V6)) @ V5)))))))))) @ ((creal_le @ (cvector_norm @ V3)) @ ((c$ @ V4) @ V5))))))))))))))))
(THAS_DERIVATIVE_TRANSFORM_WITHIN_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))) @ (((chas_derivative @ V1) @ V3) @ (cat @ V4)))))) @ (((chas_derivative @ V2) @ V3) @ (cat @ V4))))))))))))))
(TMEASURABLE_ON_SPIKE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cmeasurable_on @ V1) @ V3)) @ ((c==> @ ((c/__caret__ @ (cnegligible @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ V3) @ V0))) @ ((c= @ (V2 @ V4)) @ (V1 @ V4))))))) @ ((cmeasurable_on @ V2) @ V3))))))))))))
(TINTEGRABLE_SPIKE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cintegrable_on @ V1) @ V3)) @ ((c==> @ ((c/__caret__ @ (cnegligible @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ V3) @ V0))) @ ((c= @ (V2 @ V4)) @ (V1 @ V4))))))) @ ((cintegrable_on @ V2) @ V3))))))))))))
(TINTEGRABLE_SPIKE_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cintegrable_on @ V1) @ V3)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ V3) @ V0))) @ ((c= @ (V2 @ V4)) @ (V1 @ V4))))))) @ ((cintegrable_on @ V2) @ V3))))))))))))
(TMEASURABLE_ON_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (clebesgue_measurable @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ (V0 @ V5)) @ V5))))))) @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V3)) @ ((cmeasurable_on @ V2) @ V3)))) @ ((cmeasurable_on @ (^[V4]: (((cCOND @ (V0 @ V4)) @ (V1 @ V4)) @ (V2 @ V4)))) @ V3)))))))))))
(TCONTINUOUS_ON_CASES_LOCAL_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V3) @ V4))) @ V3)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V3) @ V4))) @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c__caret__/ @ ((c/__caret__ @ ((cIN @ V5) @ V3)) @ (c~ @ (V0 @ V5)))) @ ((c/__caret__ @ ((cIN @ V5) @ V4)) @ (V0 @ V5)))) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))))))) @ ((ccontinuous_on @ (^[V5]: (((cCOND @ (V0 @ V5)) @ (V1 @ V5)) @ (V2 @ V5)))) @ ((cUNION @ V3) @ V4))))))))))))))
(TCONTINUOUS_ON_CASES_LOCAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V3) @ V4))) @ V3)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cUNION @ V3) @ V4))) @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c__caret__/ @ ((c/__caret__ @ ((cIN @ V5) @ V3)) @ (c~ @ (V0 @ V5)))) @ ((c/__caret__ @ ((cIN @ V5) @ V4)) @ (V0 @ V5)))) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))))))) @ ((ccontinuous_on @ (^[V5]: (((cCOND @ (V0 @ V5)) @ (V1 @ V5)) @ (V2 @ V5)))) @ ((cUNION @ V3) @ V4))))))))))))))
(TCONTINUOUS_ON_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cclosed @ V3)) @ ((c/__caret__ @ (cclosed @ V4)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c__caret__/ @ ((c/__caret__ @ ((cIN @ V5) @ V3)) @ (c~ @ (V0 @ V5)))) @ ((c/__caret__ @ ((cIN @ V5) @ V4)) @ (V0 @ V5)))) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))))))) @ ((ccontinuous_on @ (^[V5]: (((cCOND @ (V0 @ V5)) @ (V1 @ V5)) @ (V2 @ V5)))) @ ((cUNION @ V3) @ V4))))))))))))))
(THAS_INTEGRAL_SPIKE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cnegligible @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ ((cDIFF @ V4) @ V0))) @ ((c= @ (V2 @ V5)) @ (V1 @ V5)))))) @ (((chas_integral @ V1) @ V3) @ V4)))) @ (((chas_integral @ V2) @ V3) @ V4)))))))))))))
(THAS_INTEGRAL_SPIKE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cnegligible @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ ((cDIFF @ V4) @ V0))) @ ((c= @ (V2 @ V5)) @ (V1 @ V5))))))) @ ((c= @ (((chas_integral @ V1) @ V3) @ V4)) @ (((chas_integral @ V2) @ V3) @ V4))))))))))))))
(THAS_INTEGRAL_SPIKE_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ ((cDIFF @ V4) @ V0))) @ ((c= @ (V2 @ V5)) @ (V1 @ V5)))))) @ (((chas_integral @ V1) @ V3) @ V4)))) @ (((chas_integral @ V2) @ V3) @ V4)))))))))))))
(THAS_INTEGRAL_SPIKE_FINITE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ ((cDIFF @ V4) @ V0))) @ ((c= @ (V2 @ V5)) @ (V1 @ V5))))))) @ ((c= @ (((chas_integral @ V1) @ V3) @ V4)) @ (((chas_integral @ V2) @ V3) @ V4))))))))))))))
(THAS_INTEGRAL_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (((chas_integral @ V1) @ V3) @ V0)) @ ((c/__caret__ @ (((chas_integral @ V2) @ V4) @ V0)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((creal_le @ ((c$ @ (V1 @ V6)) @ V5)) @ ((c$ @ (V2 @ V6)) @ V5)))))))))) @ ((creal_le @ ((c$ @ V3) @ V5)) @ ((c$ @ V4) @ V5))))))))))))))))
(TLIM_TRANSFORM_WITHIN_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ (c~ @ ((c= @ V5) @ V4)))) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))) @ (((c--> @ V1) @ V3) @ (cat @ V4)))))) @ (((c--> @ V2) @ V3) @ (cat @ V4))))))))))))))
(TLIM_TRANSFORM_WITHIN_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V5)) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ (c~ @ ((c= @ V6) @ V4)))) @ ((c= @ (V1 @ V6)) @ (V2 @ V6)))))) @ (((c--> @ V1) @ V3) @ ((cwithin @ (cat @ V4)) @ V5)))))) @ (((c--> @ V2) @ V3) @ ((cwithin @ (cat @ V4)) @ V5))))))))))))))))
(TCONTINUOUS_AGREE_ON_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ (cclosure @ V0))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ (cclosure @ V0))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V4)) @ (V2 @ V4)))))))) @ ((c==> @ ((cIN @ V3) @ (cclosure @ V0))) @ ((c= @ (V1 @ V3)) @ (V2 @ V3)))))))))))))
(TCONTINUOUS_TRANSFORM_WITHIN_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V4)) @ (V2 @ V4)))))) @ ((ccontinuous @ V1) @ (cat @ V3)))))) @ ((ccontinuous @ V2) @ (cat @ V3))))))))))))
(THAS_DERIVATIVE_WITHIN_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((chas_derivative @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ V0))) @ ((c/__caret__ @ (clinear @ V2)) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V6) @ V3))) @ V5))) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ ((cvector_sub @ (V1 @ V6)) @ (V1 @ V3))) @ (V2 @ ((cvector_sub @ V6) @ V3))))) @ ((creal_mul @ V4) @ (cvector_norm @ ((cvector_sub @ V6) @ V3))))))))))))))))))))))))
(TCONTINUOUS_TRANSFORM_WITHIN_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V4)) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))) @ ((ccontinuous @ V1) @ ((cwithin @ (cat @ V3)) @ V4)))))) @ ((ccontinuous @ V2) @ ((cwithin @ (cat @ V3)) @ V4))))))))))))))
(TMEASURABLE_ON_SPIKE_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cmeasurable_on @ V1) @ V0)) @ ((c==> @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V2)) @ ((cDIFF @ V2) @ V0)))) @ ((cmeasurable_on @ V1) @ V2))))))))))
(TINTEGRABLE_SPIKE_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cintegrable_on @ V1) @ V0)) @ ((c==> @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V2)) @ ((cDIFF @ V2) @ V0)))) @ ((cintegrable_on @ V1) @ V2))))))))))
(TINTEGRABLE_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V2) @ V0)) @ ((c= @ ((cintegrable_on @ (^[V3]: (((cCOND @ ((cIN @ V3) @ V2)) @ (V1 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))) @ V0)) @ ((cintegrable_on @ V1) @ V2))))))))))
(TDIFFERENTIABLE_ON_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdifferentiable_on @ V1) @ V0)) @ ((cSUBSET @ V2) @ V0))) @ ((cdifferentiable_on @ V1) @ V2)))))))))
(TLEBESGUE_MEASURABLE_CONTINUOUS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnegligible @ V3)) @ ((cSUBSET @ V3) @ V0))) @ (cnegligible @ ((cIMAGE @ V1) @ V3))))))) @ ((c==> @ ((c/__caret__ @ (clebesgue_measurable @ V2)) @ ((cSUBSET @ V2) @ V0))) @ (clebesgue_measurable @ ((cIMAGE @ V1) @ V2)))))))))))
(THAS_INTEGRAL_NEGLIGIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cnegligible @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cDIFF @ V2) @ V0))) @ ((c= @ (V1 @ V3)) @ (cvec @ (cNUMERAL @ c_0)))))))) @ (((chas_integral @ V1) @ (cvec @ (cNUMERAL @ c_0))) @ V2)))))))))
(TRETRACT_OF_INJECTIVE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V1 @ V3)) @ (V1 @ V4))) @ ((c= @ V3) @ V4))))))) @ ((cretract_of @ V0) @ V2)))) @ ((cretract_of @ ((cIMAGE @ V1) @ V0)) @ ((cIMAGE @ V1) @ V2))))))))))
(TCLOSED_INJECTIVE_IMAGE_SUBSET_SUBSPACE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cclosed @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ (csubspace @ V0)) @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V3) @ (cvec @ (cNUMERAL @ c_0))))))))))) @ (cclosed @ ((cIMAGE @ V1) @ V2))))))))))
(TINTEGRABLE_SPIKE_SET_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V2)) @ ((cDIFF @ V2) @ V0)))) @ ((c= @ ((cintegrable_on @ V1) @ V0)) @ ((cintegrable_on @ V1) @ V2))))))))))
(TTIETZE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ (cvector_norm @ (V1 @ V4))) @ V3)))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ V2)) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((c= @ (V4 @ V5)) @ (V1 @ V5)))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((creal_le @ (cvector_norm @ (V4 @ V5))) @ V3))))))))))))))))))
(TINTEGRAL_SPIKE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnegligible @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cDIFF @ V2) @ V0))) @ ((c= @ (V3 @ V4)) @ (V1 @ V4))))))) @ ((c= @ ((cintegral @ V2) @ V1)) @ ((cintegral @ V2) @ V3))))))))))))
(TTIETZE_OPEN_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (copen_interval @ ((c__comma__ @ V3) @ V4))) @ cEMPTY))) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ (copen_interval @ ((c__comma__ @ V3) @ V4)))))))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ V2)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((c= @ (V5 @ V6)) @ (V1 @ V6)))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((cIN @ (V5 @ V6)) @ (copen_interval @ ((c__comma__ @ V3) @ V4))))))))))))))))))))))
(TTIETZE_CLOSED_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ cEMPTY))) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((cIN @ (V1 @ V5)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ V2)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((c= @ (V5 @ V6)) @ (V1 @ V6)))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((cIN @ (V5 @ V6)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))))))))))))))
(TCONTINUOUS_CLOSED_IN_PREIMAGE_CONSTANT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous_on @ V1) @ V0)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TCONTINUOUS_CLOSED_PREIMAGE_CONSTANT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (cclosed @ V0))) @ (cclosed @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TCONTINUOUS_LEVELSET_OPEN_IN_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V4)) @ V2))) @ V4))))))))) @ ((c__caret__/ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ (V1 @ V3)) @ V2)))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2)))))))))))))
(THAS_INTEGRAL_INTEGRABLE_INTEGRAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_integral @ V1) @ V2) @ V0)) @ ((c/__caret__ @ ((cintegrable_on @ V1) @ V0)) @ ((c= @ ((cintegral @ V0) @ V1)) @ V2))))))))))
(THAS_INTEGRAL_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_integral @ V1) @ V2) @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((cintegrable_on @ (^[V5]: (((cCOND @ ((cIN @ V5) @ V0)) @ (V1 @ V5)) @ (cvec @ (cNUMERAL @ c_0))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V4))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL))) @ (^[V7]: (((cCOND @ ((cIN @ V7) @ V0)) @ (V1 @ V7)) @ (cvec @ (cNUMERAL @ c_0)))))) @ V2))) @ V3)))))))))))))))))))))
(THAS_INTEGRAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_integral @ V1) @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V4))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL)))) @ (c? @ (^[V7]: ((c/__caret__ @ (((chas_integral @ (^[V8]: (((cCOND @ ((cIN @ V8) @ V0)) @ (V1 @ V8)) @ (cvec @ (cNUMERAL @ c_0))))) @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V7) @ V2))) @ V3)))))))))))))))))))))))
(THAS_INTEGRAL_COMPONENT_NEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (((chas_integral @ V1) @ V2) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ ((c$ @ (V1 @ V4)) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))) @ ((creal_le @ ((c$ @ V2) @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))
(THAS_INTEGRAL_COMPONENT_POS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (((chas_integral @ V1) @ V2) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ (V1 @ V4)) @ V3))))))))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V2) @ V3))))))))))))
(THAS_INTEGRAL_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V0)) @ ((c= @ (((chas_integral @ (^[V4]: (((cCOND @ ((cIN @ V4) @ V3)) @ (V1 @ V4)) @ (cvec @ (cNUMERAL @ c_0))))) @ V2) @ V0)) @ (((chas_integral @ V1) @ V2) @ V3))))))))))))
(THAS_INTEGRAL_SPIKE_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V3)) @ ((cDIFF @ V3) @ V0)))) @ (((chas_integral @ V1) @ V2) @ V0))) @ (((chas_integral @ V1) @ V2) @ V3)))))))))))
(THAS_INTEGRAL_SPIKE_SET_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V3)) @ ((cDIFF @ V3) @ V0)))) @ ((c= @ (((chas_integral @ V1) @ V2) @ V0)) @ (((chas_integral @ V1) @ V2) @ V3))))))))))))
(TCONTINUOUS_ON_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((cIN @ V2) @ (cinterior @ V0)))) @ ((ccontinuous @ V1) @ (cat @ V2))))))))))
(TLINEAR_INDEP_IMAGE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cindependent @ ((cIMAGE @ V1) @ V0))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V3)) @ (V1 @ V4))))) @ ((c= @ V3) @ V4)))))))))) @ ((c==> @ ((cIN @ V2) @ (cspan @ V0))) @ ((c==> @ ((c= @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0)))))))))))))
(TLINEAR_EQ_0_SPAN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ (cvec @ (cNUMERAL @ c_0)))))))) @ ((c==> @ ((cIN @ V2) @ (cspan @ V0))) @ ((c= @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))))))))))
(TFORALL_IN_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cclosed @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ (cclosure @ V0))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V3))))))) @ ((c==> @ ((cIN @ V2) @ (cclosure @ V0))) @ ((cIN @ (V1 @ V2)) @ V3))))))))))))
(TDIFFERENTIABLE_WITHIN_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ V1) @ ((cwithin @ (cat @ V2)) @ V0))) @ ((cSUBSET @ V3) @ V0))) @ ((cdifferentiable @ V1) @ ((cwithin @ (cat @ V2)) @ V3))))))))))))
(TCONTINUOUS_CONSTANT_ON_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ (cclosure @ V0))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V4)) @ V3)))))) @ ((c==> @ ((cIN @ V2) @ (cclosure @ V0))) @ ((c= @ (V1 @ V2)) @ V3))))))))))))
(TCONTINUOUS_LEVELSET_OPEN_IN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c= @ (V1 @ V5)) @ V3))) @ V5))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V4)) @ V3)))))))) @ ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V3))))))))))))
(TCONTINUOUS_LEVELSET_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ ((c/__caret__ @ (copen @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c= @ (V1 @ V5)) @ V3))) @ V5))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V4)) @ V3)))))))) @ ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V3))))))))))))
(TINTEGRABLE_ON_SUBINTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V1) @ V0)) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V0))) @ ((cintegrable_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(TABSOLUTELY_INTEGRABLE_ON_SUBINTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cabsolutely_integrable_on @ V1) @ V0)) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V0))) @ ((cabsolutely_integrable_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(TLIM_WITHIN_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (copen @ V0))) @ ((c= @ (((c--> @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ V0))) @ (((c--> @ V1) @ V2) @ (cat @ V3)))))))))))))
(TSET_VARIATION_MONOTONE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V2) @ V1)) @ ((cSUBSET @ V0) @ V1))) @ ((creal_le @ ((cset_variation @ V0) @ V2)) @ ((cset_variation @ V1) @ V2))))))))))
(TABSOLUTE_RETRACT_IMP_AR_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V1) @ V0)) @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ ((chomeomorphic @ V1) @ V2)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V3)) @ V2)))))) @ ((cretract_of @ V2) @ V3)))))))))))
(THAUSDIST_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c= @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V5) @ cEMPTY)) @ V1))) @ V4))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V5) @ cEMPTY)) @ V0))) @ V4)))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V5) @ cEMPTY)) @ V3))) @ V4))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V5) @ cEMPTY)) @ V2))) @ V4))))))))) @ ((c= @ (chausdist @ ((c__comma__ @ V0) @ V1))) @ (chausdist @ ((c__comma__ @ V2) @ V3)))))))))))))
(TRETRACT_OF_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cretract_of @ ((cPCROSS @ V0) @ V2)) @ ((cPCROSS @ V1) @ V3))) @ ((c__caret__/ @ ((c/__caret__ @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c= @ V2) @ cEMPTY))) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c= @ V3) @ cEMPTY)))) @ ((c/__caret__ @ ((cretract_of @ V0) @ V1)) @ ((cretract_of @ V2) @ V3)))))))))))))
(TOPEN_IN_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cPCROSS @ V0) @ V2))) @ ((cPCROSS @ V1) @ V3))) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V3) @ cEMPTY)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3))))))))))))))
(TFACE_OF_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cface_of @ ((cPCROSS @ V0) @ V2)) @ ((cPCROSS @ V1) @ V3))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V2) @ cEMPTY)) @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ ((cface_of @ V2) @ V3))))))))))))))
(TCLOSED_IN_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ ((cPCROSS @ V0) @ V2))) @ ((cPCROSS @ V1) @ V3))) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V3) @ cEMPTY)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V3))))))))))))))
(TPCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cPCROSS @ V0) @ V2)) @ ((cPCROSS @ V1) @ V3))) @ ((c__caret__/ @ ((c/__caret__ @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c= @ V2) @ cEMPTY))) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c= @ V3) @ cEMPTY)))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ V3)))))))))))))
(THOMOTOPIC_NEIGHBOURHOOD_EXTENSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V1)) @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V1)) @ V2)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0)) @ ((c/__caret__ @ (cANR @ V2)) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V0) @ V2)) @ V3) @ V4)))))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((cSUBSET @ V0) @ V5)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ V5)) @ ((((chomotopic_with @ (^[V6]: cT)) @ ((c__comma__ @ V5) @ V2)) @ V3) @ V4)))))))))))))))))
(TINTEGRAL_SUBSET_DROP_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V0)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ (V2 @ V3)))))))))) @ ((creal_le @ (cdrop @ ((cintegral @ V0) @ V2))) @ (cdrop @ ((cintegral @ V1) @ V2)))))))))))
(THAS_INTEGRAL_SUBSET_DROP_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c/__caret__ @ (((chas_integral @ V2) @ V3) @ V0)) @ ((c/__caret__ @ (((chas_integral @ V2) @ V4) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ (V2 @ V5)))))))))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))))))))))))))
(TINTEGRAL_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V1) @ V0)) @ ((c= @ ((cintegral @ V0) @ (^[V3]: (((cCOND @ ((cIN @ V3) @ V1)) @ (V2 @ V3)) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((cintegral @ V1) @ V2))))))))))
(TINTEGRAL_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V0)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (cnegligible @ ((cINTER @ V0) @ V1))))) @ ((c= @ ((cintegral @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cvector_add @ ((cintegral @ V0) @ V2)) @ ((cintegral @ V1) @ V2)))))))))))
(TINTEGRAL_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V0)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ (cnegligible @ ((cDIFF @ V1) @ V0))))) @ ((c= @ ((cintegral @ ((cDIFF @ V0) @ V1)) @ V2)) @ ((cvector_sub @ ((cintegral @ V0) @ V2)) @ ((cintegral @ V1) @ V2)))))))))))
(TTIETZE_UNBOUNDED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V1)) @ ((ccontinuous_on @ V2) @ V1))) @ (c? @ (^[V3]: ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V3 @ V4)) @ (V2 @ V4))))))))))))))))
(TINTEGRAL_SPIKE_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cnegligible @ ((cUNION @ ((cDIFF @ V0) @ V1)) @ ((cDIFF @ V1) @ V0)))) @ ((c= @ ((cintegral @ V0) @ V2)) @ ((cintegral @ V1) @ V2))))))))))
(TINTEGRAL_RESTRICT_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cintegral @ V1) @ (^[V3]: (((cCOND @ ((cIN @ V3) @ V0)) @ (V2 @ V3)) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((cintegral @ ((cINTER @ V0) @ V1)) @ V2)))))))))
(TINTEGRAL_SUBSET_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V0)) @ ((c/__caret__ @ ((cintegrable_on @ V2) @ V1)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ (V2 @ V4)) @ V3))))))))))) @ ((creal_le @ ((c$ @ ((cintegral @ V0) @ V2)) @ V3)) @ ((c$ @ ((cintegral @ V1) @ V2)) @ V3))))))))))))
(TQUOTIENT_MAP_FROM_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V3)) @ (c! @ (^[V5]: ((c==> @ ((cSUBSET @ V5) @ V3)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V0)) @ ((cIN @ (V2 @ V7)) @ V5))) @ V7))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V3)) @ V5)))))))))) @ ((c==> @ ((cSUBSET @ V4) @ V3)) @ ((c= @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cIN @ (V2 @ V6)) @ V4))) @ V6))))))) @ ((copen_in @ ((csubtopology @ ceuclidean) @ V3)) @ V4)))))))))))))))
(THAS_INTEGRAL_SUBSET_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c/__caret__ @ (((chas_integral @ V2) @ V3) @ V0)) @ ((c/__caret__ @ (((chas_integral @ V2) @ V4) @ V1)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ (cdimindex @ cUNIV))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ (V2 @ V6)) @ V5))))))))))) @ ((creal_le @ ((c$ @ V3) @ V5)) @ ((c$ @ V4) @ V5))))))))))))))))
(THOMEOMORPHIC_PCROSS_SING_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((chomeomorphic @ V0) @ ((cPCROSS @ ((cINSERT @ V1) @ cEMPTY)) @ V0)))))))
(THOMEOMORPHIC_PCROSS_SING_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((chomeomorphic @ V0) @ ((cPCROSS @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))
(THOMOTOPIC_NON_MIDPOINT_SPHEREMAPS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V3) @ V0)) @ (csphere @ ((c__comma__ @ V1) @ V2)))) @ ((c/__caret__ @ ((ccontinuous_on @ V4) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ V0)) @ (csphere @ ((c__comma__ @ V1) @ V2)))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ (c~ @ ((c= @ (cmidpoint @ ((c__comma__ @ (V3 @ V5)) @ (V4 @ V5)))) @ V1)))))))))) @ ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V0) @ (csphere @ ((c__comma__ @ V1) @ V2)))) @ V3) @ V4)))))))))))))
(TCOVERING_SPACE_LOCAL_HOMEOMORPHISM_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((ccovering_space @ ((c__comma__ @ V0) @ V3)) @ V2)) @ ((c==> @ ((cIN @ V1) @ V2)) @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((c= @ (V3 @ V4)) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V5)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((c/__caret__ @ ((cIN @ V1) @ V6)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V6)) @ (c? @ (^[V7]: ((chomeomorphism @ ((c__comma__ @ V5) @ V6)) @ ((c__comma__ @ V3) @ V7))))))))))))))))))))))))))
(TMAPPING_CONNECTED_ONTO_SEGMENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconnected @ V0)) @ (c~ @ (c? @ (^[V3]: ((cSUBSET @ V0) @ ((cINSERT @ V3) @ cEMPTY))))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((ccontinuous_on @ V3) @ V0)) @ ((c= @ ((cIMAGE @ V3) @ V0)) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))))
(TCOVERING_SPACE_LOCAL_HOMEOMORPHISM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((ccovering_space @ ((c__comma__ @ V0) @ V3)) @ V2)) @ ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V1) @ V4)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V4)) @ ((c/__caret__ @ ((cIN @ (V3 @ V1)) @ V5)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V5)) @ (c? @ (^[V6]: ((chomeomorphism @ ((c__comma__ @ V4) @ V5)) @ ((c__comma__ @ V3) @ V6)))))))))))))))))))))))
(TPASTECART_IN_INTERIOR_SUBTOPOLOGY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ ((cpastecart @ V1) @ V3)) @ V4)) @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((cPCROSS @ V0) @ V2))) @ V4))) @ (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V0)) @ V5)) @ ((c/__caret__ @ ((cIN @ V1) @ V5)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V2)) @ V6)) @ ((c/__caret__ @ ((cIN @ V3) @ V6)) @ ((cSUBSET @ ((cPCROSS @ V5) @ V6)) @ V4)))))))))))))))))))))
(TDIFFERENTIAL_COMPONENT_ZERO_AT_MAXMIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (((chas_derivative @ V2) @ V3) @ (cat @ V1))) @ ((c__caret__/ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((creal_le @ ((c$ @ (V2 @ V6)) @ V5)) @ ((c$ @ (V2 @ V1)) @ V5)))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V0)) @ ((creal_le @ ((c$ @ (V2 @ V1)) @ V5)) @ ((c$ @ (V2 @ V6)) @ V5)))))))))))) @ ((c= @ ((c$ @ (V3 @ V4)) @ V5)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))))
(TCONTINUOUS_ON_AVOID,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c~ @ ((c= @ (V2 @ V1)) @ V3))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V1) @ V5))) @ V4))) @ (c~ @ ((c= @ (V2 @ V5)) @ V3))))))))))))))))))
(TCONTINUOUS_ON_OPEN_AVOID,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c~ @ ((c= @ (V2 @ V1)) @ V3)))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((creal_lt @ (cdistance @ ((c__comma__ @ V1) @ V5))) @ V4)) @ (c~ @ ((c= @ (V2 @ V5)) @ V3))))))))))))))))))
(TCONTINUOUS_WITHIN_AVOID,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V2) @ ((cwithin @ (cat @ V1)) @ V0))) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c~ @ ((c= @ (V2 @ V1)) @ V3))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V1) @ V5))) @ V4))) @ (c~ @ ((c= @ (V2 @ V5)) @ V3))))))))))))))))))
(TLIM_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c--> @ V2) @ V3) @ ((cwithin @ (cat @ V1)) @ V0))) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdistance @ ((c__comma__ @ V6) @ V1)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V6) @ V1))) @ V5)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V2 @ V6)) @ V3))) @ V4))))))))))))))))))))
(TLIM_WITHIN_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c--> @ V2) @ V3) @ ((cwithin @ (cat @ V1)) @ V0))) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdistance @ ((c__comma__ @ V6) @ V1)))) @ ((creal_le @ (cdistance @ ((c__comma__ @ V6) @ V1))) @ V5)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V2 @ V6)) @ V3))) @ V4))))))))))))))))))))
(TEVENTUALLY_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ceventually @ V2) @ ((cwithin @ (cat @ V1)) @ V0))) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdistance @ ((c__comma__ @ V4) @ V1)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V4) @ V1))) @ V3)))) @ (V2 @ V4)))))))))))))))
(TEVENTUALLY_WITHIN_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ceventually @ V2) @ ((cwithin @ (cat @ V1)) @ V0))) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdistance @ ((c__comma__ @ V4) @ V1)))) @ ((creal_le @ (cdistance @ ((c__comma__ @ V4) @ V1))) @ V3)))) @ (V2 @ V4)))))))))))))))
(THYPERPLANE_CELL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chyperplane_cell @ V1) @ V0)) @ (c? @ (^[V2]: ((c= @ V0) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ (((chyperplane_equiv @ V1) @ V2) @ V4)) @ V4))))))))))))))
(Thyperplane_cell,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chyperplane_cell @ V1) @ V0)) @ (c? @ (^[V2]: ((c= @ V0) @ ((chyperplane_equiv @ V1) @ V2))))))))))
(TDIFFERENTIABLE_IMP_PIECEWISE_DIFFERENTIABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cdifferentiable @ V0) @ (cat @ V2)))))) @ ((cpiecewise_differentiable_on @ V0) @ V1)))))))
(TPIECEWISE_DIFFERENTIABLE_ON_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpiecewise_differentiable_on @ V1) @ V0)) @ ((cSUBSET @ V2) @ V0))) @ ((cpiecewise_differentiable_on @ V1) @ V2)))))))))
(TPIECEWISE_DIFFERENTIABLE_ON_IMP_CONTINUOUS_ON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpiecewise_differentiable_on @ V0) @ V1)) @ ((ccontinuous_on @ V0) @ V1)))))))
(Tpiecewise_differentiable_on,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpiecewise_differentiable_on @ V1) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (cFINITE @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cDIFF @ V0) @ V2))) @ ((cdifferentiable @ V1) @ (cat @ V3)))))))))))))))
(TMEASURABLE_MEASURABLE_DIFF_LEGESGUE_MEASURABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ (clebesgue_measurable @ V1))) @ (cmeasurable @ ((cDIFF @ V0) @ V1))))))))
(TMEASURABLE_ON_MEASURABLE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V0)) @ (cmeasurable @ V2)))) @ ((cmeasurable_on @ V1) @ V2)))))))))
(TMEASURABLE_ON_LEBESGUE_MEASURABLE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ ((cmeasurable_on @ V1) @ V0)) @ (clebesgue_measurable @ V2)))) @ ((cmeasurable_on @ V1) @ V2)))))))))
(TMEASURABLE_ON_LIFT_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ (^[V3]: (clift @ (V0 @ V3)))) @ V2)) @ ((cmeasurable_on @ (^[V3]: (clift @ (V1 @ V3)))) @ V2))) @ ((cmeasurable_on @ (^[V3]: (clift @ ((creal_mul @ (V0 @ V3)) @ (V1 @ V3))))) @ V2)))))))))
(TMEASURABLE_ON_0,(c! @ (^[V0]: ((cmeasurable_on @ (^[V1]: (cvec @ (cNUMERAL @ c_0)))) @ V0))))
(TMEASURABLE_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cmeasurable @ ((chull @ cconvex) @ V0))))))
(THAS_MEASURE_LINEAR_IMAGE_SAME,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (cmeasurable @ V1)) @ ((c= @ (creal_abs @ (cdet @ (cmatrix @ V0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((chas_measure @ ((cIMAGE @ V0) @ V1)) @ (cmeasure @ V1))))))))
(TMEASURABLE_LINEAR_IMAGE_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (clinear @ V0)) @ (cmeasurable @ ((cIMAGE @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))
(TINTEGRABLE_ON_OPEN_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cintegrable_on @ V0) @ (copen_interval @ ((c__comma__ @ V1) @ V2)))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(THAS_INTEGRAL_OPEN_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((chas_integral @ V0) @ V1) @ (copen_interval @ ((c__comma__ @ V2) @ V3)))) @ (((chas_integral @ V0) @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(TMEASURE_ELEMENTARY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdivision_of @ V1) @ V0)) @ ((c= @ (cmeasure @ V0)) @ ((csum @ V1) @ ccontent))))))))
(THAS_MEASURE_ELEMENTARY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdivision_of @ V1) @ V0)) @ ((chas_measure @ V0) @ ((csum @ V1) @ ccontent))))))))
(TMEASURABLE_INTERIOR,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cmeasurable @ (cinterior @ V0))))))
(TMEASURABLE_CLOSURE,(c! @ (^[V0]: ((c==> @ (cbounded @ V0)) @ (cmeasurable @ (cclosure @ V0))))))
(TMEASURE_OPEN_POS_LT,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (copen @ V0)) @ ((c/__caret__ @ (cbounded @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY))))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cmeasure @ V0))))))
(THAS_MEASURE_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_measure @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V3))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ (c? @ (^[V6]: ((c/__caret__ @ ((chas_measure @ ((cINTER @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ V6)) @ ((creal_lt @ (creal_abs @ ((creal_sub @ V6) @ V1))) @ V2)))))))))))))))))))))
(TMEASURE_NEGLIGIBLE_UNION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ (cmeasurable @ V1)) @ ((c/__caret__ @ ((c= @ ((cUNION @ V0) @ V1)) @ V2)) @ (cnegligible @ ((cINTER @ V0) @ V1)))))) @ ((c= @ ((creal_add @ (cmeasure @ V0)) @ (cmeasure @ V1))) @ (cmeasure @ V2))))))))))
(TMEASURE_NEGLIGIBLE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ (cmeasurable @ V1)) @ (cnegligible @ ((cINTER @ V0) @ V1))))) @ ((c= @ (cmeasure @ ((cUNION @ V0) @ V1))) @ ((creal_add @ (cmeasure @ V0)) @ (cmeasure @ V1)))))))))
(TMEASURABLE_ALMOST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ (cnegligible @ V1)) @ ((c= @ ((cUNION @ V0) @ V1)) @ ((cUNION @ V2) @ V1))))) @ (cmeasurable @ V2)))))))))
(THAS_MEASURE_ALMOST_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cnegligible @ V0)) @ ((c= @ ((cUNION @ V1) @ V0)) @ ((cUNION @ V2) @ V0)))) @ ((c= @ ((chas_measure @ V1) @ V3)) @ ((chas_measure @ V2) @ V3))))))))))))
(THAS_MEASURE_ALMOST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_measure @ V0) @ V3)) @ ((c/__caret__ @ (cnegligible @ V1)) @ ((c= @ ((cUNION @ V0) @ V1)) @ ((cUNION @ V2) @ V1))))) @ ((chas_measure @ V2) @ V3)))))))))))
(TMEASURE_DIFF_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ (cmeasurable @ V1)) @ ((cSUBSET @ V1) @ V0)))) @ ((c= @ (cmeasure @ ((cDIFF @ V0) @ V1))) @ ((creal_sub @ (cmeasure @ V0)) @ (cmeasure @ V1)))))))))
(THAS_MEASURE_DIFF_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_measure @ V0) @ V2)) @ ((c/__caret__ @ ((chas_measure @ V1) @ V3)) @ ((cSUBSET @ V1) @ V0)))) @ ((chas_measure @ ((cDIFF @ V0) @ V1)) @ ((creal_sub @ V2) @ V3))))))))))))
(TMEASURABLE_MEASURE_POS_LT,(c! @ (^[V0]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cmeasure @ V0))) @ (c~ @ (cnegligible @ V0)))))))
(TMEASURABLE_MEASURE_EQ_0,(c! @ (^[V0]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((c= @ (cmeasure @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (cnegligible @ V0))))))
(TMEASURE_EQ_0,(c! @ (^[V0]: ((c==> @ (cnegligible @ V0)) @ ((c= @ (cmeasure @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TMEASURE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ (cmeasurable @ V1)) @ ((cSUBSET @ V0) @ V1)))) @ ((creal_le @ (cmeasure @ V0)) @ (cmeasure @ V1))))))))
(TMEASURE_POS_LE,(c! @ (^[V0]: ((c==> @ (cmeasurable @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cmeasure @ V0))))))
(TMEASURE_DISJOINT_UNION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ (cmeasurable @ V1)) @ ((c/__caret__ @ ((c= @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cDISJOINT @ V0) @ V1))))) @ ((c= @ ((creal_add @ (cmeasure @ V0)) @ (cmeasure @ V1))) @ (cmeasure @ V2))))))))))
(TMEASURE_DISJOINT_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c/__caret__ @ (cmeasurable @ V1)) @ ((cDISJOINT @ V0) @ V1)))) @ ((c= @ (cmeasure @ ((cUNION @ V0) @ V1))) @ ((creal_add @ (cmeasure @ V0)) @ (cmeasure @ V1)))))))))
(THAS_MEASURE_DISJOINT_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_measure @ V0) @ V2)) @ ((c/__caret__ @ ((chas_measure @ V1) @ V3)) @ ((cDISJOINT @ V0) @ V1)))) @ ((chas_measure @ ((cUNION @ V0) @ V1)) @ ((creal_add @ V2) @ V3))))))))))))
(TINTEGRAL_MEASURE_UNIV,(c! @ (^[V0]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cintegral @ cUNIV) @ (^[V1]: (((cCOND @ ((cIN @ V1) @ V0)) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cvec @ (cNUMERAL @ c_0)))))) @ (clift @ (cmeasure @ V0)))))))
(TINTEGRAL_MEASURE,(c! @ (^[V0]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ ((cintegral @ V0) @ (^[V1]: (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (clift @ (cmeasure @ V0)))))))
(TMEASURE_INTEGRAL_UNIV,(c! @ (^[V0]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ (cmeasure @ V0)) @ (cdrop @ ((cintegral @ cUNIV) @ (^[V1]: (((cCOND @ ((cIN @ V1) @ V0)) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cvec @ (cNUMERAL @ c_0)))))))))))
(TMEASURE_INTEGRAL,(c! @ (^[V0]: ((c==> @ (cmeasurable @ V0)) @ ((c= @ (cmeasure @ V0)) @ (cdrop @ ((cintegral @ V0) @ (^[V1]: (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TMEASURABLE_INTEGRABLE,(c! @ (^[V0]: ((c= @ (cmeasurable @ V0)) @ ((cintegrable_on @ (^[V1]: (((cCOND @ ((cIN @ V1) @ V0)) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))) @ cUNIV)))))
(TMEASURABLE,(c! @ (^[V0]: ((c= @ (cmeasurable @ V0)) @ ((cintegrable_on @ (^[V1]: (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)))))
(THAS_MEASURE_MEASURABLE_MEASURE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chas_measure @ V0) @ V1)) @ ((c/__caret__ @ (cmeasurable @ V0)) @ ((c= @ (cmeasure @ V0)) @ V1))))))))
(TMEASURE_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chas_measure @ V0) @ V1)) @ ((c= @ (cmeasure @ V0)) @ V1)))))))
(THAS_MEASURE_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((chas_measure @ V0) @ V1)) @ ((chas_measure @ V0) @ V2))) @ ((c= @ V1) @ V2)))))))))
(THAS_MEASURE_MEASURE,(c! @ (^[V0]: ((c= @ (cmeasurable @ V0)) @ ((chas_measure @ V0) @ (cmeasure @ V0))))))
(Tmeasure,(c! @ (^[V0]: ((c= @ (cmeasure @ V0)) @ (c__at__ @ (^[V1]: ((chas_measure @ V0) @ V1)))))))
(Tmeasurable,(c! @ (^[V0]: ((c= @ (cmeasurable @ V0)) @ (c? @ (^[V1]: ((chas_measure @ V0) @ V1)))))))
(TABSOLUTELY_INTEGRABLE_ABS_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cabsolutely_integrable_on @ V0) @ V1)) @ ((cabsolutely_integrable_on @ (^[V2]: (clift @ (creal_abs @ (cdrop @ (V0 @ V2)))))) @ V1)))))))
(TABSOLUTELY_INTEGRABLE_NORM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cabsolutely_integrable_on @ V0) @ V1)) @ ((cabsolutely_integrable_on @ (^[V2]: (clift @ (cvector_norm @ (V0 @ V2))))) @ V1)))))))
(TABSOLUTELY_INTEGRABLE_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cabsolutely_integrable_on @ V0) @ V1)) @ ((cabsolutely_integrable_on @ (^[V2]: (cvector_neg @ (V0 @ V2)))) @ V1)))))))
(TABSOLUTELY_INTEGRABLE_0,(c! @ (^[V0]: ((cabsolutely_integrable_on @ (^[V1]: (cvec @ (cNUMERAL @ c_0)))) @ V0))))
(TABSOLUTELY_INTEGRABLE_IMP_INTEGRABLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cabsolutely_integrable_on @ V0) @ V1)) @ ((cintegrable_on @ V0) @ V1)))))))
(Tabsolutely_integrable_on,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cabsolutely_integrable_on @ V0) @ V1)) @ ((c/__caret__ @ ((cintegrable_on @ V0) @ V1)) @ ((cintegrable_on @ (^[V2]: (clift @ (cvector_norm @ (V0 @ V2))))) @ V1))))))))
(TINTEGRABLE_ON_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ (c~ @ ((cIN @ V3) @ V0))) @ ((c= @ (V1 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((cintegrable_on @ V1) @ V0)))) @ ((cintegrable_on @ V1) @ V2)))))))))
(THAS_INTEGRAL_ON_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ (c~ @ ((cIN @ V4) @ V0))) @ ((c= @ (V1 @ V4)) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V3)) @ (((chas_integral @ V1) @ V2) @ V0)))) @ (((chas_integral @ V1) @ V2) @ V3)))))))))))
(TOPERATIVE_INTEGRABLE,(c! @ (^[V0]: ((coperative @ c/__caret__) @ (^[V1]: ((cintegrable_on @ V0) @ V1))))))
(TNEGLIGIBLE_FINITE,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cnegligible @ V0)))))
(TNEGLIGIBLE_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c__caret__/ @ (cnegligible @ V0)) @ (cnegligible @ V1))) @ (cnegligible @ ((cINTER @ V0) @ V1))))))))
(Tnegligible,(c! @ (^[V0]: ((c= @ (cnegligible @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (((chas_integral @ (cindicator @ V0)) @ (cvec @ (cNUMERAL @ c_0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TDROP_INDICATOR_ABS_LE_1,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (creal_abs @ (cdrop @ ((cindicator @ V0) @ V1)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TDROP_INDICATOR_LE_1,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cdrop @ ((cindicator @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TDROP_INDICATOR_POS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ ((cindicator @ V0) @ V1))))))))
(TINTEGRABLE_ON_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V1)) @ cNIL))))))))
(THAS_INTEGRAL_REFL,(c! @ (^[V0]: (c! @ (^[V1]: (((chas_integral @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V1)) @ cNIL))))))))
(TINTEGRAL_EMPTY,(c! @ (^[V0]: ((c= @ ((cintegral @ cEMPTY) @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))
(TINTEGRABLE_ON_EMPTY,(c! @ (^[V0]: ((cintegrable_on @ V0) @ cEMPTY))))
(THAS_INTEGRAL_EMPTY_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((chas_integral @ V0) @ V1) @ cEMPTY)) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0)))))))))
(THAS_INTEGRAL_EMPTY,(c! @ (^[V0]: (((chas_integral @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ cEMPTY))))
(TINTEGRABLE_ON_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((cintegrable_on @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(THAS_INTEGRAL_NULL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ (((chas_integral @ V0) @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((c= @ V3) @ (cvec @ (cNUMERAL @ c_0))))))))))))))
(TINTEGRABLE_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V1) @ V2)) @ (clinear @ V0))) @ ((cintegrable_on @ ((co @ V0) @ V1)) @ V2)))))))))
(TINTEGRABLE_0,(c! @ (^[V0]: ((cintegrable_on @ (^[V1]: (cvec @ (cNUMERAL @ c_0)))) @ V0))))
(TINTEGRAL_0,(c! @ (^[V0]: ((c= @ ((cintegral @ V0) @ (^[V1]: (cvec @ (cNUMERAL @ c_0))))) @ (cvec @ (cNUMERAL @ c_0))))))
(THAS_INTEGRAL_NEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_integral @ V0) @ V1) @ V2)) @ (((chas_integral @ (^[V3]: (cvector_neg @ (V0 @ V3)))) @ (cvector_neg @ V1)) @ V2)))))))))
(THAS_INTEGRAL_0_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((chas_integral @ (^[V2]: (cvec @ (cNUMERAL @ c_0)))) @ V1) @ V0)) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0)))))))))
(THAS_INTEGRAL_0,(c! @ (^[V0]: (((chas_integral @ (^[V1]: (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))) @ V0))))
(TINTEGRAL_EQ_HAS_INTEGRAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cintegrable_on @ V0) @ V2)) @ ((c= @ ((c= @ ((cintegral @ V2) @ V0)) @ V1)) @ (((chas_integral @ V0) @ V1) @ V2))))))))))
(TINTEGRAL_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_integral @ V1) @ V2) @ V0)) @ ((c= @ ((cintegral @ V0) @ V1)) @ V2)))))))))
(THAS_INTEGRAL_INTEGRAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cintegrable_on @ V0) @ V1)) @ (((chas_integral @ V0) @ ((cintegral @ V1) @ V0)) @ V1)))))))
(TINTEGRABLE_INTEGRAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cintegrable_on @ V0) @ V1)) @ (((chas_integral @ V0) @ ((cintegral @ V1) @ V0)) @ V1)))))))
(Tintegral,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cintegral @ V1) @ V0)) @ (c__at__ @ (^[V2]: (((chas_integral @ V0) @ V2) @ V1)))))))))
(Tintegrable_on,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cintegrable_on @ V0) @ V1)) @ (c? @ (^[V2]: (((chas_integral @ V0) @ V2) @ V1)))))))))
(Thas_integral_alt,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_integral @ V1) @ V2) @ V0)) @ (((cCOND @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))) @ (((chas_integral @ V1) @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V4))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL)))) @ (c? @ (^[V7]: ((c/__caret__ @ (((chas_integral @ (^[V8]: (((cCOND @ ((cIN @ V8) @ V0)) @ (V1 @ V8)) @ (cvec @ (cNUMERAL @ c_0))))) @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V7) @ V2))) @ V3))))))))))))))))))))))))
(Thas_integral_def,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_integral @ V1) @ V2) @ V0)) @ (((cCOND @ (c? @ (^[V3]: (c? @ (^[V4]: ((c= @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))) @ (((chas_integral_compact_interval @ V1) @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((cSUBSET @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V4))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL)))) @ (c? @ (^[V7]: ((c/__caret__ @ (((chas_integral_compact_interval @ (^[V8]: (((cCOND @ ((cIN @ V8) @ V0)) @ (V1 @ V8)) @ (cvec @ (cNUMERAL @ c_0))))) @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V7) @ V2))) @ V3))))))))))))))))))))))))
(Thas_integral_compact_interval,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_integral_compact_interval @ V1) @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ (cgauge @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V5) @ V0)) @ ((cfine @ V4) @ V5))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cvsum @ V5) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ ((c% @ (ccontent @ V8)) @ (V1 @ V7))))))))))) @ V2))) @ V3))))))))))))))))))
(TTAGGED_PARTIAL_DIVISION_OF_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ctagged_partial_division_of @ V1) @ V0)) @ ((cSUBSET @ V0) @ V2))) @ ((ctagged_partial_division_of @ V1) @ V2)))))))))
(TTAGGED_DIVISION_OF_ANOTHER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ctagged_partial_division_of @ V1) @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ ((c__comma__ @ V3) @ V4)) @ V1)) @ ((cSUBSET @ V4) @ V2))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ ((c__comma__ @ V4) @ V5)) @ V1)) @ ((cIN @ V3) @ V5)))))))))))) @ ((ctagged_division_of @ V1) @ V2)))))))))
(TTAGGED_DIVISION_OF_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ctagged_division_of @ V1) @ V0)) @ ((c/__caret__ @ ((ctagged_partial_division_of @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ ((c__comma__ @ V3) @ V4)) @ V1)) @ ((cIN @ V2) @ V4))))))))))))))))
(TTAGGED_DIVISION_UNION_IMAGE_SND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ctagged_division_of @ V1) @ V0)) @ ((c= @ V0) @ (cUNIONS @ ((cIMAGE @ cSND) @ V1)))))))))
(TTAGGED_DIVISION_OF_UNION_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ctagged_division_of @ V1) @ V0)) @ ((ctagged_division_of @ V1) @ (cUNIONS @ ((cIMAGE @ cSND) @ V1)))))))))
(TTAGGED_PARTIAL_DIVISION_OF_UNION_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ctagged_partial_division_of @ V1) @ V0)) @ ((ctagged_division_of @ V1) @ (cUNIONS @ ((cIMAGE @ cSND) @ V1)))))))))
(TTAG_IN_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V1) @ V3)) @ ((cIN @ ((c__comma__ @ V2) @ V0)) @ V1))) @ ((cIN @ V2) @ V3)))))))))))
(TPARTIAL_DIVISION_OF_TAGGED_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ctagged_partial_division_of @ V1) @ V0)) @ ((cdivision_of @ ((cIMAGE @ cSND) @ V1)) @ (cUNIONS @ ((cIMAGE @ cSND) @ V1)))))))))
(TTAGGED_DIVISION_OF_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ctagged_division_of @ V1) @ V0)) @ (cFINITE @ V1)))))))
(Ttagged_partial_division_of,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ctagged_partial_division_of @ V1) @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ ((c__comma__ @ V2) @ V3)) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c= @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))))))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ ((c__comma__ @ V2) @ V3)) @ V1)) @ ((c/__caret__ @ ((cIN @ ((c__comma__ @ V4) @ V5)) @ V1)) @ (c~ @ ((c= @ ((c__comma__ @ V2) @ V3)) @ ((c__comma__ @ V4) @ V5)))))) @ ((c= @ ((cINTER @ (cinterior @ V3)) @ (cinterior @ V5))) @ cEMPTY))))))))))))))))))
(TELEMENTARY_COMPACT,(c! @ (^[V0]: ((c==> @ (c? @ (^[V1]: ((cdivision_of @ V1) @ V0)))) @ (ccompact @ V0)))))
(TELEMENTARY_SUBSET_INTERVAL,(c! @ (^[V0]: ((c==> @ (c? @ (^[V1]: ((cdivision_of @ V1) @ V0)))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((cSUBSET @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TELEMENTARY_BOUNDED,(c! @ (^[V0]: ((c==> @ (c? @ (^[V1]: ((cdivision_of @ V1) @ V0)))) @ (cbounded @ V0)))))
(TELEMENTARY_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c? @ (^[V2]: ((cdivision_of @ V2) @ V0)))) @ (c? @ (^[V2]: ((cdivision_of @ V2) @ V1))))) @ (c? @ (^[V2]: ((cdivision_of @ V2) @ ((cINTER @ V0) @ V1))))))))))
(TDIVISION_OF_UNION_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdivision_of @ V1) @ V0)) @ ((cdivision_of @ V1) @ (cUNIONS @ V1))))))))
(TFORALL_IN_DIVISION_NONEMPTY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cdivision_of @ V1) @ V0)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (V2 @ V3))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ V1)) @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ cEMPTY)))) @ (V2 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))))
(TFORALL_IN_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cdivision_of @ V1) @ V0)) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (V2 @ V3))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ V1)) @ (V2 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))))
(TDIVISION_CONTAINS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cdivision_of @ V2) @ V0)) @ ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V1) @ V3)) @ ((cIN @ V3) @ V2)))))))))))))
(TEMPTY_DIVISION_OF,(c! @ (^[V0]: ((c= @ ((cdivision_of @ cEMPTY) @ V0)) @ ((c= @ V0) @ cEMPTY)))))
(TDIVISION_OF_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdivision_of @ V1) @ V0)) @ (cFINITE @ V1)))))))
(TGAUGE_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cgauge @ V0)) @ (cgauge @ V1))) @ (cgauge @ (^[V2]: ((cINTER @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TGAUGE_BALL_DEPENDENT,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V0 @ V1))))) @ (cgauge @ (^[V1]: (cball @ ((c__comma__ @ V1) @ (V0 @ V1)))))))))
(Tgauge,(c! @ (^[V0]: ((c= @ (cgauge @ V0)) @ (c! @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ (V0 @ V1))) @ (copen @ (V0 @ V1)))))))))
(TOUTERMORPHISM_MBASIS_EMPTY,(c! @ (^[V0]: ((c= @ ((coutermorphism @ V0) @ (cmbasis @ cEMPTY))) @ (cmbasis @ cEMPTY)))))
(TLINEAR_PROPERTY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ (cvec @ (cNUMERAL @ c_0)))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (V0 @ V4))) @ (V0 @ ((cvector_add @ V3) @ V4))))))))) @ ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (V0 @ (V2 @ V3))))))) @ (V0 @ ((cvsum @ V1) @ V2)))))))))))
(TDIFFERENTIABLE_ON_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdifferentiable_on @ V0) @ V2)) @ ((cdifferentiable_on @ V1) @ V2))) @ ((cdifferentiable_on @ (^[V3]: ((cvector_sub @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TDIFFERENTIABLE_ON_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdifferentiable_on @ V0) @ V2)) @ ((cdifferentiable_on @ V1) @ V2))) @ ((cdifferentiable_on @ (^[V3]: ((cvector_add @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TDIFFERENTIABLE_ON_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdifferentiable_on @ V0) @ V1)) @ ((cdifferentiable_on @ (^[V2]: (cvector_neg @ (V0 @ V2)))) @ V1)))))))
(TDIFFERENTIABLE_ON_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdifferentiable_on @ V1) @ V2)) @ ((cdifferentiable_on @ V0) @ ((cIMAGE @ V1) @ V2)))) @ ((cdifferentiable_on @ ((co @ V0) @ V1)) @ V2)))))))))
(TDIFFERENTIABLE_ON_ID,(c! @ (^[V0]: ((cdifferentiable_on @ (^[V1]: V1)) @ V0))))
(TDIFFERENTIABLE_CHAIN_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ V1) @ ((cwithin @ (cat @ V2)) @ V3))) @ ((cdifferentiable @ V0) @ ((cwithin @ (cat @ (V1 @ V2))) @ ((cIMAGE @ V1) @ V3))))) @ ((cdifferentiable @ ((co @ V0) @ V1)) @ ((cwithin @ (cat @ V2)) @ V3))))))))))))
(TDIFFERENTIABLE_CHAIN_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ V1) @ (cat @ V2))) @ ((cdifferentiable @ V0) @ (cat @ (V1 @ V2))))) @ ((cdifferentiable @ ((co @ V0) @ V1)) @ (cat @ V2))))))))))
(TDIFFERENTIABLE_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ V0) @ V2)) @ ((cdifferentiable @ V1) @ V2))) @ ((cdifferentiable @ (^[V3]: ((cvector_sub @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TDIFFERENTIABLE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cdifferentiable @ V0) @ V2)) @ ((cdifferentiable @ V1) @ V2))) @ ((cdifferentiable @ (^[V3]: ((cvector_add @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TDIFFERENTIABLE_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdifferentiable @ V0) @ V1)) @ ((cdifferentiable @ (^[V2]: (cvector_neg @ (V0 @ V2)))) @ V1)))))))
(TDIFFERENTIABLE_ON_EMPTY,(c! @ (^[V0]: ((cdifferentiable_on @ V0) @ cEMPTY))))
(THAS_DERIVATIVE_WITHIN_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_derivative @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ V0))) @ ((cSUBSET @ V4) @ V0))) @ (((chas_derivative @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ V4))))))))))))))
(TLIM_MUL_NORM_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c--> @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ ((cwithin @ (cat @ V1)) @ V2))) @ (((c--> @ (^[V3]: ((c% @ (cvector_norm @ ((cvector_sub @ V3) @ V1))) @ (V0 @ V3)))) @ (cvec @ (cNUMERAL @ c_0))) @ ((cwithin @ (cat @ V1)) @ V2))))))))))
(TJACOBIAN_WORKS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdifferentiable @ V0) @ V1)) @ (((chas_derivative @ V0) @ (^[V2]: ((cmatrix_vector_mul @ ((cjacobian @ V0) @ V1)) @ V2))) @ V1)))))))
(Tjacobian,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cjacobian @ V0) @ V1)) @ (cmatrix @ ((cfrechet_derivative @ V0) @ V1))))))))
(TLINEAR_FRECHET_DERIVATIVE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cdifferentiable @ V0) @ V1)) @ (clinear @ ((cfrechet_derivative @ V0) @ V1))))))))
(TFRECHET_DERIVATIVE_WORKS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdifferentiable @ V0) @ V1)) @ (((chas_derivative @ V0) @ ((cfrechet_derivative @ V0) @ V1)) @ V1)))))))
(Tfrechet_derivative,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cfrechet_derivative @ V0) @ V1)) @ (c__at__ @ (^[V2]: (((chas_derivative @ V0) @ V2) @ V1)))))))))
(TDIFFERENTIABLE_ON_EQ_DIFFERENTIABLE_AT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (copen @ V0)) @ ((c= @ ((cdifferentiable_on @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cdifferentiable @ V1) @ (cat @ V2))))))))))))
(TDIFFERENTIABLE_AT_IMP_DIFFERENTIABLE_ON,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cdifferentiable @ V0) @ (cat @ V2)))))) @ ((cdifferentiable_on @ V0) @ V1)))))))
(TDIFFERENTIABLE_WITHIN_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (copen @ V0))) @ ((c= @ ((cdifferentiable @ V1) @ ((cwithin @ (cat @ V2)) @ V0))) @ ((cdifferentiable @ V1) @ (cat @ V2)))))))))))
(TDIFFERENTIABLE_AT_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cdifferentiable @ V0) @ (cat @ V1))) @ ((cdifferentiable @ V0) @ ((cwithin @ (cat @ V1)) @ V2))))))))))
(THAS_DERIVATIVE_IMP_DIFFERENTIABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_derivative @ V1) @ V0) @ V2)) @ ((cdifferentiable @ V1) @ V2)))))))))
(Tdifferentiable_on,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdifferentiable_on @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cdifferentiable @ V0) @ ((cwithin @ (cat @ V2)) @ V1)))))))))))
(Tdifferentiable,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdifferentiable @ V0) @ V1)) @ (c? @ (^[V2]: (((chas_derivative @ V0) @ V2) @ V1)))))))))
(THAS_DERIVATIVE_VMUL_DROP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((chas_derivative @ V0) @ V1) @ V3)) @ (((chas_derivative @ (^[V4]: ((c% @ (cdrop @ (V0 @ V4))) @ V2))) @ (^[V4]: ((c% @ (cdrop @ (V1 @ V4))) @ V2))) @ V3)))))))))))
(THAS_DERIVATIVE_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_derivative @ V0) @ V2) @ V4)) @ (((chas_derivative @ V1) @ V3) @ V4))) @ (((chas_derivative @ (^[V5]: ((cvector_sub @ (V0 @ V5)) @ (V1 @ V5)))) @ (^[V5]: ((cvector_sub @ (V2 @ V5)) @ (V3 @ V5)))) @ V4)))))))))))))
(THAS_DERIVATIVE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((chas_derivative @ V0) @ V2) @ V4)) @ (((chas_derivative @ V1) @ V3) @ V4))) @ (((chas_derivative @ (^[V5]: ((cvector_add @ (V0 @ V5)) @ (V1 @ V5)))) @ (^[V5]: ((cvector_add @ (V2 @ V5)) @ (V3 @ V5)))) @ V4)))))))))))))
(THAS_DERIVATIVE_NEG_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_derivative @ (^[V3]: (cvector_neg @ (V0 @ V3)))) @ (^[V3]: (cvector_neg @ (V1 @ V3)))) @ V2)) @ (((chas_derivative @ V0) @ V1) @ V2)))))))))
(THAS_DERIVATIVE_NEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_derivative @ V0) @ V1) @ V2)) @ (((chas_derivative @ (^[V3]: (cvector_neg @ (V0 @ V3)))) @ (^[V3]: (cvector_neg @ (V1 @ V3)))) @ V2)))))))))
(THAS_DERIVATIVE_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((chas_derivative @ V0) @ V2) @ V3)) @ (((chas_derivative @ (^[V4]: ((c% @ V1) @ (V0 @ V4)))) @ (^[V4]: ((c% @ V1) @ (V2 @ V4)))) @ V3)))))))))))
(THAS_DERIVATIVE_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ (((chas_derivative @ V0) @ V0) @ V1)))))))
(THAS_DERIVATIVE_WITHIN_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (copen @ V0))) @ ((c= @ (((chas_derivative @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ V0))) @ (((chas_derivative @ V1) @ V2) @ (cat @ V3)))))))))))))
(THAS_DERIVATIVE_AT_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((chas_derivative @ V0) @ V1) @ (cat @ V2))) @ (((chas_derivative @ V0) @ V1) @ ((cwithin @ (cat @ V2)) @ V3))))))))))))
(THAS_DERIVATIVE_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_derivative @ V0) @ V1) @ (cat @ V2))) @ ((c/__caret__ @ (clinear @ V1)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cvector_norm @ ((cvector_sub @ V5) @ V2)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V5) @ V2))) @ V4))) @ ((creal_lt @ ((creal_div @ (cvector_norm @ ((cvector_sub @ ((cvector_sub @ (V0 @ V5)) @ (V0 @ V2))) @ (V1 @ ((cvector_sub @ V5) @ V2))))) @ (cvector_norm @ ((cvector_sub @ V5) @ V2)))) @ V3)))))))))))))))))))
(THAS_DERIVATIVE_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((chas_derivative @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ V0))) @ ((c/__caret__ @ (clinear @ V2)) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cvector_norm @ ((cvector_sub @ V6) @ V3)))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V6) @ V3))) @ V5)))) @ ((creal_lt @ ((creal_div @ (cvector_norm @ ((cvector_sub @ ((cvector_sub @ (V1 @ V6)) @ (V1 @ V3))) @ (V2 @ ((cvector_sub @ V6) @ V3))))) @ (cvector_norm @ ((cvector_sub @ V6) @ V3)))) @ V4)))))))))))))))))))))
(Thas_derivative,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chas_derivative @ V0) @ V1) @ V2)) @ ((c/__caret__ @ (clinear @ V1)) @ (((c--> @ (^[V3]: ((c% @ (creal_inv @ (cvector_norm @ ((cvector_sub @ V3) @ (cnetlimit @ V2))))) @ ((cvector_sub @ (V0 @ V3)) @ ((cvector_add @ (V0 @ (cnetlimit @ V2))) @ (V1 @ ((cvector_sub @ V3) @ (cnetlimit @ V2)))))))) @ (cvec @ (cNUMERAL @ c_0))) @ V2))))))))))
(THOMEOMORPHIC_FIXPOINT_PROPERTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomeomorphic @ V0) @ V1)) @ ((c= @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V0)) @ V0))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V2 @ V3)) @ V3)))))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V1)) @ ((cSUBSET @ ((cIMAGE @ V2) @ V1)) @ V1))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ V3))))))))))))))
(TENR_INTERIOR,(c! @ (^[V0]: (cENR @ (cinterior @ V0)))))
(TANR_INTERIOR,(c! @ (^[V0]: (cANR @ (cinterior @ V0)))))
(TENR_RELATIVE_INTERIOR,(c! @ (^[V0]: ((c==> @ (cENR @ V0)) @ (cENR @ (crelative_interior @ V0))))))
(TANR_RELATIVE_INTERIOR,(c! @ (^[V0]: ((c==> @ (cANR @ V0)) @ (cANR @ (crelative_interior @ V0))))))
(TENR,(c! @ (^[V0]: ((c= @ (cENR @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (copen @ V1)) @ ((cretract_of @ V0) @ V1))))))))
(TRETRACT_OF_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((cretract_of @ V1) @ V0))) @ (cclosed @ V1)))))))
(TRETRACT_OF_IMP_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cretract_of @ V0) @ V1)) @ ((cSUBSET @ V0) @ V1)))))))
(TRETRACT_OF_REFL,(c! @ (^[V0]: ((cretract_of @ V0) @ V0))))
(TRETRACTION_REFL,(c! @ (^[V0]: ((cretraction @ ((c__comma__ @ V0) @ V0)) @ (^[V1]: V1)))))
(TRETRACT_OF_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cretract_of @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ ((cSUBSET @ V2) @ V0)))) @ ((cretract_of @ V1) @ V2)))))))))
(TRETRACTION_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cretraction @ ((c__comma__ @ V0) @ V2)) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V1)) @ ((cSUBSET @ V1) @ V0)))) @ ((cretraction @ ((c__comma__ @ V1) @ V2)) @ V3)))))))))))
(TRETRACTION_IDEMPOTENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cretraction @ ((c__comma__ @ V1) @ V0)) @ V2)) @ ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ (V2 @ V3))) @ (V2 @ V3)))))))))))))
(TRETRACTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cretraction @ ((c__comma__ @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ V3)))))))))))))))
(Tretract_of,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cretract_of @ V1) @ V0)) @ (c? @ (^[V2]: ((cretraction @ ((c__comma__ @ V0) @ V1)) @ V2)))))))))
(TCARD_FACES_OF_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V1) @ V0)) @ ((c= @ (cCARD @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cface_of @ V3) @ V0)) @ V3))))))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cnum_of_int @ ((cint_add @ V1) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TAFF_DIM_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V1) @ V0)) @ ((c= @ (caff_dim @ V0)) @ V1)))))))
(TSIMPLEX_MINUS_1,(c! @ (^[V0]: ((c= @ ((csimplex @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)) @ ((c= @ V0) @ cEMPTY)))))
(TSIMPLEX_DIM_GE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((csimplex @ V1) @ V0)) @ ((cint_le @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V1)))))))
(TPOLYHEDRON_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cpolyhedron @ ((chull @ cconvex) @ V0))))))
(TPOLYTOPE_IMP_POLYHEDRON,(c! @ (^[V0]: ((c==> @ (cpolytope @ V0)) @ (cpolyhedron @ V0)))))
(TPOLYTOPE_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpolytope @ V0)) @ (cpolytope @ V1))) @ (cpolytope @ ((cINTER @ V0) @ V1))))))))
(TPOLYHEDRON_AFFINE_HULL,(c! @ (^[V0]: (cpolyhedron @ ((chull @ caffine) @ V0)))))
(Tpolyhedron,(c! @ (^[V0]: ((c= @ (cpolyhedron @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((c= @ V0) @ (cINTERS @ V1))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V2) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((cdot @ V3) @ V6)) @ V4)) @ V6))))))))))))))))))))))
(TPOLYTOPE_IMP_BOUNDED,(c! @ (^[V0]: ((c==> @ (cpolytope @ V0)) @ (cbounded @ V0)))))
(TPOLYTOPE_IMP_CLOSED,(c! @ (^[V0]: ((c==> @ (cpolytope @ V0)) @ (cclosed @ V0)))))
(TPOLYTOPE_IMP_CONVEX,(c! @ (^[V0]: ((c==> @ (cpolytope @ V0)) @ (cconvex @ V0)))))
(TPOLYTOPE_IMP_COMPACT,(c! @ (^[V0]: ((c==> @ (cpolytope @ V0)) @ (ccompact @ V0)))))
(TPOLYTOPE_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cpolytope @ ((chull @ cconvex) @ V0))))))
(Tpolytope,(c! @ (^[V0]: ((c= @ (cpolytope @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (cFINITE @ V1)) @ ((c= @ V0) @ ((chull @ cconvex) @ V1)))))))))
(TKREIN_MILMAN_POLYTOPE,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((chull @ cconvex) @ V0)) @ ((chull @ cconvex) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cextreme_point_of @ V2) @ ((chull @ cconvex) @ V0))) @ V2)))))))))))
(TEDGE_OF_IMP_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cedge_of @ V0) @ V1)) @ ((cSUBSET @ V0) @ V1)))))))
(Tedge_of,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cedge_of @ V1) @ V0)) @ ((c/__caret__ @ ((cface_of @ V1) @ V0)) @ ((c= @ (caff_dim @ V1)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TFACET_OF_IMP_PROPER_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cfacet_of @ V1) @ V0)) @ (c~ @ ((c= @ V1) @ cEMPTY))))))))
(TFACET_OF_IMP_PROPER_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cfacet_of @ V0) @ V1)) @ (c~ @ ((c= @ V0) @ V1))))))))
(TFACET_OF_IMP_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cfacet_of @ V0) @ V1)) @ ((cSUBSET @ V0) @ V1)))))))
(TFACET_OF_IMP_FACE_OF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cfacet_of @ V0) @ V1)) @ ((cface_of @ V0) @ V1)))))))
(TFACET_OF_REFL,(c! @ (^[V0]: (c~ @ ((cfacet_of @ V0) @ V0)))))
(TFACET_OF_EMPTY,(c! @ (^[V0]: (c~ @ ((cfacet_of @ V0) @ cEMPTY)))))
(Tfacet_of,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cfacet_of @ V0) @ V1)) @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c= @ (caff_dim @ V0)) @ ((cint_sub @ (caff_dim @ V1)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TEXTREME_POINTS_OF_CONVEX_HULL,(c! @ (^[V0]: ((cSUBSET @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cextreme_point_of @ V2) @ ((chull @ cconvex) @ V0))) @ V2)))))) @ V0))))
(TEXTREME_POINT_OF_FACE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cface_of @ V2) @ V0)) @ ((c= @ ((cextreme_point_of @ V1) @ V2)) @ ((c/__caret__ @ ((cextreme_point_of @ V1) @ V0)) @ ((cIN @ V1) @ V2)))))))))))
(Textreme_point_of,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cextreme_point_of @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V0))) @ (c~ @ ((cIN @ V1) @ (copen_segment @ ((c__comma__ @ V2) @ V3))))))))))))))))
(Texposed_face_of,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cexposed_face_of @ V0) @ V1)) @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((creal_le @ ((cdot @ V2) @ V5)) @ V3)) @ V5))))))) @ ((c= @ V0) @ ((cINTER @ V1) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V2) @ V5)) @ V3)) @ V5)))))))))))))))))))
(TFACE_OF_IMP_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (ccompact @ V0)) @ ((cface_of @ V1) @ V0)))) @ (ccompact @ V1)))))))
(TFACE_OF_IMP_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (cclosed @ V0)) @ ((cface_of @ V1) @ V0)))) @ (cclosed @ V1)))))))
(TFACE_OF_IMP_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cface_of @ V1) @ V0)) @ (cconvex @ V1)))))))
(TFACE_OF_IMP_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cface_of @ V0) @ V1)) @ ((cSUBSET @ V0) @ V1)))))))
(TFACE_OF_INTER_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cface_of @ V0) @ V2)) @ ((cface_of @ V1) @ V3))) @ ((cface_of @ ((cINTER @ V0) @ V1)) @ ((cINTER @ V2) @ V3))))))))))))
(TFACE_OF_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cface_of @ V0) @ V2)) @ ((cface_of @ V1) @ V2))) @ ((cface_of @ ((cINTER @ V0) @ V1)) @ V2)))))))))
(TFACE_OF_SLICE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cface_of @ V0) @ V1)) @ (cconvex @ V2))) @ ((cface_of @ ((cINTER @ V0) @ V2)) @ ((cINTER @ V1) @ V2))))))))))
(TFACE_OF_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cface_of @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V2)) @ ((cSUBSET @ V2) @ V0)))) @ ((cface_of @ V1) @ V2)))))))))
(TFACE_OF_FACE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cface_of @ V2) @ V0)) @ ((c= @ ((cface_of @ V1) @ V2)) @ ((c/__caret__ @ ((cface_of @ V1) @ V0)) @ ((cSUBSET @ V1) @ V2)))))))))))
(TFACE_OF_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cface_of @ V1) @ V0)) @ ((cface_of @ V0) @ V2))) @ ((cface_of @ V1) @ V2)))))))))
(TFACE_OF_EMPTY,(c! @ (^[V0]: ((c= @ ((cface_of @ V0) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TEMPTY_FACE_OF,(c! @ (^[V0]: ((cface_of @ cEMPTY) @ V0))))
(TFACE_OF_REFL_EQ,(c! @ (^[V0]: ((c= @ ((cface_of @ V0) @ V0)) @ (cconvex @ V0)))))
(TFACE_OF_REFL,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ ((cface_of @ V0) @ V0)))))
(Tface_of,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cface_of @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ (cconvex @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ V4) @ (copen_segment @ ((c__comma__ @ V2) @ V3))))))) @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((cIN @ V3) @ V1)))))))))))))))))
(Tcontractible,(c! @ (^[V0]: ((c= @ (ccontractible @ V0)) @ (c? @ (^[V1]: ((((chomotopic_with @ (^[V2]: cT)) @ ((c__comma__ @ V0) @ V0)) @ (^[V2]: V2)) @ (^[V2]: V1))))))))
(THOMOTOPIC_PATHS_IMP_HOMOTOPIC_LOOPS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((chomotopic_paths @ V0) @ V1) @ V2)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))) @ ((c= @ (cpathfinish @ V2)) @ (cpathstart @ V1))))) @ (((chomotopic_loops @ V0) @ V1) @ V2)))))))))
(THOMOTOPIC_LOOPS_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chomotopic_loops @ V0) @ V2) @ V3)) @ ((cSUBSET @ V0) @ V1))) @ (((chomotopic_loops @ V1) @ V2) @ V3)))))))))))
(THOMOTOPIC_LOOPS_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((chomotopic_loops @ V0) @ V2) @ V1)) @ (((chomotopic_loops @ V0) @ V1) @ V2)))))))))
(THOMOTOPIC_LOOPS_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((chomotopic_loops @ V0) @ V1) @ V1)) @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((cSUBSET @ (cpath_image @ V1)) @ V0)) @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))))))))))
(THOMOTOPIC_LOOPS_IMP_PATH_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chomotopic_loops @ V0) @ V2) @ V1)) @ (cpath @ V2)))))))))
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(THOMOTOPIC_LOOPS_IMP_LOOP_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chomotopic_loops @ V0) @ V2) @ V1)) @ ((c= @ (cpathfinish @ V2)) @ (cpathstart @ V2))))))))))
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(TRELATIVE_INTERIOR,(c! @ (^[V0]: ((c= @ (crelative_interior @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ (copen @ V3)) @ ((c/__caret__ @ ((cIN @ V2) @ V3)) @ ((cSUBSET @ ((cINTER @ V3) @ ((chull @ caffine) @ V0))) @ V0))))))) @ V2)))))))))
(Trelative_frontier,(c! @ (^[V0]: ((c= @ (crelative_frontier @ V0)) @ ((cDIFF @ (cclosure @ V0)) @ (crelative_interior @ V0))))))
(Trelative_interior,(c! @ (^[V0]: ((c= @ (crelative_interior @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ ((chull @ caffine) @ V0))) @ V3)) @ ((c/__caret__ @ ((cIN @ V2) @ V3)) @ ((cSUBSET @ V3) @ V0)))))) @ V2)))))))))
(TBETWEEN_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c= @ (V0 @ V4)) @ (V0 @ V5))) @ ((c= @ V4) @ V5)))))))) @ ((c= @ ((cbetween @ (V0 @ V1)) @ ((c__comma__ @ (V0 @ V2)) @ (V0 @ V3)))) @ ((cbetween @ V1) @ ((c__comma__ @ V2) @ V3)))))))))))))
(TSTARLIKE_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cstarlike @ ((cIMAGE @ V0) @ V1))) @ (cstarlike @ V1))))))))
(TSTARLIKE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cstarlike @ V1)) @ (clinear @ V0))) @ (cstarlike @ ((cIMAGE @ V0) @ V1))))))))
(TCONVEX_IMP_STARLIKE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (cstarlike @ V0)))))
(Tstarlike,(c! @ (^[V0]: ((c= @ (cstarlike @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V0)))))))))))
(TCONVEX_EPIGRAPH_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cconvex @ V0)) @ ((c= @ ((cconvex_on @ V1) @ V0)) @ (cconvex @ ((cepigraph @ V0) @ V1)))))))))
(TCONVEX_EPIGRAPH,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cconvex_on @ V1) @ V0)) @ (cconvex @ V0))) @ (cconvex @ ((cepigraph @ V0) @ V1))))))))
(TIN_EPIGRAPH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cIN @ ((cpastecart @ V2) @ (clift @ V3))) @ ((cepigraph @ V0) @ V1))) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((creal_le @ (V1 @ V2)) @ V3))))))))))))
(TCONVEX_CONE_NEGATIONS,(c! @ (^[V0]: ((c==> @ (cconvex_cone @ V0)) @ (cconvex_cone @ ((cIMAGE @ cvector_neg) @ V0))))))
(TCONVEX_CONE_SPAN,(c! @ (^[V0]: (cconvex_cone @ (cspan @ V0)))))
(TSUBSPACE_IMP_CONVEX_CONE,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ (cconvex_cone @ V0)))))
(TCONIC_HULL_SUBSET_CONVEX_CONE_HULL,(c! @ (^[V0]: ((cSUBSET @ ((chull @ cconic) @ V0)) @ ((chull @ cconvex_cone) @ V0)))))
(TCONVEX_HULL_SUBSET_CONVEX_CONE_HULL,(c! @ (^[V0]: ((cSUBSET @ ((chull @ cconvex) @ V0)) @ ((chull @ cconvex_cone) @ V0)))))
(TCONVEX_CONE_HULL_CONTAINS_0,(c! @ (^[V0]: ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ ((chull @ cconvex_cone) @ V0)))))
(TCONVEX_CONE_HULL_NONEMPTY,(c! @ (^[V0]: (c~ @ ((c= @ ((chull @ cconvex_cone) @ V0)) @ cEMPTY)))))
(TCONIC_CONVEX_CONE_HULL,(c! @ (^[V0]: (cconic @ ((chull @ cconvex_cone) @ V0)))))
(TCONVEX_CONVEX_CONE_HULL,(c! @ (^[V0]: (cconvex @ ((chull @ cconvex_cone) @ V0)))))
(TCONVEX_CONE_CONVEX_CONE_HULL,(c! @ (^[V0]: (cconvex_cone @ ((chull @ cconvex_cone) @ V0)))))
(TCONVEX_CONE_NONEMPTY,(c! @ (^[V0]: ((c==> @ (cconvex_cone @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY))))))
(Tconvex_cone,(c! @ (^[V0]: ((c= @ (cconvex_cone @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (cconvex @ V0)) @ (cconic @ V0)))))))
(TCONVEX_HULL_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((c= @ ((chull @ cconvex) @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ ((chull @ cconvex) @ V1)))))))))
(TCONTINUOUS_ON_CLOSEST_POINT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (cclosed @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY))))) @ ((ccontinuous_on @ (cclosest_point @ V0)) @ V1)))))))
(TCONTINUOUS_AT_CLOSEST_POINT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (cclosed @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY))))) @ ((ccontinuous @ (cclosest_point @ V0)) @ (cat @ V1))))))))
(TCLOSEST_POINT_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ ((c/__caret__ @ (cclosed @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c~ @ ((c= @ V2) @ ((cclosest_point @ V0) @ V1))))))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V1) @ ((cclosest_point @ V0) @ V1)))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))))))))
(TAFF_DIM_PSUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cPSUBSET @ ((chull @ caffine) @ V0)) @ ((chull @ caffine) @ V1))) @ ((cint_lt @ (caff_dim @ V0)) @ (caff_dim @ V1))))))))
(TAFF_DIM_AFFINE_HULL,(c! @ (^[V0]: ((c= @ (caff_dim @ ((chull @ caffine) @ V0))) @ (caff_dim @ V0)))))
(TAFF_DIM,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ ((c= @ ((chull @ caffine) @ V1)) @ ((chull @ caffine) @ V0))) @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V1))) @ ((c= @ (caff_dim @ V0)) @ ((cint_sub @ (cint_of_num @ (cCARD @ V1))) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))
(Taff_dim,(c! @ (^[V0]: ((c= @ (caff_dim @ V0)) @ (c__at__ @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c= @ ((chull @ caffine) @ V2)) @ ((chull @ caffine) @ V0))) @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V2))) @ ((c= @ (cint_of_num @ (cCARD @ V2))) @ ((cint_add @ V1) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))))
(TINDEPENDENT_IMP_AFFINE_DEPENDENT_0,(c! @ (^[V0]: ((c==> @ (cindependent @ V0)) @ (c~ @ (caffine_dependent @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ V0)))))))
(TAFFINE_DEPENDENT_IMP_DEPENDENT,(c! @ (^[V0]: ((c==> @ (caffine_dependent @ V0)) @ (cdependent @ V0)))))
(TCLOSURE_SUBSET_AFFINE_HULL,(c! @ (^[V0]: ((cSUBSET @ (cclosure @ V0)) @ ((chull @ caffine) @ V0)))))
(TCLOSED_AFFINE_HULL,(c! @ (^[V0]: (cclosed @ ((chull @ caffine) @ V0)))))
(TAFFINE_IMP_SUBSPACE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (caffine @ V0)) @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V0))) @ (csubspace @ V0)))))
(TCONVEX_SPAN,(c! @ (^[V0]: (cconvex @ (cspan @ V0)))))
(TAFFINE_SPAN,(c! @ (^[V0]: (caffine @ (cspan @ V0)))))
(TCONVEX_HULL_SUBSET_AFFINE_HULL,(c! @ (^[V0]: ((cSUBSET @ ((chull @ cconvex) @ V0)) @ ((chull @ caffine) @ V0)))))
(TCONVEX_HULL_SUBSET_SPAN,(c! @ (^[V0]: ((cSUBSET @ ((chull @ cconvex) @ V0)) @ (cspan @ V0)))))
(TAFFINE_HULL_SUBSET_SPAN,(c! @ (^[V0]: ((cSUBSET @ ((chull @ caffine) @ V0)) @ (cspan @ V0)))))
(TSUBSPACE_IMP_CONVEX,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ (cconvex @ V0)))))
(TAFFINE_IMP_CONVEX,(c! @ (^[V0]: ((c==> @ (caffine @ V0)) @ (cconvex @ V0)))))
(TSUBSPACE_IMP_AFFINE,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ (caffine @ V0)))))
(TCONVEX_HULL_EQ_EMPTY,(c! @ (^[V0]: ((c= @ ((c= @ ((chull @ cconvex) @ V0)) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TFINITE_IMP_BOUNDED_CONVEX_HULL,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cbounded @ ((chull @ cconvex) @ V0))))))
(TBOUNDED_CONVEX_HULL_EQ,(c! @ (^[V0]: ((c= @ (cbounded @ ((chull @ cconvex) @ V0))) @ (cbounded @ V0)))))
(TIS_CONVEX_HULL,(c! @ (^[V0]: ((c= @ (cconvex @ V0)) @ (c? @ (^[V1]: ((c= @ V0) @ ((chull @ cconvex) @ V1))))))))
(TCONVEX_HULL_EQ,(c! @ (^[V0]: ((c= @ ((c= @ ((chull @ cconvex) @ V0)) @ V0)) @ (cconvex @ V0)))))
(TCONVEX_CONVEX_HULL,(c! @ (^[V0]: (cconvex @ ((chull @ cconvex) @ V0)))))
(TEQ_SUMS_RCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (cclosed @ V2)) @ ((c/__caret__ @ (cconvex @ V2)) @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c= @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ V5) @ V0))) @ ((cvector_add @ V4) @ V5))))))))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((cIN @ V5) @ V0))) @ ((cvector_add @ V4) @ V5)))))))))))))))) @ ((c= @ V1) @ V2)))))))))
(TEQ_SUMS_LCANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c/__caret__ @ (cbounded @ V0)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (cclosed @ V2)) @ ((c/__caret__ @ (cconvex @ V2)) @ ((c= @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ V1))) @ ((cvector_add @ V4) @ V5))))))))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ V2))) @ ((cvector_add @ V4) @ V5)))))))))))))))) @ ((c= @ V1) @ V2)))))))))
(TCONVEX_DIFFERENCES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (cconvex @ V1))) @ (cconvex @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_sub @ V3) @ V4)))))))))))))))
(TCONVEX_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (cconvex @ V1))) @ (cconvex @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TCONVEX_NEGATIONS,(c! @ (^[V0]: ((c==> @ (cconvex @ V0)) @ (cconvex @ ((cIMAGE @ cvector_neg) @ V0))))))
(TCONVEX_LOWER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V4) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c= @ ((creal_add @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))) @ ((creal_le @ (V4 @ ((cvector_add @ ((c% @ V1) @ V3)) @ ((c% @ V2) @ V5)))) @ ((creal_max @ (V4 @ V3)) @ (V4 @ V5)))))))))))))))))
(TCONVEX_MAX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V0) @ V2)) @ ((cconvex_on @ V1) @ V2))) @ ((cconvex_on @ (^[V3]: ((creal_max @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TCONVEX_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V0) @ V2)) @ ((cconvex_on @ V1) @ V2))) @ ((cconvex_on @ (^[V3]: ((creal_add @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TCONVEX_ON_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cconvex_on @ V1) @ V0)) @ ((cSUBSET @ V2) @ V0))) @ ((cconvex_on @ V1) @ V2)))))))))
(Tconvex_on,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cconvex_on @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((c= @ ((creal_add @ V4) @ V5)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((creal_le @ (V1 @ ((cvector_add @ ((c% @ V4) @ V2)) @ ((c% @ V5) @ V3)))) @ ((creal_add @ ((creal_mul @ V4) @ (V1 @ V2))) @ ((creal_mul @ V5) @ (V1 @ V3)))))))))))))))))))
(TCOPLANAR_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccoplanar @ V0)) @ ((cSUBSET @ V1) @ V0))) @ (ccoplanar @ V1)))))))
(TCOPLANAR_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (ccoplanar @ ((cIMAGE @ V0) @ V1))) @ (ccoplanar @ V1))))))))
(TCOPLANAR_AFFINE_HULL_COPLANAR,(c! @ (^[V0]: ((c= @ (ccoplanar @ ((chull @ caffine) @ V0))) @ (ccoplanar @ V0)))))
(TCOLLINEAR_AFFINE_HULL_COLLINEAR,(c! @ (^[V0]: ((c= @ (ccollinear @ ((chull @ caffine) @ V0))) @ (ccollinear @ V0)))))
(TCOPLANAR_SMALL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c<= @ (cCARD @ V0)) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ (ccoplanar @ V0)))))
(TCOLLINEAR_IMP_COPLANAR,(c! @ (^[V0]: ((c==> @ (ccollinear @ V0)) @ (ccoplanar @ V0)))))
(Tcoplanar,(c! @ (^[V0]: ((c= @ (ccoplanar @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: ((cSUBSET @ V0) @ ((chull @ caffine) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ ((cINSERT @ V3) @ cEMPTY)))))))))))))))
(TAFFINE_INDEPENDENT_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (caffine_dependent @ V0))) @ (c~ @ (caffine_dependent @ ((cDELETE @ V0) @ V1)))))))))
(TAFFINE_INDEPENDENT_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V0))) @ ((cSUBSET @ V1) @ V0))) @ (c~ @ (caffine_dependent @ V1))))))))
(TCONIC_HULL_EQ_EMPTY,(c! @ (^[V0]: ((c= @ ((c= @ ((chull @ cconic) @ V0)) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TCONIC_HULL_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((c= @ ((chull @ cconic) @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ ((chull @ cconic) @ V1)))))))))
(TCONIC_SPAN,(c! @ (^[V0]: (cconic @ (cspan @ V0)))))
(TCONIC_NEGATIONS,(c! @ (^[V0]: ((c==> @ (cconic @ V0)) @ (cconic @ ((cIMAGE @ cvector_neg) @ V0))))))
(TCONIC_HULL_EQ,(c! @ (^[V0]: ((c= @ ((c= @ ((chull @ cconic) @ V0)) @ V0)) @ (cconic @ V0)))))
(TCONIC_CONIC_HULL,(c! @ (^[V0]: (cconic @ ((chull @ cconic) @ V0)))))
(TCONIC_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cconic @ ((cIMAGE @ V0) @ V1))) @ (cconic @ V1))))))))
(TCONIC_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconic @ V1)) @ (clinear @ V0))) @ (cconic @ ((cIMAGE @ V0) @ V1))))))))
(TSUBSPACE_IMP_CONIC,(c! @ (^[V0]: ((c==> @ (csubspace @ V0)) @ (cconic @ V0)))))
(Tconic,(c! @ (^[V0]: ((c= @ (cconic @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2))) @ ((cIN @ ((c% @ V2) @ V1)) @ V0))))))))))
(TCONVEX_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cconvex @ ((cIMAGE @ V0) @ V1))) @ (cconvex @ V1))))))))
(TCONVEX_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ (clinear @ V0))) @ (cconvex @ ((cIMAGE @ V0) @ V1))))))))
(TCONVEX_HULLS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ ((chull @ cconvex) @ V1))) @ ((cSUBSET @ V1) @ ((chull @ cconvex) @ V0)))) @ ((c= @ ((chull @ cconvex) @ V0)) @ ((chull @ cconvex) @ V1))))))))
(TCONVEX_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V0)) @ (cconvex @ V1))) @ (cconvex @ ((cINTER @ V0) @ V1))))))))
(TCONVEX_CONTAINS_OPEN_SEGMENT,(c! @ (^[V0]: ((c= @ (cconvex @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((cSUBSET @ (copen_segment @ ((c__comma__ @ V1) @ V2))) @ V0))))))))))
(TCONVEX_CONTAINS_SEGMENT,(c! @ (^[V0]: ((c= @ (cconvex @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V0))))))))))
(TCONVEX_ALT,(c! @ (^[V0]: ((c= @ (cconvex @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((creal_le @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cIN @ ((cvector_add @ ((c% @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3)) @ V1)) @ ((c% @ V3) @ V2))) @ V0))))))))))))
(Tconvex,(c! @ (^[V0]: ((c= @ (cconvex @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((c= @ ((creal_add @ V3) @ V4)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ ((cIN @ ((cvector_add @ ((c% @ V3) @ V1)) @ ((c% @ V4) @ V2))) @ V0))))))))))))))
(TAFFINE_HULL_EQ_EMPTY,(c! @ (^[V0]: ((c= @ ((c= @ ((chull @ caffine) @ V0)) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TAFFINE_HULL_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (clinear @ V0)) @ ((c= @ ((chull @ caffine) @ ((cIMAGE @ V0) @ V1))) @ ((cIMAGE @ V0) @ ((chull @ caffine) @ V1)))))))))
(TAFFINE_HULLS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ ((chull @ caffine) @ V1))) @ ((cSUBSET @ V1) @ ((chull @ caffine) @ V0)))) @ ((c= @ ((chull @ caffine) @ V0)) @ ((chull @ caffine) @ V1))))))))
(TIS_AFFINE_HULL,(c! @ (^[V0]: ((c= @ (caffine @ V0)) @ (c? @ (^[V1]: ((c= @ V0) @ ((chull @ caffine) @ V1))))))))
(TAFFINE_HULL_EQ,(c! @ (^[V0]: ((c= @ ((c= @ ((chull @ caffine) @ V0)) @ V0)) @ (caffine @ V0)))))
(TAFFINE_AFFINE_HULL,(c! @ (^[V0]: (caffine @ ((chull @ caffine) @ V0)))))
(TAFFINE_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V0)) @ (caffine @ V1))) @ (caffine @ ((cINTER @ V0) @ V1))))))))
(TAFFINE_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (caffine @ ((cIMAGE @ V0) @ V1))) @ (caffine @ V1))))))))
(TAFFINE_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V1)) @ (clinear @ V0))) @ (caffine @ ((cIMAGE @ V0) @ V1))))))))
(TAFFINE_DIFFERENCES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V0)) @ (caffine @ V1))) @ (caffine @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_sub @ V3) @ V4)))))))))))))))
(TAFFINE_SUMS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (caffine @ V0)) @ (caffine @ V1))) @ (caffine @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cvector_add @ V3) @ V4)))))))))))))))
(TAFFINE_NEGATIONS,(c! @ (^[V0]: ((c==> @ (caffine @ V0)) @ (caffine @ ((cIMAGE @ cvector_neg) @ V0))))))
(TAFFINE_ALT,(c! @ (^[V0]: ((c= @ (caffine @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((cIN @ ((cvector_add @ ((c% @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3)) @ V1)) @ ((c% @ V3) @ V2))) @ V0))))))))))))
(Taffine,(c! @ (^[V0]: ((c= @ (caffine @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ ((creal_add @ V3) @ V4)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((cIN @ ((cvector_add @ ((c% @ V3) @ V1)) @ ((c% @ V4) @ V2))) @ V0))))))))))))))
(TUNCOUNTABLE_CONTAINS_LIMIT_POINT,(c! @ (^[V0]: ((c==> @ (c~ @ (cCOUNTABLE @ V0))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ V0)) @ ((climit_point_of @ V1) @ V0))))))))
(TSETDIST_EQ_0_CLOSED_IN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((cIN @ V1) @ V0))) @ ((c= @ ((c= @ (csetdist @ ((c__comma__ @ ((cINSERT @ V1) @ cEMPTY)) @ V2))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V2) @ cEMPTY)) @ ((cIN @ V1) @ V2)))))))))))
(TSETDIST_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csetdist @ ((c__comma__ @ V1) @ V0))) @ (csetdist @ ((c__comma__ @ V0) @ V1))))))))
(TSETDIST_POS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (csetdist @ ((c__comma__ @ V0) @ V1))))))))
(TSETDIST_EMPTY_conjunct1,(c! @ (^[V0]: ((c= @ (csetdist @ ((c__comma__ @ V0) @ cEMPTY))) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TSETDIST_EMPTY_conjunct0,(c! @ (^[V0]: ((c= @ (csetdist @ ((c__comma__ @ cEMPTY) @ V0))) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(Tsetdist,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csetdist @ ((c__comma__ @ V0) @ V1))) @ (((cCOND @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c= @ V1) @ cEMPTY))) @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cinf @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ (cdistance @ ((c__comma__ @ V3) @ V4)))))))))))))))))
(TCONTINUOUS_ON_DIST_CLOSEST_POINT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((ccontinuous_on @ (^[V2]: (clift @ (cdistance @ ((c__comma__ @ V2) @ ((cclosest_point @ V0) @ V2)))))) @ V1)))))))
(TCLOSEST_POINT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ ((cIN @ V2) @ V0))) @ ((creal_le @ (cdistance @ ((c__comma__ @ V1) @ ((cclosest_point @ V0) @ V1)))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))))))))
(TCLOSEST_POINT_EXISTS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (cdistance @ ((c__comma__ @ V1) @ ((cclosest_point @ V0) @ V1)))) @ (cdistance @ ((c__comma__ @ V1) @ V2))))))))))))
(Tclosest_point,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cclosest_point @ V0) @ V1)) @ (c__at__ @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (cdistance @ ((c__comma__ @ V1) @ V2))) @ (cdistance @ ((c__comma__ @ V1) @ V3)))))))))))))))
(TINFSUM_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((csummable @ V1) @ V2)) @ (clinear @ V0))) @ ((c= @ ((cinfsum @ V1) @ (^[V3]: (V0 @ (V2 @ V3))))) @ (V0 @ ((cinfsum @ V1) @ V2)))))))))))
(TCLOSED_SPAN,(c! @ (^[V0]: (cclosed @ (cspan @ V0)))))
(TCLOSURE_NEGATIONS,(c! @ (^[V0]: ((c= @ (cclosure @ ((cIMAGE @ cvector_neg) @ V0))) @ ((cIMAGE @ cvector_neg) @ (cclosure @ V0))))))
(TINTERIOR_NEGATIONS,(c! @ (^[V0]: ((c= @ (cinterior @ ((cIMAGE @ cvector_neg) @ V0))) @ ((cIMAGE @ cvector_neg) @ (cinterior @ V0))))))
(TCLOSED_INJECTIVE_IMAGE_SUBSPACE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V1)) @ ((c/__caret__ @ (clinear @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c= @ (V0 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))))) @ (cclosed @ V1))))) @ (cclosed @ ((cIMAGE @ V0) @ V1))))))))
(TOPEN_IMP_INFINITE,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ (cINFINITE @ V0))))))
(THOMEOMORPHIC_CONNECTEDNESS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomeomorphic @ V0) @ V1)) @ ((c= @ (cconnected @ V0)) @ (cconnected @ V1))))))))
(THOMEOMORPHIC_COMPACTNESS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((chomeomorphic @ V0) @ V1)) @ ((c= @ (ccompact @ V0)) @ (ccompact @ V1))))))))
(THOMEOMORPHIC_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V0) @ V1)) @ V2)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V0 @ V3)) @ (V0 @ V4))))) @ ((c= @ V3) @ V4)))))))))) @ ((chomeomorphic @ V1) @ V2)))))))))
(THOMEOMORPHISM_COMPACT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V0)) @ V1)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4)))))))))) @ (c? @ (^[V3]: ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))))))))))))
(THOMEOMORPHIC_MINIMAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chomeomorphic @ V0) @ V1)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((cIN @ (V2 @ V4)) @ V1)) @ ((c= @ (V3 @ (V2 @ V4))) @ V4)))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ ((cIN @ (V3 @ V4)) @ V0)) @ ((c= @ (V2 @ (V3 @ V4))) @ V4)))))) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ V0)) @ ((ccontinuous_on @ V3) @ V1))))))))))))))
(THOMEOMORPHIC_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chomeomorphic @ V1) @ V0)) @ ((chomeomorphic @ V0) @ V1)))))))
(THOMEOMORPHISM_OF_SUBSETS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V4) @ V5))) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V1)) @ ((c= @ ((cIMAGE @ V4) @ V2)) @ V3))))) @ ((chomeomorphism @ ((c__comma__ @ V2) @ V3)) @ ((c__comma__ @ V4) @ V5))))))))))))))))
(Thomeomorphic,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chomeomorphic @ V0) @ V1)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((chomeomorphism @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))))))))))))
(Thomeomorphism,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((chomeomorphism @ ((c__comma__ @ V1) @ V3)) @ ((c__comma__ @ V0) @ V2))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ (V0 @ V4))) @ V4))))) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V0) @ V1)) @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((c= @ (V0 @ (V2 @ V4))) @ V4))))) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V2) @ V3)) @ V1)) @ ((ccontinuous_on @ V2) @ V3))))))))))))))))
(TCONTINUOUS_ON_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cclosed @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V0) @ V1)) @ ((ccontinuous_on @ V0) @ V2))))) @ ((ccontinuous_on @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TLIM_WITHIN_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((c--> @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ ((cUNION @ V0) @ V4)))) @ ((c/__caret__ @ (((c--> @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ V0))) @ (((c--> @ V1) @ V2) @ ((cwithin @ (cat @ V3)) @ V4)))))))))))))))
(TCLOSED_SEGMENT_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (clinear @ V0)) @ ((c= @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ (V0 @ V1)) @ (V0 @ V2))) @ cNIL))) @ ((cIMAGE @ V0) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))
(Tdiameter,(c! @ (^[V0]: ((c= @ (cdiameter @ V0)) @ (((cCOND @ ((c= @ V0) @ cEMPTY)) @ (creal_of_num @ (cNUMERAL @ c_0))) @ (csup @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V3) @ V0))) @ (cvector_norm @ ((cvector_sub @ V2) @ V3)))))))))))))))
(TCONTINUOUS_ON_INV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ ((co @ clift) @ V0)) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c~ @ ((c= @ (V0 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ ((ccontinuous_on @ ((co @ clift) @ ((co @ creal_inv) @ V0))) @ V1)))))))
(TCONTINUOUS_AT_INV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ ((co @ clift) @ V0)) @ (cat @ V1))) @ (c~ @ ((c= @ (V0 @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((ccontinuous @ ((co @ clift) @ ((co @ creal_inv) @ V0))) @ (cat @ V1))))))))
(TCONTINUOUS_ON_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ ((co @ clift) @ V0)) @ V2)) @ ((ccontinuous_on @ V1) @ V2))) @ ((ccontinuous_on @ (^[V3]: ((c% @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TCONTINUOUS_ON_VMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous_on @ ((co @ clift) @ V0)) @ V2)) @ ((ccontinuous_on @ (^[V3]: ((c% @ (V0 @ V3)) @ V1))) @ V2)))))))))
(TDISTANCE_ATTAINS_SUP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (cdistance @ ((c__comma__ @ V1) @ V3))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))))))))))))
(TCONTINUOUS_ON_LIFT_NORM,(c! @ (^[V0]: ((ccontinuous_on @ ((co @ clift) @ cvector_norm)) @ V0))))
(TCONTINUOUS_ON_LIFT_RANGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous_on @ ((co @ clift) @ V1)) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V5) @ V2))) @ V4))) @ ((creal_lt @ (creal_abs @ ((creal_sub @ (V1 @ V5)) @ (V1 @ V2)))) @ V3)))))))))))))))))))
(TCONTINUOUS_AT_LIFT_RANGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous @ ((co @ clift) @ V0)) @ (cat @ V1))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ V4) @ V1))) @ V3)) @ ((creal_lt @ (creal_abs @ ((creal_sub @ (V0 @ V4)) @ (V0 @ V1)))) @ V2))))))))))))))))
(TCONNECTED_EQ_CONNECTED_COMPONENTS_EQ,(c! @ (^[V0]: ((c= @ (cconnected @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ (ccomponents @ V0))) @ ((cIN @ V2) @ (ccomponents @ V0)))) @ ((c= @ V1) @ V2))))))))))
(TCOMPONENTS_EQ_EMPTY,(c! @ (^[V0]: ((c= @ ((c= @ (ccomponents @ V0)) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TCOMPONENTS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ (ccomponents @ V0))) @ ((cIN @ V2) @ (ccomponents @ V0)))) @ ((c= @ ((c= @ V1) @ V2)) @ (c~ @ ((c= @ ((cINTER @ V1) @ V2)) @ cEMPTY)))))))))))
(TCOMPONENTS_NONOVERLAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ (ccomponents @ V0))) @ ((cIN @ V2) @ (ccomponents @ V0)))) @ ((c= @ ((c= @ ((cINTER @ V1) @ V2)) @ cEMPTY)) @ (c~ @ ((c= @ V1) @ V2)))))))))))
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(TBOUNDED_LINEAR_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3)))))))) @ ((c= @ (cbounded @ ((cIMAGE @ V0) @ V1))) @ (cbounded @ V1))))))))
(TBOUNDED_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cbounded @ V0)) @ (cbounded @ ((cDIFF @ V0) @ V1))))))))
(TBOUNDED_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c__caret__/ @ (cbounded @ V0)) @ (cbounded @ V1))) @ (cbounded @ ((cINTER @ V0) @ V1))))))))
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(TLIM_WITHIN_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (((c--> @ V0) @ V1) @ ((cwithin @ (cat @ V2)) @ cEMPTY)))))))))
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(TFRONTIER_SUBSET_CLOSED,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ ((cSUBSET @ (cfrontier @ V0)) @ V0)))))
(TFRONTIER_CLOSED,(c! @ (^[V0]: (cclosed @ (cfrontier @ V0)))))
(Tfrontier,(c! @ (^[V0]: ((c= @ (cfrontier @ V0)) @ ((cDIFF @ (cclosure @ V0)) @ (cinterior @ V0))))))
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(TCLOSURE_EQ_EMPTY,(c! @ (^[V0]: ((c= @ ((c= @ (cclosure @ V0)) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
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(TCLOSURE_SUBSET,(c! @ (^[V0]: ((cSUBSET @ V0) @ (cclosure @ V0)))))
(TCLOSURE_CLOSURE,(c! @ (^[V0]: ((c= @ (cclosure @ (cclosure @ V0))) @ (cclosure @ V0)))))
(TCLOSURE_CLOSED,(c! @ (^[V0]: ((c==> @ (cclosed @ V0)) @ ((c= @ (cclosure @ V0)) @ V0)))))
(TCLOSURE_EQ,(c! @ (^[V0]: ((c= @ ((c= @ (cclosure @ V0)) @ V0)) @ (cclosed @ V0)))))
(TCLOSURE_HULL,(c! @ (^[V0]: ((c= @ (cclosure @ V0)) @ ((chull @ cclosed) @ V0)))))
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(TINTERIOR_INTERIOR,(c! @ (^[V0]: ((c= @ (cinterior @ (cinterior @ V0))) @ (cinterior @ V0)))))
(TOPEN_INTERIOR,(c! @ (^[V0]: (copen @ (cinterior @ V0)))))
(TINTERIOR_OPEN,(c! @ (^[V0]: ((c==> @ (copen @ V0)) @ ((c= @ (cinterior @ V0)) @ V0)))))
(TINTERIOR_EQ,(c! @ (^[V0]: ((c= @ ((c= @ (cinterior @ V0)) @ V0)) @ (copen @ V0)))))
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(TCLOSED_IN_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V0)) @ V2)) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V0))) @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ V2)))))))))
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(TOPEN_CONTAINS_BALL,(c! @ (^[V0]: ((c= @ (copen @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((cSUBSET @ (cball @ ((c__comma__ @ V1) @ V2))) @ V0)))))))))))
(TCLOSED_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V0)) @ (copen @ V1))) @ (cclosed @ ((cDIFF @ V0) @ V1))))))))
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(TOPEN_SUBOPEN,(c! @ (^[V0]: ((c= @ (copen @ V0)) @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ ((cIN @ V1) @ V2)) @ ((cSUBSET @ V2) @ V0))))))))))))
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(TLINEAR_COMPOSE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (clinear @ V0)) @ (clinear @ V1))) @ (clinear @ (^[V2]: ((cvector_add @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TLINEAR_COMPOSE_NEG,(c! @ (^[V0]: ((c==> @ (clinear @ V0)) @ (clinear @ (^[V1]: (cvector_neg @ (V0 @ V1))))))))
(TMATRIX_WLOG_INVERTIBLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (cinvertible @ V2)) @ (V0 @ V2))))) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (cclosed @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V3)))) @ (V0 @ ((cmatrix_add @ V2) @ ((c%% @ (cdrop @ V5)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ V5))))))))))))) @ (V0 @ V1)))))))
(TINDUCT_MATRIX_ROW_OPERATIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c= @ ((crow @ V3) @ V2)) @ (cvec @ (cNUMERAL @ c_0)))))) @ (V0 @ V2))))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V3) @ V4))))))) @ ((c= @ ((c$ @ ((c$ @ V2) @ V3)) @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ (V0 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V3) @ V4)))))))) @ (V0 @ (clambda @ (^[V5]: (clambda @ (^[V6]: ((c$ @ ((c$ @ V2) @ V5)) @ ((cswap @ ((c__comma__ @ V3) @ V4)) @ V6))))))))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V3) @ V4)))))))) @ (V0 @ (clambda @ (^[V6]: (((cCOND @ ((c= @ V6) @ V3)) @ ((cvector_add @ ((crow @ V3) @ V2)) @ ((c% @ V5) @ ((crow @ V4) @ V2)))) @ ((crow @ V6) @ V2)))))))))))))))))) @ (V0 @ V1)))))))
(TINDUCT_MATRIX_ELEMENTARY_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cmatrix_mul @ V2) @ V3)))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c= @ ((crow @ V3) @ V2)) @ (cvec @ (cNUMERAL @ c_0)))))) @ (V0 @ V2))))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V3) @ V4))))))) @ ((c= @ ((c$ @ ((c$ @ V2) @ V3)) @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ (V0 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V2) @ V3))))))) @ (V0 @ (clambda @ (^[V4]: (clambda @ (^[V5]: ((c$ @ ((c$ @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V4)) @ ((cswap @ ((c__comma__ @ V2) @ V3)) @ V5))))))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V2) @ V3))))))) @ (V0 @ (clambda @ (^[V4]: (clambda @ (^[V5]: (((cCOND @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V4) @ V2)) @ ((c= @ V5) @ V3))) @ ((c= @ V4) @ V5))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))))) @ (V0 @ V1)))))))
(TINDUCT_MATRIX_ELEMENTARY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((cmatrix_mul @ V2) @ V3)))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c= @ ((crow @ V3) @ V2)) @ (cvec @ (cNUMERAL @ c_0)))))) @ (V0 @ V2))))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ V4) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V3) @ V4))))))) @ ((c= @ ((c$ @ ((c$ @ V2) @ V3)) @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ (V0 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V2) @ V3))))))) @ (V0 @ (clambda @ (^[V4]: (clambda @ (^[V5]: ((c$ @ ((c$ @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V4)) @ ((cswap @ ((c__comma__ @ V2) @ V3)) @ V5))))))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V2) @ V3))))))) @ (V0 @ (clambda @ (^[V5]: (clambda @ (^[V6]: (((cCOND @ ((c/__caret__ @ ((c= @ V5) @ V2)) @ ((c= @ V6) @ V3))) @ V4) @ (((cCOND @ ((c= @ V5) @ V6)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))))))))))) @ (V0 @ V1)))))))
(TEXISTS_VECTOR_4,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (V0 @ (cvector @ ((cCONS @ V1) @ ((cCONS @ V2) @ ((cCONS @ V3) @ ((cCONS @ V4) @ cNIL))))))))))))))))))
(TFORALL_VECTOR_4,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (V0 @ (cvector @ ((cCONS @ V1) @ ((cCONS @ V2) @ ((cCONS @ V3) @ ((cCONS @ V4) @ cNIL))))))))))))))))))
(TEXISTS_VECTOR_3,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (V0 @ (cvector @ ((cCONS @ V1) @ ((cCONS @ V2) @ ((cCONS @ V3) @ cNIL)))))))))))))))
(TFORALL_VECTOR_3,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (V0 @ (cvector @ ((cCONS @ V1) @ ((cCONS @ V2) @ ((cCONS @ V3) @ cNIL)))))))))))))))
(TEXISTS_VECTOR_2,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c? @ (^[V2]: (V0 @ (cvector @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL))))))))))))
(TFORALL_VECTOR_2,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (c! @ (^[V2]: (V0 @ (cvector @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL))))))))))))
(TEXISTS_VECTOR_1,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (V0 @ (cvector @ ((cCONS @ V1) @ cNIL)))))))))
(TFORALL_VECTOR_1,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (V0 @ (cvector @ ((cCONS @ V1) @ cNIL)))))))))
(TCARD_EQ_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c=_c @ ((cPCROSS @ V0) @ V1)) @ ((c*_c @ V0) @ V1)))))))
(TFINITE_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ (cFINITE @ ((cPCROSS @ V0) @ V1))))))))
(TCOUNTABLE_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (cCOUNTABLE @ V1))) @ (cCOUNTABLE @ ((cPCROSS @ V0) @ V1))))))))
(TPCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cPCROSS @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((cpastecart @ V3) @ V4))))))))))))))
(TFINITE_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cFINITE @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))))))))))
(TCOUNTABLE_PCROSS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cCOUNTABLE @ ((cPCROSS @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (cCOUNTABLE @ V1))))))))))
(THAS_SIZE_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V0) @ V2)) @ ((cHAS_SIZE @ V1) @ V3))) @ ((cHAS_SIZE @ ((cPCROSS @ V0) @ V1)) @ ((c* @ V2) @ V3))))))))))))
(TPCROSS_UNIONS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cPCROSS @ V0) @ (cUNIONS @ V1))) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ ((cPCROSS @ V0) @ V3)))))))))))))
(TINTER_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cINTER @ ((cPCROSS @ V0) @ V2)) @ ((cPCROSS @ V1) @ V3))) @ ((cPCROSS @ ((cINTER @ V0) @ V1)) @ ((cINTER @ V2) @ V3))))))))))))
(TPCROSS_DIFF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cPCROSS @ ((cDIFF @ V0) @ V1)) @ V2)) @ ((cDIFF @ ((cPCROSS @ V0) @ V2)) @ ((cPCROSS @ V1) @ V2))))))))))
(TPCROSS_DIFF_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cPCROSS @ V0) @ ((cDIFF @ V1) @ V2))) @ ((cDIFF @ ((cPCROSS @ V0) @ V1)) @ ((cPCROSS @ V0) @ V2))))))))))
(TPCROSS_UNION_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cPCROSS @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cUNION @ ((cPCROSS @ V0) @ V2)) @ ((cPCROSS @ V1) @ V2))))))))))
(TPCROSS_UNION_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cPCROSS @ V0) @ ((cUNION @ V1) @ V2))) @ ((cUNION @ ((cPCROSS @ V0) @ V1)) @ ((cPCROSS @ V0) @ V2))))))))))
(TPCROSS_INTER_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cPCROSS @ ((cINTER @ V0) @ V1)) @ V2)) @ ((cINTER @ ((cPCROSS @ V0) @ V2)) @ ((cPCROSS @ V1) @ V2))))))))))
(TPCROSS_INTER_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cPCROSS @ V0) @ ((cINTER @ V1) @ V2))) @ ((cINTER @ ((cPCROSS @ V0) @ V1)) @ ((cPCROSS @ V0) @ V2))))))))))
(TPCROSS_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((cSUBSET @ V1) @ V3))) @ ((cSUBSET @ ((cPCROSS @ V0) @ V1)) @ ((cPCROSS @ V2) @ V3))))))))))))
(TSUBSET_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cSUBSET @ ((cPCROSS @ V0) @ V2)) @ ((cPCROSS @ V1) @ V3))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V2) @ cEMPTY)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((cSUBSET @ V2) @ V3))))))))))))))
(TPCROSS_EMPTY_conjunct1,(c! @ (^[V0]: ((c= @ ((cPCROSS @ cEMPTY) @ V0)) @ cEMPTY))))
(TPCROSS_EMPTY_conjunct0,(c! @ (^[V0]: ((c= @ ((cPCROSS @ V0) @ cEMPTY)) @ cEMPTY))))
(TPCROSS_EQ_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cPCROSS @ V0) @ V1)) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c= @ V1) @ cEMPTY))))))))
(TEXISTS_IN_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ ((cPCROSS @ V0) @ V1))) @ (V2 @ V3))))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (V2 @ ((cpastecart @ V3) @ V4))))))))))))))))
(TFORALL_IN_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cPCROSS @ V0) @ V1))) @ (V2 @ V3))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ (V2 @ ((cpastecart @ V3) @ V4)))))))))))))))
(TIN_ELIM_PASTECART_THM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ ((cpastecart @ V1) @ V2)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((V0 @ V4) @ V5)) @ ((cpastecart @ V4) @ V5)))))))))) @ ((V0 @ V1) @ V2)))))))))
(TEXISTS_PASTECART,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c? @ (^[V2]: (V0 @ ((cpastecart @ V1) @ V2))))))))))
(TFORALL_PASTECART,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (c! @ (^[V2]: (V0 @ ((cpastecart @ V1) @ V2))))))))))
(Tchar_RECURSION,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c= @ (V1 @ ((((((((cASCII @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9))) @ ((((((((V0 @ V2) @ V3) @ V4) @ V5) @ V6) @ V7) @ V8) @ V9)))))))))))))))))))))))
(TEXISTS_BOOL_THM,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (V0 @ V1)))) @ ((c__caret__/ @ (V0 @ cT)) @ (V0 @ cF))))))
(TFORALL_BOOL_THM,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (V0 @ V1)))) @ ((c/__caret__ @ (V0 @ cT)) @ (V0 @ cF))))))
(Tbool_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V0 @ cF)) @ (V0 @ cT))) @ (V0 @ V1)))))))
(Tedges,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cedges @ ((c__comma__ @ V2) @ ((c__comma__ @ V0) @ V1)))) @ V2))))))))
(TSUCHTHAT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (clevel @ ((csuchthat @ V1) @ V0))) @ (clevel @ V1)))))))
(TI_SET_EXISTS,(c! @ (^[V0]: ((c==> @ ((c<_c @ V0) @ cUNIV)) @ (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))))))))
(TMK_V_SET_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ (csetlevel @ V1))) @ ((c= @ (clevel @ (cmk_V @ ((c__comma__ @ (cPowerset @ V1)) @ ((cI_SET @ (csetlevel @ V1)) @ V0))))) @ (cPowerset @ V1))))))))
(TI_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c<_c @ V0) @ cUNIV)) @ ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c= @ ((cI_SET @ V0) @ V1)) @ ((cI_SET @ V0) @ V2))))) @ ((c= @ V1) @ V2))))))))))
(Tone_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (V0 @ cone)) @ (V0 @ V1)))))))
(TNOT,(c! @ (^[V0]: ((c= @ (cNOT @ V0)) @ (^[V1]: (c~ @ (V0 @ V1)))))))
(TCORRECT_WHILE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cWF @ V1)) @ ((c/__caret__ @ ((cIMPLIES @ V2) @ V0)) @ ((c/__caret__ @ ((cIMPLIES @ ((cAND @ (cNOT @ V3)) @ V0)) @ V5)) @ (c! @ (^[V6]: (((ccorrect @ ((cAND @ V0) @ ((cAND @ V3) @ (^[V7]: ((c= @ V6) @ V7))))) @ V4) @ ((cAND @ V0) @ (^[V7]: ((V1 @ V7) @ V6)))))))))) @ (((ccorrect @ V2) @ ((cWhile @ V3) @ V4)) @ V5)))))))))))))))
(TAWHILE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((cAWHILE @ V0) @ V1) @ V2) @ V3)) @ ((cWhile @ V2) @ V3)))))))))))
(TCORRECT_DO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cWF @ V1)) @ ((c/__caret__ @ ((cIMPLIES @ ((cAND @ V4) @ V0)) @ V2)) @ ((c/__caret__ @ ((cIMPLIES @ ((cAND @ (cNOT @ V4)) @ V0)) @ V5)) @ (c! @ (^[V6]: (((ccorrect @ ((cAND @ V2) @ (^[V7]: ((c= @ V6) @ V7)))) @ V3) @ ((cAND @ V0) @ (^[V7]: ((V1 @ V7) @ V6)))))))))) @ (((ccorrect @ V2) @ ((cDO @ V3) @ V4)) @ V5)))))))))))))))
(TADO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((cADO @ V0) @ V1) @ V2) @ V3)) @ ((cDO @ V2) @ V3)))))))))))
(TOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cOR @ V0) @ V1)) @ (^[V2]: ((c__caret__/ @ (V0 @ V2)) @ (V1 @ V2)))))))))
(TIMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIMP @ V0) @ V1)) @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2)))))))))
(TAND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cAND @ V0) @ V1)) @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ (V1 @ V2)))))))))
(TIMPLIES,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIMPLIES @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TVC_AWHILE_MEASURE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIMPLIES @ V0) @ V1)) @ ((c/__caret__ @ ((cIMPLIES @ ((cAND @ (cNOT @ V3)) @ V1)) @ V5)) @ (c! @ (^[V6]: (((ccorrect @ ((cAND @ V1) @ ((cAND @ V3) @ (^[V7]: ((c= @ V6) @ (V2 @ V7)))))) @ V4) @ ((cAND @ V1) @ (^[V7]: ((c< @ (V2 @ V7)) @ V6))))))))) @ (((ccorrect @ V0) @ ((((cAWHILE @ V1) @ (cMEASURE @ V2)) @ V3) @ V4)) @ V5)))))))))))))))
(TVC_ADO_MEASURE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIMPLIES @ ((cAND @ V4) @ V1)) @ V0)) @ ((c/__caret__ @ ((cIMPLIES @ ((cAND @ (cNOT @ V4)) @ V1)) @ V5)) @ (c! @ (^[V6]: (((ccorrect @ ((cAND @ V0) @ (^[V7]: ((c= @ V6) @ (V2 @ V7))))) @ V3) @ ((cAND @ V1) @ (^[V7]: ((c< @ (V2 @ V7)) @ V6))))))))) @ (((ccorrect @ V0) @ ((((cADO @ V1) @ (cMEASURE @ V2)) @ V3) @ V4)) @ V5)))))))))))))))
(TVC_SEQ_ASSIGN_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ ((co @ V0) @ V1)) @ V0)) @ ((c/__caret__ @ ((c= @ ((co @ V1) @ V1)) @ V1)) @ (((ccorrect @ ((cAND @ V0) @ (^[V4]: ((c= @ V4) @ (V1 @ V4))))) @ V2) @ V3)))) @ (((ccorrect @ V0) @ ((cSeq @ (cAssign @ V1)) @ V2)) @ V3)))))))))))
(Tcommand_INJECTIVE_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cWhile @ V0) @ V1)) @ ((cWhile @ V2) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V2)) @ ((c= @ V1) @ V3))))))))))))
(Tcommand_DISTINCT_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c~ @ ((c= @ (((cIte @ V0) @ V1) @ V2)) @ ((cWhile @ V3) @ V4))))))))))))))
(Tcommand_INJECTIVE_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c= @ ((c= @ (((cIte @ V0) @ V1) @ V2)) @ (((cIte @ V3) @ V4) @ V5))) @ ((c/__caret__ @ ((c= @ V0) @ V3)) @ ((c/__caret__ @ ((c= @ V1) @ V4)) @ ((c= @ V2) @ V5)))))))))))))))))
(Tcommand_DISTINCT_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c~ @ ((c= @ (cAssign @ V0)) @ ((cWhile @ V1) @ V2))))))))))
(Tcommand_DISTINCT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c~ @ ((c= @ (cAssign @ V0)) @ (((cIte @ V1) @ V2) @ V3))))))))))))
(Tcommand_INJECTIVE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cAssign @ V0)) @ (cAssign @ V1))) @ ((c= @ V0) @ V1)))))))
(Tcommand_DISTINCT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c~ @ ((c= @ (cAssign @ V0)) @ ((cSeq @ V1) @ V2))))))))))
(TKUHN_COUNTING_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (cFINITE @ V4)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ (V3 @ V6))) @ ((c= @ (cCARD @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V4)) @ ((V0 @ V6) @ V8))) @ V8))))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ (c~ @ (V3 @ V6)))) @ ((c= @ (cCARD @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V4)) @ ((V0 @ V6) @ V8))) @ V8))))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V4)) @ (V5 @ V6))) @ ((c= @ (cCARD @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V1)) @ ((c/__caret__ @ ((V0 @ V8) @ V6)) @ (V2 @ V8)))) @ V8))))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V4)) @ (c~ @ (V5 @ V6)))) @ ((c__caret__/ @ ((c= @ (cCARD @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V1)) @ ((c/__caret__ @ ((V0 @ V8) @ V6)) @ (V2 @ V8)))) @ V8))))))) @ (cNUMERAL @ c_0))) @ ((c= @ (cCARD @ (cGSPEC @ (^[V7]: (c? @ (^[V8]: (((cSETSPEC @ V7) @ ((c/__caret__ @ ((cIN @ V8) @ V1)) @ ((c/__caret__ @ ((V0 @ V8) @ V6)) @ (V2 @ V8)))) @ V8))))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))) @ ((c==> @ (cODD @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((c/__caret__ @ (V2 @ V7)) @ (V3 @ V7)))) @ V7)))))))) @ (cODD @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V4)) @ (V5 @ V7))) @ V7))))))))))))))))))))))
(Ttermini,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (ctermini @ ((c__comma__ @ V0) @ ((c__comma__ @ V1) @ V2)))) @ V2))))))))
(Tvertices,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cvertices @ ((c__comma__ @ V0) @ ((c__comma__ @ V2) @ V1)))) @ V2))))))))
(TITERATE_IMAGE_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V0)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V4) @ V5))) @ ((c= @ (V3 @ V4)) @ (V3 @ V5)))))) @ ((c= @ (V2 @ (V3 @ V4))) @ (cneutral @ V0))))))))) @ ((c= @ (((citerate @ V0) @ ((cIMAGE @ V3) @ V1)) @ V2)) @ (((citerate @ V0) @ V1) @ ((co @ V2) @ V3))))))))))))))
(TITERATE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V0)) @ ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c= @ (V3 @ V4)) @ (V3 @ V5))))) @ ((c= @ V4) @ V5))))))) @ ((c= @ (((citerate @ V0) @ ((cIMAGE @ V3) @ V1)) @ V2)) @ (((citerate @ V0) @ V1) @ ((co @ V2) @ V3))))))))))))))
(TITERATE_ITERATE_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V0)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ (cFINITE @ (V2 @ V4))))))) @ ((c= @ (((citerate @ V0) @ V1) @ (^[V4]: (((citerate @ V0) @ (V2 @ V4)) @ (V3 @ V4))))) @ (((citerate @ V0) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cIN @ V6) @ (V2 @ V5)))) @ ((c__comma__ @ V5) @ V6))))))))) @ (cGABS @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((cGEQ @ (V4 @ ((c__comma__ @ V5) @ V6))) @ ((V3 @ V5) @ V6)))))))))))))))))))))
(To_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((co @ V0) @ ((co @ V1) @ V2))) @ ((co @ ((co @ V0) @ V1)) @ V2)))))))))
(TITERATE_RELATED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ ((V0 @ (cneutral @ V1)) @ (cneutral @ V1))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((V0 @ V2) @ V4)) @ ((V0 @ V3) @ V5))) @ ((V0 @ ((V1 @ V2) @ V3)) @ ((V1 @ V4) @ V5))))))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cFINITE @ V4)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V4)) @ ((V0 @ (V2 @ V5)) @ (V3 @ V5))))))) @ ((V0 @ (((citerate @ V1) @ V4) @ V2)) @ (((citerate @ V1) @ V4) @ V3))))))))))))))))
(TWF_MEASURE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cWF @ V0)) @ (cWF @ (^[V2]: (^[V3]: ((V0 @ (V1 @ V2)) @ (V1 @ V3)))))))))))
(TITERATE_CLAUSES_GEN_conjunct0,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ (c! @ (^[V1]: ((c= @ (((citerate @ V0) @ cEMPTY) @ V1)) @ (cneutral @ V0))))))))
(TITERATE_CLAUSES_GEN_conjunct1,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cmonoidal @ V0)) @ (cFINITE @ (((csupport @ V0) @ V1) @ V3)))) @ ((c= @ (((citerate @ V0) @ ((cINSERT @ V2) @ V3)) @ V1)) @ (((cCOND @ ((cIN @ V2) @ V3)) @ (((citerate @ V0) @ V3) @ V1)) @ ((V0 @ (V1 @ V2)) @ (((citerate @ V0) @ V3) @ V1)))))))))))))))
(TITERATE_BIJECTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V0)) @ ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((cIN @ (V3 @ V4)) @ V1))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ (c?! @ (^[V5]: ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c= @ (V3 @ V5)) @ V4))))))))) @ ((c= @ (((citerate @ V0) @ V1) @ V2)) @ (((citerate @ V0) @ V1) @ ((co @ V2) @ V3))))))))))))))
(TITERATE_SING,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cmonoidal @ V0)) @ ((c= @ (((citerate @ V0) @ ((cINSERT @ V2) @ cEMPTY)) @ V1)) @ (V1 @ V2))))))))))
(TADMISSIBLE_SUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((((cadmissible @ V0) @ (^[V6]: (cGABS @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((cGEQ @ (V7 @ ((c__comma__ @ V8) @ V9))) @ ((c/__caret__ @ ((c<= @ (V3 @ V9)) @ V8)) @ ((c/__caret__ @ ((c<= @ V8) @ (V4 @ V9))) @ ((V1 @ V6) @ V9)))))))))))) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ (V2 @ V8))))))))) @ (^[V6]: (cGABS @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((cGEQ @ (V7 @ ((c__comma__ @ V8) @ V9))) @ (((V5 @ V6) @ V9) @ V8))))))))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: ((csum @ ((c.. @ (V3 @ V7)) @ (V4 @ V7))) @ ((V5 @ V6) @ V7)))))))))))))))))))
(TADMISSIBLE_NSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((((cadmissible @ V0) @ (^[V6]: (cGABS @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((cGEQ @ (V7 @ ((c__comma__ @ V8) @ V9))) @ ((c/__caret__ @ ((c<= @ (V3 @ V9)) @ V8)) @ ((c/__caret__ @ ((c<= @ V8) @ (V4 @ V9))) @ ((V1 @ V6) @ V9)))))))))))) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ (V2 @ V8))))))))) @ (^[V6]: (cGABS @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((cGEQ @ (V7 @ ((c__comma__ @ V8) @ V9))) @ (((V5 @ V6) @ V9) @ V8))))))))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: ((cnsum @ ((c.. @ (V3 @ V7)) @ (V4 @ V7))) @ ((V5 @ V6) @ V7)))))))))))))))))))
(TINV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cINV @ V0) @ V2) @ V1)) @ ((V0 @ V1) @ V2)))))))))
(TITERATE_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ (V0 @ (cneutral @ V1))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ (V0 @ ((V1 @ V2) @ V3))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V3)) @ (c~ @ ((c= @ (V2 @ V4)) @ (cneutral @ V1))))) @ (V0 @ (V2 @ V4)))))) @ (V0 @ (((citerate @ V1) @ V3) @ V2))))))))))))))
(TUNIFORM_LIM_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V7)) @ ((ceventually @ (^[V8]: (c! @ (^[V9]: ((c==> @ (V0 @ V9)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((V1 @ V9) @ V8)) @ (V3 @ V9)))) @ V7)))))) @ V6))))) @ (c! @ (^[V7]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V7)) @ ((ceventually @ (^[V8]: (c! @ (^[V9]: ((c==> @ (V0 @ V9)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((V2 @ V9) @ V8)) @ (V4 @ V9)))) @ V7)))))) @ V6)))))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((ceventually @ (^[V7]: (c! @ (^[V8]: ((c==> @ (V0 @ V8)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cvector_sub @ ((V1 @ V8) @ V7)) @ ((V2 @ V8) @ V7))) @ ((cvector_sub @ (V3 @ V8)) @ (V4 @ V8))))) @ V5)))))) @ V6))))))))))))))))))
(TUNIFORM_LIM_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (c! @ (^[V7]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V7)) @ ((ceventually @ (^[V8]: (c! @ (^[V9]: ((c==> @ (V0 @ V9)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((V1 @ V9) @ V8)) @ (V3 @ V9)))) @ V7)))))) @ V6))))) @ (c! @ (^[V7]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V7)) @ ((ceventually @ (^[V8]: (c! @ (^[V9]: ((c==> @ (V0 @ V9)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((V2 @ V9) @ V8)) @ (V4 @ V9)))) @ V7)))))) @ V6)))))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((ceventually @ (^[V7]: (c! @ (^[V8]: ((c==> @ (V0 @ V8)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cvector_add @ ((V1 @ V8) @ V7)) @ ((V2 @ V8) @ V7))) @ ((cvector_add @ (V3 @ V8)) @ (V4 @ V8))))) @ V5)))))) @ V6))))))))))))))))))
(TEVENTUALLY_FORALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ ((ceventually @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((V1 @ V4) @ V3)))))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((ceventually @ (V1 @ V3)) @ V2)))))))))))))
(TFORALL_EVENTUALLY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY)))) @ ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((ceventually @ (V1 @ V3)) @ V2))))) @ ((ceventually @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((V1 @ V4) @ V3)))))) @ V2))))))))))
(TCONTINUOUS_LIFT_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((ccontinuous @ (^[V4]: (clift @ ((V1 @ V4) @ V3)))) @ V2)))))) @ ((ccontinuous @ (^[V3]: (clift @ ((cproduct @ V0) @ (V1 @ V3))))) @ V2)))))))))
(TCARD_LT_TOTAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((c=_c @ V1) @ V0)) @ ((c__caret__/ @ ((c<_c @ V1) @ V0)) @ ((c<_c @ V0) @ V1))))))))
(TCARD_LTE_TOTAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c__caret__/ @ ((c<_c @ V1) @ V0)) @ ((c<=_c @ V0) @ V1)))))))
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(TSUM_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((csum @ V1) @ (^[V4]: (((cCOND @ (V2 @ V4)) @ (V0 @ V4)) @ (V3 @ V4))))) @ ((creal_add @ ((csum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (V2 @ V5))) @ V5)))))) @ V0)) @ ((csum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (c~ @ (V2 @ V5)))) @ V5)))))) @ V3)))))))))))))
(Tmultiset_tybij_conjunct1,(c! @ (^[V0]: ((c= @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c~ @ ((c= @ (V0 @ V2)) @ (cNUMERAL @ c_0)))) @ V2))))))) @ ((c= @ (cmultiplicity @ (cmultiset @ V0))) @ V0)))))
(TWF_MEASURE,(c! @ (^[V0]: (cWF @ (cMEASURE @ V0)))))
(TNSUM_BOUND_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c<= @ (V0 @ V3)) @ V2))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c< @ (V0 @ V3)) @ V2))))))) @ ((c< @ ((cnsum @ V1) @ V0)) @ ((c* @ (cCARD @ V1)) @ V2))))))))))
(TNSUM_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c<= @ (V0 @ V3)) @ V2)))))) @ ((c<= @ ((cnsum @ V1) @ V0)) @ ((c* @ (cCARD @ V1)) @ V2))))))))))
(TNSUM_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c<= @ (V0 @ V3)) @ (V2 @ V3)))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c< @ (V0 @ V3)) @ (V2 @ V3)))))))) @ ((c< @ ((cnsum @ V1) @ V0)) @ ((cnsum @ V1) @ V2))))))))))
(TNSUM_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cnsum @ V1) @ (^[V4]: (((cCOND @ (V2 @ V4)) @ (V0 @ V4)) @ (V3 @ V4))))) @ ((c+ @ ((cnsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (V2 @ V5))) @ V5)))))) @ V0)) @ ((cnsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (c~ @ (V2 @ V5)))) @ V5)))))) @ V3)))))))))))))
(TWF_INT_MEASURE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ (V0 @ V3))))) @ (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((cint_lt @ (V0 @ V4)) @ (V0 @ V3))) @ (V1 @ V4))))) @ (V1 @ V3)))))) @ (V1 @ V2)))))))))
(TINTERS_OVER_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cINTERS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ (cUNIONS @ (V0 @ V3))))))))) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((cIN @ (V3 @ V4)) @ (V0 @ V4)))))) @ (cINTERS @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ V1)) @ (V3 @ V5)))))))))))))))))))
(TOPEN_EXISTS,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (copen @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((V0 @ V1) @ V3)) @ V3))))))))) @ (copen @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c? @ (^[V3]: ((V0 @ V3) @ V2)))) @ V2))))))))))
(TCLOSED_FORALL,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (cclosed @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((V0 @ V1) @ V3)) @ V3))))))))) @ (cclosed @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((V0 @ V3) @ V2)))) @ V2))))))))))
(TCONTINUOUS_UNIFORM_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V1))) @ ((c/__caret__ @ ((ceventually @ (^[V4]: ((ccontinuous_on @ (V0 @ V4)) @ V3))) @ V1)) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((ceventually @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V3)) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((V0 @ V5) @ V6)) @ (V2 @ V6)))) @ V4)))))) @ V1))))))) @ ((ccontinuous_on @ V2) @ V3)))))))))))
(THAS_INTEGRAL_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ (((chas_integral @ (V0 @ V4)) @ (V2 @ V4)) @ V3)))))) @ (((chas_integral @ (^[V4]: ((cvsum @ V1) @ (^[V5]: ((V0 @ V5) @ V4))))) @ ((cvsum @ V1) @ V2)) @ V3)))))))))))
(TWF_INT_MEASURE_2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((cint_le @ (cint_of_num @ (cNUMERAL @ c_0))) @ ((V0 @ V4) @ V5))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((cint_lt @ ((V0 @ V6) @ V7)) @ ((V0 @ V4) @ V5))) @ ((V1 @ V6) @ V7))))))) @ ((V1 @ V4) @ V5)))))))) @ ((V1 @ V2) @ V3)))))))))))
(TLIM_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ (((c--> @ (V0 @ V4)) @ (V2 @ V4)) @ V3)))))) @ (((c--> @ (^[V4]: ((cvsum @ V1) @ (^[V5]: ((V0 @ V5) @ V4))))) @ ((cvsum @ V1) @ V2)) @ V3)))))))))))
(Tprod_tybij_conjunct1,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (c? @ (^[V2]: ((c= @ V0) @ ((cmk_pair @ V1) @ V2))))))) @ ((c= @ (cREP_prod @ (cABS_prod @ V0))) @ V0)))))
(TSWAP_EXISTS_THM,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (c? @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TUNIQUE_SKOLEM_THM,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c?! @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (c?! @ (^[V1]: (c! @ (^[V2]: ((V0 @ V2) @ (V1 @ V2))))))))))
(TUNIQUE_SKOLEM_ALT,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c?! @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((V0 @ V2) @ V3)) @ ((c= @ (V1 @ V2)) @ V3))))))))))))
(TSKOLEM_THM,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((V0 @ V2) @ (V1 @ V2))))))))))
(TSWAP_FORALL_THM,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((V0 @ V1) @ V2)))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((V0 @ V2) @ V1)))))))))
(TCARD_LE_RELATIONAL_FULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((V0 @ V4) @ V3)))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ ((V0 @ V3) @ V4)) @ ((V0 @ V3) @ V5)))))) @ ((c= @ V4) @ V5)))))))))) @ ((c<=_c @ V1) @ V2)))))))))
(TMONO_ALL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((cALL2 @ V0) @ V2) @ V3)) @ ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ (((cALL2 @ V1) @ V2) @ V3))))))))))))
(TCARD_LE_RELATIONAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((V0 @ V2) @ V3)) @ ((V0 @ V2) @ V4)))) @ ((c= @ V3) @ V4))))))))) @ ((c<=_c @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((V0 @ V4) @ V3))))) @ V3)))))) @ V1)))))))
(TINJ_INVERSE2,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((c= @ ((V0 @ V1) @ V2)) @ ((V0 @ V3) @ V4))) @ ((c/__caret__ @ ((c= @ V1) @ V3)) @ ((c= @ V2) @ V4)))))))))))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c/__caret__ @ ((c= @ (V1 @ ((V0 @ V3) @ V4))) @ V3)) @ ((c= @ (V2 @ ((V0 @ V3) @ V4))) @ V4))))))))))))))
(Tpair_RECURSION,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (V1 @ ((c__comma__ @ V2) @ V3))) @ ((V0 @ V2) @ V3)))))))))))
(TUNCURRY_DEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cUNCURRY @ V0) @ ((c__comma__ @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TFINREC_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((((cFINREC @ V0) @ V3) @ V1) @ V2) @ (cNUMERAL @ c_0))) @ ((c/__caret__ @ ((c= @ V1) @ cEMPTY)) @ ((c= @ V2) @ V3))))))))))))
(TFINITE_RECURSION_DELETE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c~ @ ((c= @ V2) @ V3))) @ ((c= @ ((V0 @ V2) @ ((V0 @ V3) @ V4))) @ ((V0 @ V3) @ ((V0 @ V2) @ V4))))))))))) @ ((c= @ (((cITSET @ V0) @ cEMPTY) @ V1)) @ V1)))))))
(TFINITE_RECURSION_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c~ @ ((c= @ V2) @ V3))) @ ((c= @ ((V0 @ V2) @ ((V0 @ V3) @ V4))) @ ((V0 @ V3) @ ((V0 @ V2) @ V4))))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cFINITE @ V3)) @ ((c= @ (((cITSET @ V0) @ ((cINSERT @ V2) @ V3)) @ V1)) @ (((cCOND @ ((cIN @ V2) @ V3)) @ (((cITSET @ V0) @ V3) @ V1)) @ ((V0 @ V2) @ (((cITSET @ V0) @ V3) @ V1)))))))))))))))
(TFINITE_RECURSION_DELETE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c~ @ ((c= @ V2) @ V3))) @ ((c= @ ((V0 @ V2) @ ((V0 @ V3) @ V4))) @ ((V0 @ V3) @ ((V0 @ V2) @ V4))))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cFINITE @ V3)) @ ((c= @ (((cITSET @ V0) @ V3) @ V1)) @ (((cCOND @ ((cIN @ V2) @ V3)) @ ((V0 @ V2) @ (((cITSET @ V0) @ ((cDELETE @ V3) @ V2)) @ V1))) @ (((cITSET @ V0) @ ((cDELETE @ V3) @ V2)) @ V1))))))))))))))
(TFINREC_EXISTS_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V2)) @ (c? @ (^[V3]: (c? @ (^[V4]: (((((cFINREC @ V0) @ V1) @ V2) @ V3) @ V4)))))))))))))
(TFINREC_UNIQUE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ (c~ @ ((c= @ V7) @ V8))) @ ((c= @ ((V0 @ V7) @ ((V0 @ V8) @ V9))) @ ((V0 @ V8) @ ((V0 @ V7) @ V9))))))))))) @ ((c==> @ ((c/__caret__ @ (((((cFINREC @ V0) @ V1) @ V2) @ V3) @ V5)) @ (((((cFINREC @ V0) @ V1) @ V2) @ V4) @ V6))) @ ((c/__caret__ @ ((c= @ V3) @ V4)) @ ((c= @ V5) @ V6)))))))))))))))))))
(TSYMMETRY_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((((V0 @ V5) @ V6) @ V7) @ V8)) @ ((((V0 @ V5) @ V6) @ V8) @ V7))))))))))) @ (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V5) @ V6))) @ ((c/__caret__ @ (c~ @ ((c= @ V7) @ V8))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V5) @ V7)) @ ((c= @ V6) @ V8))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V5) @ V7)) @ (c~ @ ((c= @ V6) @ V8)))) @ ((c__caret__/ @ ((c/__caret__ @ (c~ @ ((c= @ V5) @ V7))) @ ((c= @ V6) @ V8))) @ ((c/__caret__ @ (c~ @ ((c= @ V5) @ V7))) @ ((c/__caret__ @ (c~ @ ((c= @ V5) @ V8))) @ ((c/__caret__ @ (c~ @ ((c= @ V6) @ V7))) @ (c~ @ ((c= @ V6) @ V8))))))))))) @ ((((V0 @ V5) @ V6) @ V7) @ V8)))))))))))) @ ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ (c~ @ ((c= @ V3) @ V4)))) @ ((((V0 @ V1) @ V2) @ V3) @ V4))))))))))))))
(TKOENIG_LEMMA,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cTREE @ V0)) @ ((c/__caret__ @ (cLF @ V0)) @ (cSN @ V0)))) @ (cFINITE @ (cFL @ V0))))))
(TNEWMAN_LEMMA,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cSN @ V0)) @ (cWCR @ V0))) @ (cCR @ (cRTC @ V0))))))
(TWF_FINITE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (c! @ (^[V1]: (c~ @ ((V0 @ V1) @ V1))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V3))) @ ((V0 @ V1) @ V3))))))))) @ (c! @ (^[V1]: (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((V0 @ V3) @ V1)) @ V3))))))))))) @ (cWF @ V0)))))
(TNORM_CR,(c! @ (^[V0]: ((c==> @ (cWN @ V0)) @ ((c= @ (cCR @ (cRTC @ V0))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cRTC @ V0) @ V1) @ V2)) @ ((c/__caret__ @ ((cNORMAL @ V0) @ V2)) @ ((c/__caret__ @ (((cRTC @ V0) @ V1) @ V3)) @ ((cNORMAL @ V0) @ V3))))) @ ((c= @ V2) @ V3)))))))))))))
(TTREE_FL,(c! @ (^[V0]: ((c==> @ (cTREE @ V0)) @ (c? @ (^[V1]: ((c= @ (cFL @ V0)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (((cRTC @ V0) @ V1) @ V3)) @ V3))))))))))))
(TSN_WN,(c! @ (^[V0]: ((c==> @ (cSN @ V0)) @ (cWN @ V0)))))
(TLF_SN_BOUND,(c! @ (^[V0]: ((c==> @ (cLF @ V0)) @ ((c= @ (cSN @ V0)) @ (c! @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((cRELPOW @ V3) @ V0) @ V1) @ V4)) @ ((c<= @ V3) @ V2)))))))))))))))
(TTC_CR,(c! @ (^[V0]: ((c==> @ (cCR @ V0)) @ (cCR @ (cTC @ V0))))))
(TRTC_CR,(c! @ (^[V0]: ((c==> @ (cCR @ V0)) @ (cCR @ (cRTC @ V0))))))
(TRC_CR,(c! @ (^[V0]: ((c==> @ (cCR @ V0)) @ (cCR @ (cRC @ V0))))))
(TWF_REC_WF,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: ((c==> @ ((V0 @ V5) @ V4)) @ ((c= @ (V2 @ V5)) @ (V3 @ V5)))))) @ ((c= @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c= @ (V2 @ V3)) @ ((V1 @ V2) @ V3)))))))))) @ (cWF @ V0)))))
(TWF_UREC_WF,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: ((c==> @ ((V0 @ V5) @ V4)) @ ((c= @ (V2 @ V5)) @ (V3 @ V5)))))) @ ((c= @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c= @ (V2 @ V4)) @ ((V1 @ V2) @ V4))))) @ (c! @ (^[V4]: ((c= @ (V3 @ V4)) @ ((V1 @ V3) @ V4)))))) @ ((c= @ V2) @ V3)))))))))) @ (cWF @ V0)))))
(TBOUND_SN,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((cRELPOW @ V3) @ V0) @ V1) @ V4)) @ ((c<= @ V3) @ V2))))))))))) @ (cSN @ V0)))))
(TQSORT_conjunct0,(c! @ (^[V0]: ((c= @ ((cQSORT @ V0) @ cNIL)) @ cNIL))))
(TTC_IDEMP,(c! @ (^[V0]: ((c= @ (cTC @ (cTC @ V0))) @ (cTC @ V0)))))
(TTC_RC,(c! @ (^[V0]: ((c= @ (cTC @ (cRC @ V0))) @ (cRC @ (cTC @ V0))))))
(TSTC_IDEMP,(c! @ (^[V0]: ((c= @ (cSTC @ (cSTC @ V0))) @ (cSTC @ V0)))))
(TSTC,(c! @ (^[V0]: ((c= @ (cSTC @ V0)) @ (cTC @ (cSC @ V0))))))
(TSC_IDEMP,(c! @ (^[V0]: ((c= @ (cSC @ (cSC @ V0))) @ (cSC @ V0)))))
(TSC_RC,(c! @ (^[V0]: ((c= @ (cSC @ (cRC @ V0))) @ (cRC @ (cSC @ V0))))))
(TRTC_IDEMP,(c! @ (^[V0]: ((c= @ (cRTC @ (cRTC @ V0))) @ (cRTC @ V0)))))
(TRTC,(c! @ (^[V0]: ((c= @ (cRTC @ V0)) @ (cRC @ (cTC @ V0))))))
(TRSTC_IDEMP,(c! @ (^[V0]: ((c= @ (cRSTC @ (cRSTC @ V0))) @ (cRSTC @ V0)))))
(TRSTC,(c! @ (^[V0]: ((c= @ (cRSTC @ V0)) @ (cRC @ (cTC @ (cSC @ V0)))))))
(TRSC_IDEMP,(c! @ (^[V0]: ((c= @ (cRSC @ (cRSC @ V0))) @ (cRSC @ V0)))))
(TRSC,(c! @ (^[V0]: ((c= @ (cRSC @ V0)) @ (cRC @ (cSC @ V0))))))
(TRC_TC,(c! @ (^[V0]: ((c= @ (cRC @ (cTC @ V0))) @ (cTC @ (cRC @ V0))))))
(TRC_SC,(c! @ (^[V0]: ((c= @ (cRC @ (cSC @ V0))) @ (cSC @ (cRC @ V0))))))
(TRC_IDEMP,(c! @ (^[V0]: ((c= @ (cRC @ (cRC @ V0))) @ (cRC @ V0)))))
(TPAIRWISE_conjunct0,(c! @ (^[V0]: ((c= @ ((cPAIRWISE @ V0) @ cNIL)) @ cT))))
(TTC_CLOSED,(c! @ (^[V0]: ((c= @ ((c= @ (cTC @ V0)) @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V3))) @ ((V0 @ V1) @ V3))))))))))))
(TSTC_CLOSED,(c! @ (^[V0]: ((c= @ ((c= @ (cSTC @ V0)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V3))) @ ((V0 @ V1) @ V3)))))))))))))
(TSC_CLOSED,(c! @ (^[V0]: ((c= @ ((c= @ (cSC @ V0)) @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TRTC_CLOSED,(c! @ (^[V0]: ((c= @ ((c= @ (cRTC @ V0)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((V0 @ V1) @ V1)))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V3))) @ ((V0 @ V1) @ V3)))))))))))))
(TRSTC_CLOSED,(c! @ (^[V0]: ((c= @ ((c= @ (cRSTC @ V0)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((V0 @ V1) @ V1)))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V3))) @ ((V0 @ V1) @ V3))))))))))))))
(TRSC_CLOSED,(c! @ (^[V0]: ((c= @ ((c= @ (cRSC @ V0)) @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((V0 @ V1) @ V1)))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1)))))))))))
(TRC_CLOSED,(c! @ (^[V0]: ((c= @ ((c= @ (cRC @ V0)) @ V0)) @ (c! @ (^[V1]: ((V0 @ V1) @ V1)))))))
(TCR_NORM,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ (cWN @ V0)) @ (cCR @ (cRTC @ V0)))) @ (c! @ (^[V1]: (c?! @ (^[V2]: ((c/__caret__ @ (((cRTC @ V0) @ V1) @ V2)) @ ((cNORMAL @ V0) @ V2))))))))))
(TWN_TC,(c! @ (^[V0]: ((c= @ (cWN @ (cTC @ V0))) @ (cWN @ V0)))))
(TWN,(c! @ (^[V0]: ((c= @ (cWN @ V0)) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (((cRTC @ V0) @ V1) @ V2)) @ ((cNORMAL @ V0) @ V2))))))))))
(TWF_TC,(c! @ (^[V0]: ((c= @ (cWF @ (cTC @ V0))) @ (cWF @ V0)))))
(TWFP_WF,(c! @ (^[V0]: ((c= @ (cWF @ V0)) @ ((c= @ (cWFP @ V0)) @ cUNIV)))))
(TWF_DCHAIN,(c! @ (^[V0]: ((c= @ (cWF @ V0)) @ (c~ @ (c? @ (^[V1]: (c! @ (^[V2]: ((V0 @ (V1 @ (cSUC @ V2))) @ (V1 @ V2)))))))))))
(TWF,(c! @ (^[V0]: ((c= @ (cWF @ V0)) @ (c! @ (^[V1]: ((c==> @ (c? @ (^[V2]: (V1 @ V2)))) @ (c? @ (^[V2]: ((c/__caret__ @ (V1 @ V2)) @ (c! @ (^[V3]: ((c==> @ ((V0 @ V3) @ V2)) @ (c~ @ (V1 @ V3)))))))))))))))
(TWF_IND,(c! @ (^[V0]: ((c= @ (cWF @ V0)) @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((V0 @ V3) @ V2)) @ (V1 @ V3))))) @ (V1 @ V2))))) @ (c! @ (^[V2]: (V1 @ V2))))))))))
(TWF_EQ,(c! @ (^[V0]: ((c= @ (cWF @ V0)) @ (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (V1 @ V2)))) @ (c? @ (^[V2]: ((c/__caret__ @ (V1 @ V2)) @ (c! @ (^[V3]: ((c==> @ ((V0 @ V3) @ V2)) @ (c~ @ (V1 @ V3)))))))))))))))
(TWCR,(c! @ (^[V0]: ((c= @ (cWCR @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V0 @ V1) @ V2)) @ ((V0 @ V1) @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ (((cRTC @ V0) @ V2) @ V4)) @ (((cRTC @ V0) @ V3) @ V4)))))))))))))))
(TTREE,(c! @ (^[V0]: ((c= @ (cTREE @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: (c~ @ (((cTC @ V0) @ V1) @ V1))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ (cFL @ V0))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (cFL @ V0))) @ ((c__caret__/ @ ((c= @ V2) @ V1)) @ ((c/__caret__ @ (((cTC @ V0) @ V1) @ V2)) @ (c?! @ (^[V3]: ((V0 @ V3) @ V2))))))))))))))))
(TSN_TC,(c! @ (^[V0]: ((c= @ (cSN @ (cTC @ V0))) @ (cSN @ V0)))))
(TSN,(c! @ (^[V0]: ((c= @ (cSN @ V0)) @ (c~ @ (c? @ (^[V1]: (c! @ (^[V2]: ((V0 @ (V1 @ V2)) @ (V1 @ (cSUC @ V2))))))))))))
(TSN_WF,(c! @ (^[V0]: ((c= @ (cSN @ V0)) @ (cWF @ (cINV @ V0))))))
(TSN_NOETHERIAN,(c! @ (^[V0]: ((c= @ (cSN @ V0)) @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((V0 @ V2) @ V3)) @ (V1 @ V3))))) @ (V1 @ V2))))) @ (c! @ (^[V2]: (V1 @ V2))))))))))
(TSN_PRESERVE,(c! @ (^[V0]: ((c= @ (cSN @ V0)) @ (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (V1 @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (V1 @ V3)) @ ((V0 @ V2) @ V3)))))))) @ (c~ @ (c? @ (^[V2]: (V1 @ V2)))))))))))
(TLF,(c! @ (^[V0]: ((c= @ (cLF @ V0)) @ (c! @ (^[V1]: (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((V0 @ V1) @ V3)) @ V3))))))))))))
(TSTC_CR,(c! @ (^[V0]: ((c= @ (cCR @ (cRTC @ V0))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cRSTC @ V0) @ V1) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (((cRTC @ V0) @ V1) @ V3)) @ (((cRTC @ V0) @ V2) @ V3)))))))))))))
(TCR,(c! @ (^[V0]: ((c= @ (cCR @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V0 @ V1) @ V2)) @ ((V0 @ V1) @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ ((V0 @ V2) @ V4)) @ ((V0 @ V3) @ V4)))))))))))))))
(Tnet_tybij_conjunct1,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c__caret__/ @ (c! @ (^[V3]: ((c==> @ ((V0 @ V3) @ V1)) @ ((V0 @ V3) @ V2))))) @ (c! @ (^[V3]: ((c==> @ ((V0 @ V3) @ V2)) @ ((V0 @ V3) @ V1)))))))))) @ ((c= @ (cnetord @ (cmk_net @ V0))) @ V0)))))
(TSYM_ALT,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TCANTOR,(c! @ (^[V0]: (c~ @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))))))
(TEQUIVALENCE_UNIFORM_PARTITION_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((V0 @ V3) @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((V0 @ V3) @ V4)))) @ ((V0 @ V4) @ V3))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V5)))))) @ ((V0 @ V3) @ V5))))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c= @ (cCARD @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((V0 @ V3) @ V5))) @ V5))))))) @ V1))))))))) @ ((cnum_divides @ V1) @ (cCARD @ V2))))))))))
(TEQUIVALENCE_UNIFORM_PARTITION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((V0 @ V3) @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V5))) @ ((V0 @ V3) @ V5))))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c= @ (cCARD @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((V0 @ V3) @ V5))) @ V5))))))) @ V1))))))))) @ ((cnum_divides @ V1) @ (cCARD @ V2))))))))))
(TWF_REC_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cWF @ V0)) @ ((cALL @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ (c? @ (^[V5]: (c? @ (^[V6]: (c? @ (^[V7]: ((c/__caret__ @ (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: ((c==> @ ((c/__caret__ @ ((V5 @ V8) @ V9)) @ ((V0 @ V10) @ ((V6 @ V8) @ V9)))) @ ((V0 @ V10) @ (V3 @ V9)))))))))) @ ((c/__caret__ @ (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: ((c==> @ (c! @ (^[V11]: ((c==> @ ((V0 @ V11) @ (V3 @ V10))) @ ((c= @ (V8 @ V11)) @ (V9 @ V11)))))) @ ((c/__caret__ @ ((c= @ ((V5 @ V8) @ V10)) @ ((V5 @ V9) @ V10))) @ ((c/__caret__ @ ((c= @ ((V6 @ V8) @ V10)) @ ((V6 @ V9) @ V10))) @ ((c= @ ((V7 @ V8) @ V10)) @ ((V7 @ V9) @ V10)))))))))))) @ (c! @ (^[V8]: (c! @ (^[V9]: ((c= @ ((V4 @ V8) @ V9)) @ (((cCOND @ ((V5 @ V8) @ V9)) @ (V8 @ ((V6 @ V8) @ V9))) @ ((V7 @ V8) @ V9))))))))))))))))))))))) @ V1))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c= @ (V2 @ V3)) @ (((cCASEWISE @ V1) @ V2) @ V3))))))))))))
(TWF_REC_CASES',(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cWF @ V0)) @ ((cALL @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ ((((ctailadmissible @ V0) @ (^[V5]: (^[V6]: cT))) @ V3) @ V4))))))))) @ V1))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c= @ (V2 @ V3)) @ (((cCASEWISE @ V1) @ V2) @ V3))))))))))))
(TQSORT_PERMUTED,(c! @ (^[V0]: (c! @ (^[V1]: ((cPERMUTED @ ((cQSORT @ V0) @ V1)) @ V1))))))
(TORDERED_QSORT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c__caret__/ @ ((V0 @ V2) @ V3)) @ ((V0 @ V3) @ V2))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c__caret__/ @ ((V0 @ V2) @ V3)) @ ((V0 @ V3) @ V4))) @ ((V0 @ V2) @ V4)))))))))) @ ((cORDERED @ V0) @ ((cQSORT @ V0) @ V1))))))))
(TORDERED_APPEND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cORDERED @ V0) @ ((cAPPEND @ V2) @ V1))) @ ((c/__caret__ @ ((cORDERED @ V0) @ V2)) @ ((c/__caret__ @ ((cORDERED @ V0) @ V1)) @ ((cALL @ (^[V3]: ((cALL @ (V0 @ V3)) @ V1))) @ V2)))))))))))
(TADMISSIBLE_COMB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V3)) @ ((((cadmissible @ V0) @ V1) @ V2) @ V4))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V5]: (^[V6]: (((V3 @ V5) @ V6) @ ((V4 @ V5) @ V6)))))))))))))))))
(TSUPERADMISSIBLE_COND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V3)) @ ((c/__caret__ @ ((((csuperadmissible @ V0) @ (^[V6]: (^[V7]: ((c/__caret__ @ ((V1 @ V6) @ V7)) @ ((V3 @ V6) @ V7))))) @ V2) @ V4)) @ ((((csuperadmissible @ V0) @ (^[V6]: (^[V7]: ((c/__caret__ @ ((V1 @ V6) @ V7)) @ (c~ @ ((V3 @ V6) @ V7)))))) @ V2) @ V5)))) @ ((((csuperadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: (((cCOND @ ((V3 @ V6) @ V7)) @ ((V4 @ V6) @ V7)) @ ((V5 @ V6) @ V7)))))))))))))))))))
(TADMISSIBLE_IMP_SUPERADMISSIBLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((((cadmissible @ V0) @ V1) @ V2) @ V3)) @ ((((csuperadmissible @ V0) @ V1) @ V2) @ V3)))))))))))
(TADMISSIBLE_NEST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V3)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V1 @ V4) @ V5)) @ ((V0 @ ((V3 @ V4) @ V5)) @ (V2 @ V5))))))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V4]: (^[V5]: (V4 @ ((V3 @ V4) @ V5)))))))))))))))
(TSUPERADMISSIBLE_TAIL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V3)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V1 @ V4) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((V0 @ V6) @ ((V3 @ V4) @ V5))) @ ((V0 @ V6) @ (V2 @ V5)))))))))))) @ ((((csuperadmissible @ V0) @ V1) @ V2) @ (^[V4]: (^[V5]: (V4 @ ((V3 @ V4) @ V5)))))))))))))))
(TADMISSIBLE_LAMBDA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((((cadmissible @ V0) @ (^[V4]: (cGABS @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((cGEQ @ (V5 @ ((c__comma__ @ V6) @ V7))) @ ((V1 @ V4) @ V7)))))))))) @ (cGABS @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((cGEQ @ (V4 @ ((c__comma__ @ V5) @ V6))) @ (V2 @ V6))))))))) @ (^[V4]: (cGABS @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((cGEQ @ (V5 @ ((c__comma__ @ V6) @ V7))) @ (((V3 @ V4) @ V6) @ V7))))))))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V4]: (^[V5]: (^[V6]: (((V3 @ V4) @ V6) @ V5)))))))))))))))
(TADMISSIBLE_RAND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((cadmissible @ V0) @ V1) @ V2) @ V4)) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V5]: (^[V6]: ((V3 @ V6) @ ((V4 @ V5) @ V6)))))))))))))))))
(TSUPERADMISSIBLE_MATCH_GUARDED_PATTERN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: ((c==> @ ((c/__caret__ @ ((V1 @ V7) @ V8)) @ ((c/__caret__ @ ((c= @ (V4 @ V9)) @ (V3 @ V8))) @ ((c/__caret__ @ ((V5 @ V8) @ V9)) @ ((c/__caret__ @ ((c= @ (V4 @ V10)) @ (V3 @ V8))) @ ((V5 @ V8) @ V10)))))) @ ((c= @ ((V6 @ V8) @ V9)) @ ((V6 @ V8) @ V10)))))))))))) @ (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((V1 @ V7) @ V8)) @ ((c/__caret__ @ ((V5 @ V8) @ V9)) @ ((c= @ (V4 @ V9)) @ (V3 @ V8))))) @ (c! @ (^[V10]: ((c==> @ ((V0 @ V10) @ ((V6 @ V8) @ V9))) @ ((V0 @ V10) @ (V2 @ V8)))))))))))))) @ ((((csuperadmissible @ V0) @ V1) @ V2) @ (^[V7]: (^[V8]: ((c_MATCH @ (V3 @ V8)) @ (^[V9]: (^[V10]: (c? @ (^[V11]: (((c_GUARDED_PATTERN @ ((cGEQ @ (V4 @ V11)) @ V9)) @ ((V5 @ V8) @ V11)) @ ((cGEQ @ (V7 @ ((V6 @ V8) @ V11))) @ V10))))))))))))))))))))))))))
(TSUPERADMISSIBLE_MATCH_UNGUARDED_PATTERN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((V1 @ V6) @ V7)) @ ((c/__caret__ @ ((c= @ (V4 @ V8)) @ (V3 @ V7))) @ ((c= @ (V4 @ V9)) @ (V3 @ V7))))) @ ((c= @ ((V5 @ V7) @ V8)) @ ((V5 @ V7) @ V9)))))))))))) @ (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((V1 @ V6) @ V7)) @ ((c= @ (V4 @ V8)) @ (V3 @ V7)))) @ (c! @ (^[V9]: ((c==> @ ((V0 @ V9) @ ((V5 @ V7) @ V8))) @ ((V0 @ V9) @ (V2 @ V7)))))))))))))) @ ((((csuperadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: ((c_MATCH @ (V3 @ V7)) @ (^[V8]: (^[V9]: (c? @ (^[V10]: ((c_UNGUARDED_PATTERN @ ((cGEQ @ (V4 @ V10)) @ V8)) @ ((cGEQ @ (V6 @ ((V5 @ V7) @ V10))) @ V9))))))))))))))))))))))))
(TADMISSIBLE_BASE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V1 @ V4) @ V5)) @ ((V0 @ (V3 @ V5)) @ (V2 @ V5)))))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V4]: (^[V5]: (V4 @ (V3 @ V5)))))))))))))))
(TWF_REC_TAIL_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cWF @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (c! @ (^[V7]: ((c==> @ ((V0 @ V7) @ V6)) @ ((c= @ (V4 @ V7)) @ (V5 @ V7)))))) @ ((c/__caret__ @ ((c= @ ((V1 @ V4) @ V6)) @ ((V1 @ V5) @ V6))) @ ((c/__caret__ @ ((c= @ ((V2 @ V4) @ V6)) @ ((V2 @ V5) @ V6))) @ ((c= @ ((V3 @ V4) @ V6)) @ ((V3 @ V5) @ V6)))))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (c! @ (^[V7]: ((c==> @ ((V0 @ V7) @ V6)) @ ((c= @ (V4 @ V7)) @ (V5 @ V7)))))) @ ((c= @ ((V3 @ V4) @ V6)) @ ((V3 @ V5) @ V6)))))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V1 @ V4) @ V5)) @ ((V0 @ V6) @ ((V2 @ V4) @ V5)))) @ ((V0 @ V6) @ V5)))))))))))) @ (c? @ (^[V4]: (c! @ (^[V5]: ((c= @ (V4 @ V5)) @ (((cCOND @ ((V1 @ V4) @ V5)) @ (V4 @ ((V2 @ V4) @ V5))) @ ((V3 @ V4) @ V5)))))))))))))))))
(TWF_EREC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cWF @ V0)) @ ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: ((c==> @ ((V0 @ V5) @ V4)) @ ((c= @ (V2 @ V5)) @ (V3 @ V5)))))) @ ((c= @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))) @ (c?! @ (^[V2]: (c! @ (^[V3]: ((c= @ (V2 @ V3)) @ ((V1 @ V2) @ V3)))))))))))))
(TWF_REC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cWF @ V0)) @ ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: ((c==> @ ((V0 @ V5) @ V4)) @ ((c= @ (V2 @ V5)) @ (V3 @ V5)))))) @ ((c= @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c= @ (V2 @ V3)) @ ((V1 @ V2) @ V3)))))))))))))
(TWF_UREC,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cWF @ V0)) @ ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: ((c==> @ ((V0 @ V5) @ V4)) @ ((c= @ (V2 @ V5)) @ (V3 @ V5)))))) @ ((c= @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c= @ (V2 @ V4)) @ ((V1 @ V2) @ V4))))) @ (c! @ (^[V4]: ((c= @ (V3 @ V4)) @ ((V1 @ V3) @ V4)))))) @ ((c= @ V2) @ V3)))))))))))))
(Ttailadmissible,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((ctailadmissible @ V0) @ V2) @ V1) @ V3)) @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((V4 @ V7) @ V8)) @ ((V0 @ V9) @ ((V5 @ V7) @ V8)))) @ ((V0 @ V9) @ (V1 @ V8)))))))))) @ ((c/__caret__ @ (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ (c! @ (^[V10]: ((c==> @ ((V0 @ V10) @ (V1 @ V9))) @ ((c= @ (V7 @ V10)) @ (V8 @ V10)))))) @ ((c/__caret__ @ ((c= @ ((V4 @ V7) @ V9)) @ ((V4 @ V8) @ V9))) @ ((c/__caret__ @ ((c= @ ((V5 @ V7) @ V9)) @ ((V5 @ V8) @ V9))) @ ((c= @ ((V6 @ V7) @ V9)) @ ((V6 @ V8) @ V9)))))))))))) @ (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((V2 @ V7) @ V8)) @ ((c= @ ((V3 @ V7) @ V8)) @ (((cCOND @ ((V4 @ V7) @ V8)) @ (V7 @ ((V5 @ V7) @ V8))) @ ((V6 @ V7) @ V8))))))))))))))))))))))))))
(TWF_LEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cWF @ V0)) @ (cWF @ V1))) @ (cWF @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ (cGABS @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((cGEQ @ (V5 @ ((c__comma__ @ V6) @ V7))) @ ((c__caret__/ @ ((V0 @ V3) @ V6)) @ ((c/__caret__ @ ((c= @ V3) @ V6)) @ ((V1 @ V4) @ V7))))))))))))))))))))))))
(TWF_POINTWISE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cWF @ V0)) @ (cWF @ V1))) @ (cWF @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ (cGABS @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((cGEQ @ (V5 @ ((c__comma__ @ V6) @ V7))) @ ((c/__caret__ @ ((V0 @ V3) @ V6)) @ ((V1 @ V4) @ V7)))))))))))))))))))))))
(TWF_LEX_DEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cWF @ V0)) @ (c! @ (^[V2]: (cWF @ (V1 @ V2)))))) @ (cWF @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ (cGABS @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((cGEQ @ (V5 @ ((c__comma__ @ V6) @ V7))) @ ((c__caret__/ @ ((V0 @ V3) @ V6)) @ ((c/__caret__ @ ((c= @ V3) @ V6)) @ (((V1 @ V3) @ V4) @ V7))))))))))))))))))))))))
(TWF_REC_INVARIANT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cWF @ V0)) @ ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (c! @ (^[V6]: ((c==> @ ((V0 @ V6) @ V5)) @ ((c/__caret__ @ ((c= @ (V3 @ V6)) @ (V4 @ V6))) @ ((V1 @ V6) @ (V3 @ V6))))))) @ ((c/__caret__ @ ((c= @ ((V2 @ V3) @ V5)) @ ((V2 @ V4) @ V5))) @ ((V1 @ V5) @ ((V2 @ V3) @ V5))))))))))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c= @ (V3 @ V4)) @ ((V2 @ V3) @ V4)))))))))))))))
(TWF_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((V1 @ V2) @ V3)) @ ((V0 @ V2) @ V3))))))) @ (cWF @ V0))) @ (cWF @ V1)))))))
(TTRANS_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c? @ (^[V5]: ((c/__caret__ @ ((V0 @ V3) @ V5)) @ ((V1 @ V5) @ V4))))) @ ((V2 @ V3) @ V4))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((V0 @ V3) @ V4)) @ ((V1 @ V4) @ V5))) @ ((V2 @ V3) @ V5))))))))))))))))
(TRTC_INDUCT_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((V1 @ V4) @ V4)))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V1 @ V4) @ V5)) @ ((V0 @ V5) @ V6))) @ ((V1 @ V4) @ V6)))))))))) @ ((c==> @ (((cRTC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TRTC_INDUCT_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((V1 @ V4) @ V4)))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V0 @ V4) @ V5)) @ ((V1 @ V5) @ V6))) @ ((V1 @ V4) @ V6)))))))))) @ ((c==> @ (((cRTC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TRSTC_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((V1 @ V4) @ V4)))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V4))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V6))) @ ((V1 @ V4) @ V6)))))))))))) @ ((c==> @ (((cRSTC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TRSC_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((V1 @ V4) @ V4)))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V4))))))))) @ ((c==> @ (((cRSC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TRTC_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((V1 @ V4) @ V4)))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V6))) @ ((V1 @ V4) @ V6))))))))))) @ ((c==> @ (((cRTC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TSTC_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V4))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V6))) @ ((V1 @ V4) @ V6))))))))))) @ ((c==> @ (((cSTC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TRC_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ (c! @ (^[V4]: ((V1 @ V4) @ V4))))) @ ((c==> @ (((cRC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TSC_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V4)))))))) @ ((c==> @ (((cSC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TTC_INDUCT_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (c? @ (^[V6]: ((c/__caret__ @ ((V0 @ V4) @ V6)) @ ((V1 @ V6) @ V5))))) @ ((V1 @ V4) @ V5)))))))) @ ((c==> @ (((cTC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TTC_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V6))) @ ((V1 @ V4) @ V6)))))))))) @ ((c==> @ (((cTC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TTC_INDUCT_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V1 @ V4) @ V5)) @ ((V0 @ V5) @ V6))) @ ((V1 @ V4) @ V6)))))))))) @ ((c==> @ (((cTC @ V0) @ V2) @ V3)) @ ((V1 @ V2) @ V3))))))))))))
(TTC_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c==> @ (((cTC @ V0) @ V2) @ V3)) @ (((cTC @ V1) @ V2) @ V3))))))))))))
(TSTC_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c==> @ (((cSTC @ V0) @ V2) @ V3)) @ (((cSTC @ V1) @ V2) @ V3))))))))))))
(TSC_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c==> @ (((cSC @ V0) @ V2) @ V3)) @ (((cSC @ V1) @ V2) @ V3))))))))))))
(TRTC_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c==> @ (((cRTC @ V0) @ V2) @ V3)) @ (((cRTC @ V1) @ V2) @ V3))))))))))))
(TRSTC_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c==> @ (((cRSTC @ V0) @ V2) @ V3)) @ (((cRSTC @ V1) @ V2) @ V3))))))))))))
(TRSC_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c==> @ (((cRSC @ V0) @ V2) @ V3)) @ (((cRSC @ V1) @ V2) @ V3))))))))))))
(TRC_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))))) @ ((c==> @ (((cRC @ V0) @ V2) @ V3)) @ (((cRC @ V1) @ V2) @ V3))))))))))))
(TELEMENTS_PAIR_UP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c~ @ ((V0 @ V2) @ V2)))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((V0 @ V2) @ V3)))) @ ((V0 @ V3) @ V2))))))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c?! @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((V0 @ V2) @ V3))))))))))) @ (cEVEN @ (cCARD @ V1))))))))
(TFINITE_TRANSITIVITY_CHAIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: (c~ @ ((V0 @ V2) @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((V0 @ V2) @ V3)) @ ((V0 @ V3) @ V4))) @ ((V0 @ V2) @ V4))))))))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((V0 @ V2) @ V3))))))))))) @ ((c= @ V1) @ cEMPTY)))))))
(TWFP_PART_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cWFP @ V0))) @ (c! @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ (V1 @ V4)))))) @ (V1 @ V3))))) @ ((c==> @ ((cIN @ V2) @ (cWFP @ V0))) @ (V1 @ V2))))))))))
(TRTC_REFL,(c! @ (^[V0]: (c! @ (^[V1]: (((cRTC @ V0) @ V1) @ V1))))))
(TRSTC_REFL,(c! @ (^[V0]: (c! @ (^[V1]: (((cRSTC @ V0) @ V1) @ V1))))))
(TRSC_REFL,(c! @ (^[V0]: (c! @ (^[V1]: (((cRSC @ V0) @ V1) @ V1))))))
(TRC_REFL,(c! @ (^[V0]: (c! @ (^[V1]: (((cRC @ V0) @ V1) @ V1))))))
(TLF_TC_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cLF @ V0)) @ (cSN @ V0))) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (((cTC @ V0) @ V1) @ V3)) @ V3))))))))))))
(TFC_FINITE_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (((cRTC @ V0) @ V1) @ V3)) @ V3))))))) @ (c! @ (^[V2]: (c~ @ (((cTC @ V0) @ V2) @ V2)))))) @ (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((cRELPOW @ V3) @ V0) @ V1) @ V4)) @ ((c<= @ V3) @ V2))))))))))))))
(TWF_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cWF @ V0)) @ (c~ @ ((V0 @ V1) @ V1))))))))
(TSN_NOLOOP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cSN @ V0)) @ (c~ @ (((cTC @ V0) @ V1) @ V1))))))))
(TTC_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((V0 @ V2) @ V2)))) @ (((cTC @ V0) @ V1) @ V1)))))))
(TSTC_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((V0 @ V2) @ V2)))) @ (((cSTC @ V0) @ V1) @ V1)))))))
(TSC_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((V0 @ V2) @ V2)))) @ (((cSC @ V0) @ V1) @ V1)))))))
(TRTC_TC_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (((cRTC @ V0) @ V1) @ V3)) @ V3)))))) @ ((cINSERT @ V1) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (((cTC @ V0) @ V1) @ V3)) @ V3))))))))))))
(TNORMAL_TC,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cNORMAL @ (cTC @ V0)) @ V1)) @ ((cNORMAL @ V0) @ V1)))))))
(TNORMAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cNORMAL @ V0) @ V1)) @ (c~ @ (c? @ (^[V2]: ((V0 @ V1) @ V2))))))))))
(TFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cFL @ V0) @ V1)) @ ((c__caret__/ @ (c? @ (^[V2]: ((V0 @ V1) @ V2)))) @ (c? @ (^[V2]: ((V0 @ V2) @ V1))))))))))
(TFC_FINITE_BOUND_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c~ @ (((cTC @ V0) @ V3) @ V3))))) @ ((c==> @ ((cHAS_SIZE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ (((cRTC @ V0) @ V1) @ V4)) @ V4)))))) @ V2)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((((cRELPOW @ V3) @ V0) @ V1) @ V4)) @ ((c<= @ V3) @ V2)))))))))))))))
(TQSORT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cQSORT @ V0) @ ((cCONS @ V1) @ V2))) @ ((cAPPEND @ ((cQSORT @ V0) @ ((cFILTER @ (^[V3]: (c~ @ ((V0 @ V1) @ V3)))) @ V2))) @ ((cCONS @ V1) @ ((cQSORT @ V0) @ ((cFILTER @ (^[V3]: ((V0 @ V1) @ V3))) @ V2))))))))))))
(TORDERED_CONS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cORDERED @ V0) @ ((cCONS @ V1) @ V2))) @ ((c/__caret__ @ ((cORDERED @ V0) @ V2)) @ ((cALL @ (V0 @ V1)) @ V2))))))))))
(TSTC_INC_TC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cTC @ V0) @ V1) @ V2)) @ (((cSTC @ V0) @ V1) @ V2)))))))))
(TRTC_INC_TC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cTC @ V0) @ V1) @ V2)) @ (((cRTC @ V0) @ V1) @ V2)))))))))
(TRSTC_INC_TC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cTC @ V0) @ V1) @ V2)) @ (((cRSTC @ V0) @ V1) @ V2)))))))))
(TSTC_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cSTC @ V0) @ V2) @ V1)) @ (((cSTC @ V0) @ V1) @ V2)))))))))
(TRSTC_INC_STC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cSTC @ V0) @ V1) @ V2)) @ (((cRSTC @ V0) @ V1) @ V2)))))))))
(TSC_TC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cSC @ (cTC @ V0)) @ V1) @ V2)) @ (((cTC @ (cSC @ V0)) @ V1) @ V2)))))))))
(TSC_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cSC @ V0) @ V2) @ V1)) @ (((cSC @ V0) @ V1) @ V2)))))))))
(TSTC_INC_SC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cSC @ V0) @ V1) @ V2)) @ (((cSTC @ V0) @ V1) @ V2)))))))))
(TSC_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cSC @ V0) @ V1) @ V2)) @ (((cSC @ V0) @ V2) @ V1)))))))))
(TRSTC_INC_SC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cSC @ V0) @ V1) @ V2)) @ (((cRSTC @ V0) @ V1) @ V2)))))))))
(TRSC_INC_SC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cSC @ V0) @ V1) @ V2)) @ (((cRSC @ V0) @ V1) @ V2)))))))))
(TRSTC_INC_RTC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cRTC @ V0) @ V1) @ V2)) @ (((cRSTC @ V0) @ V1) @ V2)))))))))
(TRSTC_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cRSTC @ V0) @ V2) @ V1)) @ (((cRSTC @ V0) @ V1) @ V2)))))))))
(TRSTC_RULES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cRSTC @ V0) @ V1) @ V2)) @ (((cRSTC @ V0) @ V2) @ V1)))))))))
(TRSC_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cRSC @ V0) @ V2) @ V1)) @ (((cRSC @ V0) @ V1) @ V2)))))))))
(TRSTC_INC_RSC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cRSC @ V0) @ V1) @ V2)) @ (((cRSTC @ V0) @ V1) @ V2)))))))))
(TRTC_INC_RC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cRC @ V0) @ V1) @ V2)) @ (((cRTC @ V0) @ V1) @ V2)))))))))
(TRSTC_INC_RC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cRC @ V0) @ V1) @ V2)) @ (((cRSTC @ V0) @ V1) @ V2)))))))))
(TRSC_INC_RC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((cRC @ V0) @ V1) @ V2)) @ (((cRSC @ V0) @ V1) @ V2)))))))))
(TNORMAL_RTC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cNORMAL @ V0) @ V1)) @ ((c= @ (((cRTC @ V0) @ V1) @ V2)) @ ((c= @ V1) @ V2))))))))))
(TTC_INC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cTC @ V0) @ V1) @ V2)))))))))
(TSTC_INC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cSTC @ V0) @ V1) @ V2)))))))))
(TSC_INC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cSC @ V0) @ V1) @ V2)))))))))
(TRTC_INC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cRTC @ V0) @ V1) @ V2)))))))))
(TRSTC_INC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cRSTC @ V0) @ V1) @ V2)))))))))
(TRSC_INC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cRSC @ V0) @ V1) @ V2)))))))))
(TRC_INC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((V0 @ V1) @ V2)) @ (((cRC @ V0) @ V1) @ V2)))))))))
(TCR_RSTC_JOINABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cCR @ (cRTC @ V0))) @ ((c= @ (((cRSTC @ V0) @ V1) @ V2)) @ (((cJOINABLE @ V0) @ V1) @ V2))))))))))
(TTC_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))) @ ((c==> @ (((cTC @ V0) @ V2) @ V1)) @ (((cTC @ V0) @ V1) @ V2))))))))))
(TRTC_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))) @ ((c==> @ (((cRTC @ V0) @ V2) @ V1)) @ (((cRTC @ V0) @ V1) @ V2))))))))))
(TRC_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((V0 @ V3) @ V4)) @ ((V0 @ V4) @ V3))))))) @ ((c==> @ (((cRC @ V0) @ V2) @ V1)) @ (((cRC @ V0) @ V1) @ V2))))))))))
(TRELPOW_R_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((((cRELPOW @ (cNUMERAL @ c_0)) @ V0) @ V1) @ V2)) @ ((c= @ V1) @ V2)))))))))
(TTC_RELPOW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cTC @ V0) @ V1) @ V2)) @ (c? @ (^[V3]: ((((cRELPOW @ (cSUC @ V3)) @ V0) @ V1) @ V2)))))))))))
(TSC_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cSC @ V0) @ V2) @ V1)) @ ((c__caret__/ @ ((V0 @ V2) @ V1)) @ (((cSC @ V0) @ V1) @ V2))))))))))
(TSC_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cSC @ V0) @ V2) @ V1)) @ ((c__caret__/ @ ((V0 @ V2) @ V1)) @ ((V0 @ V1) @ V2))))))))))
(TRTC_RELPOW,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cRTC @ V0) @ V1) @ V2)) @ (c? @ (^[V3]: ((((cRELPOW @ V3) @ V0) @ V1) @ V2)))))))))))
(TRSC_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cRSC @ V0) @ V2) @ V1)) @ ((c__caret__/ @ ((c= @ V2) @ V1)) @ ((c__caret__/ @ ((V0 @ V2) @ V1)) @ ((V0 @ V1) @ V2)))))))))))
(TRC_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cRC @ V0) @ V2) @ V1)) @ ((c__caret__/ @ ((V0 @ V2) @ V1)) @ ((c= @ V1) @ V2))))))))))
(TRC_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cRC @ V0) @ V1) @ V2)) @ ((c__caret__/ @ ((V0 @ V1) @ V2)) @ ((c= @ V1) @ V2))))))))))
(Tcong,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c== @ V1) @ V2) @ V0)) @ ((V0 @ V1) @ V2)))))))))
(TTC_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cTC @ V0) @ V1) @ V2)) @ (((cTC @ V0) @ V2) @ V3))) @ (((cTC @ V0) @ V1) @ V3)))))))))))
(TRTC_RULES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cRTC @ V0) @ V1) @ V2)) @ (((cRTC @ V0) @ V2) @ V3))) @ (((cRTC @ V0) @ V1) @ V3)))))))))))
(TRSTC_RULES_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cRSTC @ V0) @ V1) @ V2)) @ (((cRSTC @ V0) @ V2) @ V3))) @ (((cRSTC @ V0) @ V1) @ V3)))))))))))
(TCANTOR_LAWVERE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c? @ (^[V3]: ((c= @ (V0 @ V3)) @ V2)))))) @ (c? @ (^[V2]: ((c= @ (V1 @ V2)) @ V2)))))))))
(Tmonoidal,(c! @ (^[V0]: ((c= @ (cmonoidal @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))) @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((V0 @ V1) @ ((V0 @ V2) @ V3))) @ ((V0 @ ((V0 @ V1) @ V2)) @ V3))))))))) @ (c! @ (^[V1]: ((c= @ ((V0 @ (cneutral @ V0)) @ V1)) @ V1)))))))))
(TITERATE_ITERATE_DIVISORS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cmonoidal @ V0)) @ ((c= @ (((citerate @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ (^[V3]: (((citerate @ V0) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cnum_divides @ V5) @ V3)) @ V5)))))) @ (V2 @ V3))))) @ (((citerate @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ (^[V3]: (((citerate @ V0) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ ((cDIV @ V1) @ V3))) @ (^[V4]: ((V2 @ ((c* @ V4) @ V3)) @ V3))))))))))))))
(TOPERATIVE_TAGGED_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cmonoidal @ V0)) @ ((c/__caret__ @ ((coperative @ V0) @ V2)) @ ((ctagged_division_of @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))) @ ((c= @ (((citerate @ V0) @ V1) @ (cGABS @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((cGEQ @ (V5 @ ((c__comma__ @ V6) @ V7))) @ (V2 @ V7)))))))))) @ (V2 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))))))))
(TOPERATIVE_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cmonoidal @ V0)) @ ((c/__caret__ @ ((coperative @ V0) @ V2)) @ ((cdivision_of @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))) @ ((c= @ (((citerate @ V0) @ V1) @ V2)) @ (V2 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))))))))))))))))
(Toperative,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((coperative @ V0) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (cneutral @ V0)))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV)))) @ ((c= @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((V0 @ (V1 @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_le @ ((c$ @ V7) @ V5)) @ V4)) @ V7)))))))) @ (V1 @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_ge @ ((c$ @ V7) @ V5)) @ V4)) @ V7)))))))))))))))))))))))))
(TADMISSIBLE_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V4)) @ ((((cadmissible @ V0) @ (^[V5]: (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ ((c/__caret__ @ ((V1 @ V5) @ V8)) @ ((cMEM @ V7) @ ((V4 @ V5) @ V8)))))))))))) @ (cGABS @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((cGEQ @ (V5 @ ((c__comma__ @ V6) @ V7))) @ (V2 @ V7))))))))) @ (^[V5]: (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ (((V3 @ V5) @ V8) @ V7)))))))))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V5]: (^[V6]: ((cMAP @ ((V3 @ V5) @ V6)) @ ((V4 @ V5) @ V6)))))))))))))))))
(TLIM_DROP_LBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V3) @ V1)) @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V1))) @ ((ceventually @ (^[V4]: ((creal_le @ V2) @ (cdrop @ (V0 @ V4))))) @ V1)))) @ ((creal_le @ V2) @ (cdrop @ V3))))))))))))
(TLIM_DROP_UBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V1)) @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V1))) @ ((ceventually @ (^[V4]: ((creal_le @ (cdrop @ (V0 @ V4))) @ V3))) @ V1)))) @ ((creal_le @ (cdrop @ V2)) @ V3)))))))))))
(TLIM_DROP_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V2))) @ ((c/__caret__ @ (((c--> @ V0) @ V3) @ V2)) @ ((c/__caret__ @ (((c--> @ V1) @ V4) @ V2)) @ ((ceventually @ (^[V5]: ((creal_le @ (cdrop @ (V0 @ V5))) @ (cdrop @ (V1 @ V5))))) @ V2))))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))))))))))))))
(TCONTINUOUS_LIFT_COMPONENT_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous @ V0) @ V2)) @ ((ccontinuous @ (^[V3]: (clift @ ((c$ @ (V0 @ V3)) @ V1)))) @ V2)))))))))
(TCONTINUOUS_LIFT_NORM_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ccontinuous @ V0) @ V1)) @ ((ccontinuous @ (^[V2]: (clift @ (cvector_norm @ (V0 @ V2))))) @ V1)))))))
(TCONTINUOUS_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ccontinuous @ V0) @ V1)) @ ((ccontinuous @ (^[V2]: (clambda @ (^[V3]: (creal_abs @ ((c$ @ (V0 @ V2)) @ V3)))))) @ V1)))))))
(TCONTINUOUS_COMPONENTWISE_LIFT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((ccontinuous @ (^[V3]: (clift @ ((c$ @ (V0 @ V3)) @ V2)))) @ V1))))))))))
(TLIM_NORM_LBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V1))) @ ((c/__caret__ @ (((c--> @ V0) @ V3) @ V1)) @ ((ceventually @ (^[V4]: ((creal_le @ V2) @ (cvector_norm @ (V0 @ V4))))) @ V1)))) @ ((creal_le @ V2) @ (cvector_norm @ V3))))))))))))
(TLIM_COMPONENT_LBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V1))) @ ((c/__caret__ @ (((c--> @ V0) @ V3) @ V1)) @ ((c/__caret__ @ ((ceventually @ (^[V5]: ((creal_le @ V2) @ ((c$ @ (V0 @ V5)) @ V4)))) @ V1)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ (cdimindex @ cUNIV))))))) @ ((creal_le @ V2) @ ((c$ @ V3) @ V4))))))))))))))
(TLIM_NORM_UBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V1))) @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V1)) @ ((ceventually @ (^[V4]: ((creal_le @ (cvector_norm @ (V0 @ V4))) @ V3))) @ V1)))) @ ((creal_le @ (cvector_norm @ V2)) @ V3)))))))))))
(TLIM_COMPONENT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V1)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V1))) @ ((ceventually @ (^[V5]: ((c= @ ((c$ @ (V0 @ V5)) @ V3)) @ V4))) @ V1)))))) @ ((c= @ ((c$ @ V2) @ V3)) @ V4)))))))))))))
(TLIM_COMPONENT_UBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V1))) @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V1)) @ ((c/__caret__ @ ((ceventually @ (^[V5]: ((creal_le @ ((c$ @ (V0 @ V5)) @ V3)) @ V4))) @ V1)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV))))))) @ ((creal_le @ ((c$ @ V2) @ V3)) @ V4)))))))))))))
(TLIM_IN_CLOSED_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cclosed @ V3)) @ ((c/__caret__ @ ((ceventually @ (^[V4]: ((cIN @ (V0 @ V4)) @ V3))) @ V1)) @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V1))) @ (((c--> @ V0) @ V2) @ V1))))) @ ((cIN @ V2) @ V3)))))))))))
(TLIM_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V1))) @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V1)) @ (((c--> @ V0) @ V3) @ V1)))) @ ((c= @ V2) @ V3)))))))))))
(TCONTINUOUS_LIFT_DOT2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V0) @ V2)) @ ((ccontinuous @ V1) @ V2))) @ ((ccontinuous @ (^[V3]: (clift @ ((cdot @ (V0 @ V3)) @ (V1 @ V3))))) @ V2)))))))))
(TCONTINUOUS_MIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V0) @ V2)) @ ((ccontinuous @ V1) @ V2))) @ ((ccontinuous @ (^[V3]: (clambda @ (^[V4]: ((creal_min @ ((c$ @ (V0 @ V3)) @ V4)) @ ((c$ @ (V1 @ V3)) @ V4)))))) @ V2)))))))))
(TCONTINUOUS_MAX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V0) @ V2)) @ ((ccontinuous @ V1) @ V2))) @ ((ccontinuous @ (^[V3]: (clambda @ (^[V4]: ((creal_max @ ((c$ @ (V0 @ V3)) @ V4)) @ ((c$ @ (V1 @ V3)) @ V4)))))) @ V2)))))))))
(TLIM_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c~ @ (ctrivial_limit @ V2))) @ ((c/__caret__ @ (((c--> @ V0) @ V3) @ V2)) @ ((c/__caret__ @ (((c--> @ V1) @ V4) @ V2)) @ ((c/__caret__ @ ((ceventually @ (^[V6]: ((creal_le @ ((c$ @ (V0 @ V6)) @ V5)) @ ((c$ @ (V1 @ V6)) @ V5)))) @ V2)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV)))))))) @ ((creal_le @ ((c$ @ V3) @ V5)) @ ((c$ @ V4) @ V5))))))))))))))))
(TLIM_TRANSFORM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((c--> @ (^[V4]: ((cvector_sub @ (V0 @ V4)) @ (V1 @ V4)))) @ (cvec @ (cNUMERAL @ c_0))) @ V3)) @ ((c= @ (((c--> @ V0) @ V2) @ V3)) @ (((c--> @ V1) @ V2) @ V3))))))))))))
(TLIM_MIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V4)) @ (((c--> @ V1) @ V3) @ V4))) @ (((c--> @ (^[V5]: (clambda @ (^[V6]: ((creal_min @ ((c$ @ (V0 @ V5)) @ V6)) @ ((c$ @ (V1 @ V5)) @ V6)))))) @ (clambda @ (^[V5]: ((creal_min @ ((c$ @ V2) @ V5)) @ ((c$ @ V3) @ V5))))) @ V4)))))))))))))
(TLIM_MAX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V4)) @ (((c--> @ V1) @ V3) @ V4))) @ (((c--> @ (^[V5]: (clambda @ (^[V6]: ((creal_max @ ((c$ @ (V0 @ V5)) @ V6)) @ ((c$ @ (V1 @ V5)) @ V6)))))) @ (clambda @ (^[V5]: ((creal_max @ ((c$ @ V2) @ V5)) @ ((c$ @ V3) @ V5))))) @ V4)))))))))))))
(TVSUM_NORM_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (cvector_norm @ (V0 @ V3))) @ (V2 @ V3))))))) @ ((creal_le @ (cvector_norm @ ((cvsum @ V1) @ V0))) @ ((csum @ V1) @ V2))))))))))
(TVSUM_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cvsum @ V1) @ (^[V4]: (((cCOND @ (V2 @ V4)) @ (V0 @ V4)) @ (V3 @ V4))))) @ ((cvector_add @ ((cvsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (V2 @ V5))) @ V5)))))) @ V0)) @ ((cvsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (c~ @ (V2 @ V5)))) @ V5)))))) @ V3)))))))))))))
(TLIM_NORM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c--> @ V0) @ V1) @ V2)) @ (((c--> @ (^[V3]: (clift @ (cvector_norm @ (V0 @ V3))))) @ (clift @ (cvector_norm @ V1))) @ V2)))))))))
(TLIM_ABS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c--> @ V0) @ V1) @ V2)) @ (((c--> @ (^[V3]: (clambda @ (^[V4]: (creal_abs @ ((c$ @ (V0 @ V3)) @ V4)))))) @ (clambda @ (^[V3]: (creal_abs @ ((c$ @ V1) @ V3))))) @ V2)))))))))
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(TCONTINUOUS_PASTECART,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V0) @ V2)) @ ((ccontinuous @ V1) @ V2))) @ ((ccontinuous @ (^[V3]: ((cpastecart @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TLIM_BILINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V3) @ V5)) @ ((c/__caret__ @ (((c--> @ V1) @ V4) @ V5)) @ (cbilinear @ V2)))) @ (((c--> @ (^[V6]: ((V2 @ (V0 @ V6)) @ (V1 @ V6)))) @ ((V2 @ V3) @ V4)) @ V5)))))))))))))))
(TLIM_PASTECART,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V4)) @ (((c--> @ V1) @ V3) @ V4))) @ (((c--> @ (^[V5]: ((cpastecart @ (V0 @ V5)) @ (V1 @ V5)))) @ ((cpastecart @ V2) @ V3)) @ V4)))))))))))))
(TLIM_PASTECART_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((c--> @ (^[V5]: ((cpastecart @ (V0 @ V5)) @ (V2 @ V5)))) @ ((cpastecart @ V1) @ V3)) @ V4)) @ ((c/__caret__ @ (((c--> @ V0) @ V1) @ V4)) @ (((c--> @ V2) @ V3) @ V4))))))))))))))
(TLIM_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V4)) @ (((c--> @ V1) @ V3) @ V4))) @ (((c--> @ (^[V5]: ((cvector_sub @ (V0 @ V5)) @ (V1 @ V5)))) @ ((cvector_sub @ V2) @ V3)) @ V4)))))))))))))
(TLIM_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V4)) @ (((c--> @ V1) @ V3) @ V4))) @ (((c--> @ (^[V5]: ((cvector_add @ (V0 @ V5)) @ (V1 @ V5)))) @ ((cvector_add @ V2) @ V3)) @ V4)))))))))))))
(TLIM_LINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V2) @ V3)) @ (clinear @ V1))) @ (((c--> @ (^[V4]: (V1 @ (V0 @ V4)))) @ (V1 @ V2)) @ V3)))))))))))
(TVSUM_NORM_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (cvector_norm @ (V0 @ V3))) @ V2)))))) @ ((creal_le @ (cvector_norm @ ((cvsum @ V1) @ V0))) @ ((creal_mul @ (creal_of_num @ (cCARD @ V1))) @ V2))))))))))
(TCONTINUOUS_LIFT_DET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))))) @ ((ccontinuous @ (^[V4]: (clift @ ((c$ @ ((c$ @ (V0 @ V4)) @ V2)) @ V3)))) @ V1))))))) @ ((ccontinuous @ (^[V2]: (clift @ (cdet @ (V0 @ V2))))) @ V1)))))))
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(TSUBSETA_REFL,(c! @ (^[V0]: ((cre_subset @ V0) @ V0))))
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(TEMPTY_SUBSET,(c! @ (^[V0]: ((cSUBSET @ cEMPTY) @ V0))))
(TSUBSET_UNIV,(c! @ (^[V0]: ((cSUBSET @ V0) @ cUNIV))))
(TSUBSET_REFL,(c! @ (^[V0]: ((cSUBSET @ V0) @ V0))))
(THAS_SIZE_FINITE_IMAGE,(c! @ (^[V0]: ((cHAS_SIZE @ cUNIV) @ (cdimindex @ V0)))))
(TDISJOINT_EMPTY_conjunct0,(c! @ (^[V0]: ((cDISJOINT @ cEMPTY) @ V0))))
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(TCARD_EQ_LIST_GEN,(c! @ (^[V0]: ((c==> @ (cINFINITE @ V0)) @ ((c=_c @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c! @ (^[V3]: ((c==> @ ((cMEM @ V3) @ V2)) @ ((cIN @ V3) @ V0))))) @ V2)))))) @ V0)))))
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(TINFINITE_CARD_LE,(c! @ (^[V0]: ((c= @ (cINFINITE @ V0)) @ ((c<=_c @ cUNIV) @ V0)))))
(TINFINITE,(c! @ (^[V0]: ((c= @ (cINFINITE @ V0)) @ (c~ @ (cFINITE @ V0))))))
(TFINITE_CASES,(c! @ (^[V0]: ((c= @ (cFINITE @ V0)) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c= @ V0) @ ((cINSERT @ V1) @ V2))) @ (cFINITE @ V2)))))))))))
(TFINITE_CARD_LT,(c! @ (^[V0]: ((c= @ (cFINITE @ V0)) @ ((c<_c @ V0) @ cUNIV)))))
(TFINITE_INDEX_NUMBERS,(c! @ (^[V0]: ((c= @ (cFINITE @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c= @ V0) @ ((cIMAGE @ V2) @ V1))))))))))))
(TFINITE_INDEX_NUMSEG,(c! @ (^[V0]: ((c= @ (cFINITE @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cCARD @ V0)))) @ ((c/__caret__ @ ((cIN @ V3) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cCARD @ V0)))) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))) @ ((c= @ V0) @ ((cIMAGE @ V1) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cCARD @ V0)))))))))))
(TCOUNTABLE_AS_IMAGE_SUBSET_EQ,(c! @ (^[V0]: ((c= @ (cCOUNTABLE @ V0)) @ (c? @ (^[V1]: ((cSUBSET @ V0) @ ((cIMAGE @ V1) @ cUNIV))))))))
(TEXISTS_UNIQUE_THM,(c! @ (^[V0]: ((c= @ (c?! @ (^[V1]: (V0 @ V1)))) @ ((c/__caret__ @ (c? @ (^[V1]: (V0 @ V1)))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2)))))))))))
(TEXISTS_UNIQUE,(c! @ (^[V0]: ((c= @ (c?! @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: ((c/__caret__ @ (V0 @ V1)) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((c= @ V2) @ V1)))))))))))
(TEXISTS_UNIQUE_ALT,(c! @ (^[V0]: ((c= @ (c?! @ (^[V1]: (V0 @ V1)))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c= @ (V0 @ V2)) @ ((c= @ V1) @ V2))))))))))
(TMEMBER_NOT_EMPTY,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((cIN @ V1) @ V0)))) @ (c~ @ ((c= @ V0) @ cEMPTY))))))
(TEXISTS_NOT_THM,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: (c~ @ (V0 @ V1))))) @ (c~ @ (c! @ (^[V1]: (V0 @ V1))))))))
(TEQ_UNIV,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((cIN @ V1) @ V0)))) @ ((c= @ V0) @ cUNIV)))))
(TFORALL_NOT_THM,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c~ @ (V0 @ V1))))) @ (c~ @ (c? @ (^[V1]: (V0 @ V1))))))))
(TGABS_DEF,(c! @ (^[V0]: ((c= @ (cGABS @ V0)) @ (c__at__ @ V0)))))
(TCHOICE,(c! @ (^[V0]: ((c= @ (cCHOICE @ V0)) @ (c__at__ @ (^[V1]: ((cIN @ V1) @ V0)))))))
(TCANTOR_THM,(c! @ (^[V0]: ((c<_c @ V0) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cSUBSET @ V2) @ V0)) @ V2)))))))))
(TCARD_LE_SQUARE,(c! @ (^[V0]: ((c<=_c @ V0) @ ((c*_c @ V0) @ V0)))))
(TCARD_LE_UNIV,(c! @ (^[V0]: ((c<=_c @ V0) @ cUNIV))))
(TCARD_LE_REFL,(c! @ (^[V0]: ((c<=_c @ V0) @ V0))))
(TDIMINDEX_GE_1,(c! @ (^[V0]: ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ V0)))))
(TNOT_UNIV_PSUBSET,(c! @ (^[V0]: (c~ @ ((cPSUBSET @ cUNIV) @ V0)))))
(TNOT_PSUBSET_EMPTY,(c! @ (^[V0]: (c~ @ ((cPSUBSET @ V0) @ cEMPTY)))))
(TPSUBSET_IRREFL,(c! @ (^[V0]: (c~ @ ((cPSUBSET @ V0) @ V0)))))
(TDIMINDEX_NONZERO,(c! @ (^[V0]: (c~ @ ((c= @ (cdimindex @ V0)) @ (cNUMERAL @ c_0))))))
(TCARD_LT_REFL,(c! @ (^[V0]: (c~ @ ((c<_c @ V0) @ V0)))))
(TWO,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ (cwoset @ V1)) @ ((c= @ (cfl @ V1)) @ V0)))))))
(TSUBTOPOLOGY_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ (ctopspace @ V1)) @ V0)) @ ((c= @ ((csubtopology @ V1) @ V0)) @ V1)))))))
(TOPEN_IN_SUBTOPOLOGY_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((copen_in @ ((csubtopology @ V1) @ V0)) @ V0)) @ ((cSUBSET @ V0) @ (ctopspace @ V1))))))))
(TCLOSED_IN_SUBTOPOLOGY_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cclosed_in @ ((csubtopology @ V1) @ V0)) @ V0)) @ ((cSUBSET @ V0) @ (ctopspace @ V1))))))))
(THAS_SIZE_POWERSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cHAS_SIZE @ V0) @ V1)) @ ((cHAS_SIZE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cSUBSET @ V3) @ V0)) @ V3)))))) @ ((cEXP @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))))))))
(THAS_SIZE_PERMUTATIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cHAS_SIZE @ V0) @ V1)) @ ((cHAS_SIZE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cpermutes @ V3) @ V0)) @ V3)))))) @ (cFACT @ V1))))))))
(THAS_SIZE_INDEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cHAS_SIZE @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((c< @ V3) @ V1)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c?! @ (^[V4]: ((c/__caret__ @ ((c< @ V4) @ V1)) @ ((c= @ (V2 @ V4)) @ V3))))))))))))))))
(TCHOOSE_SUBSET_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c==> @ (cFINITE @ V0)) @ ((c<= @ V1) @ (cCARD @ V0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((cHAS_SIZE @ V2) @ V1))))))))))
(TCHOOSE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c==> @ ((c<= @ V1) @ (cCARD @ V0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((cHAS_SIZE @ V2) @ V1)))))))))))
(THAS_SIZE_SUC,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cHAS_SIZE @ V0) @ (cSUC @ V1))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cHAS_SIZE @ ((cDELETE @ V0) @ V2)) @ V1)))))))))))
(TNUMBER_OF_COMBINATIONS_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cHAS_SIZE @ V0) @ V1)) @ ((cHAS_SIZE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V0)) @ ((cHAS_SIZE @ V4) @ V2))) @ V4)))))) @ (((cCOND @ ((c< @ V1) @ V2)) @ (cNUMERAL @ c_0)) @ ((cDIV @ (cFACT @ V1)) @ ((c* @ (cFACT @ V2)) @ (cFACT @ ((c- @ V1) @ V2))))))))))))))
(TNUMBER_OF_COMBINATIONS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cHAS_SIZE @ V0) @ V1)) @ ((cHAS_SIZE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V0)) @ ((cHAS_SIZE @ V4) @ V2))) @ V4)))))) @ (cbinom @ ((c__comma__ @ V1) @ V2)))))))))))
(TTOPOLOGICAL_SORT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((V2 @ V3) @ V4)) @ ((V2 @ V4) @ V3))) @ ((c= @ V3) @ V4))))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((V2 @ V3) @ V4)) @ ((V2 @ V4) @ V5))) @ ((V2 @ V3) @ V5)))))))))) @ ((c==> @ ((cHAS_SIZE @ V0) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ ((cIMAGE @ V3) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1))) @ ((c/__caret__ @ ((cIN @ V5) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1))) @ ((c< @ V4) @ V5)))) @ (c~ @ ((V2 @ (V3 @ V5)) @ (V3 @ V4))))))))))))))))))))
(TPIGEONHOLE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c< @ ((c* @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cCARD @ ((cIMAGE @ V2) @ V0)))) @ (cCARD @ V0)))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c/__caret__ @ ((cHAS_SIZE @ V3) @ V1)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((c= @ (V2 @ V5)) @ V4))))))))))))))))))
(TLENGTH_FILTER_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ (cLENGTH @ ((cFILTER @ V0) @ V1))) @ (cLENGTH @ V1)))))))
(TEPSILON_DELTA_MINIMAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V0 @ V3)) @ V3))))))) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V4)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((creal_lt @ V3) @ V2)))) @ ((c==> @ ((V1 @ V2) @ V4)) @ ((V1 @ V3) @ V4)))))))))) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((V1 @ V3) @ V2)))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((V1 @ V2) @ V3)))))))))))))
(TWOSET_WELL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cwoset @ V1)) @ ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ ((cfl @ V1) @ V2))))) @ (c? @ (^[V2]: (V0 @ V2))))) @ (c? @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V1 @ ((c__comma__ @ V2) @ V3)))))))))))))))
(TKL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cposet @ V1)) @ ((c==> @ ((cchain @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((c/__caret__ @ ((cchain @ V1) @ V2)) @ ((cSUBSET @ V0) @ V2))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cchain @ V1) @ V3)) @ ((cSUBSET @ V2) @ V3))) @ ((c= @ V3) @ V2))))))))))))))
(Tchain,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cchain @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ ((c__caret__/ @ (V1 @ ((c__comma__ @ V2) @ V3))) @ (V1 @ ((c__comma__ @ V3) @ V2))))))))))))))
(TKL_POSET_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (cposet @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V4)) @ ((cchain @ V1) @ V4))))))))))))))))
(TCHAIN_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cchain @ V1) @ V0)) @ ((cSUBSET @ V2) @ V0))) @ ((cchain @ V1) @ V2)))))))))
(TFL_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cwoset @ V1)) @ ((c= @ ((cfl @ (cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ ((c/__caret__ @ (V0 @ V4)) @ ((c/__caret__ @ (V0 @ V5)) @ (V1 @ ((c__comma__ @ V4) @ V5)))))))))))) @ V2)) @ ((c/__caret__ @ (V0 @ V2)) @ ((cfl @ V1) @ V2)))))))))))
(TUNIFORMLY_CONVERGENT_EQ_CAUCHY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((c<= @ V4) @ V5)) @ (V0 @ V6))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ ((V1 @ V5) @ V6)) @ (V2 @ V6)))) @ V3)))))))))))))) @ (c! @ (^[V2]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c? @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((c<= @ V3) @ V4)) @ ((c/__caret__ @ ((c<= @ V3) @ V5)) @ (V0 @ V6)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ ((V1 @ V4) @ V6)) @ ((V1 @ V5) @ V6)))) @ V2)))))))))))))))))))
(TUNIFORMLY_CAUCHY_IMP_UNIFORMLY_CONVERGENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((c<= @ V5) @ V6)) @ ((c/__caret__ @ ((c<= @ V5) @ V7)) @ (V0 @ V8)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ ((V1 @ V6) @ V8)) @ ((V1 @ V7) @ V8)))) @ V4)))))))))))))) @ (c! @ (^[V4]: ((c==> @ (V0 @ V4)) @ (c! @ (^[V5]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ (c? @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c<= @ V6) @ V7)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ ((V1 @ V7) @ V4)) @ (V2 @ V4)))) @ V5)))))))))))))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((c<= @ V4) @ V5)) @ (V0 @ V6))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ ((V1 @ V5) @ V6)) @ (V2 @ V6)))) @ V3)))))))))))))))))))
(TSERIES_CAUCHY_UNIFORM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((c<= @ V5) @ V6)) @ (V0 @ V7))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ ((cvsum @ ((cINTER @ V1) @ ((c.. @ (cNUMERAL @ c_0)) @ V6))) @ (V2 @ V7))) @ (V3 @ V7)))) @ V4)))))))))))))) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((c<= @ V4) @ V5)) @ (V0 @ V7))) @ ((creal_lt @ (cvector_norm @ ((cvsum @ ((cINTER @ V1) @ ((c.. @ V5) @ V6))) @ (V2 @ V7)))) @ V3)))))))))))))))))))))
(TMULTISET_INDUCT_LEMMA2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (V1 @ cmempty)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ (V1 @ ((cmunion @ V3) @ (cmsing @ V2)))))))))) @ ((c==> @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cSUBSET @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ (c~ @ ((c= @ ((cmultiplicity @ V2) @ V4)) @ (cNUMERAL @ c_0)))) @ V4)))))) @ V0)) @ (V1 @ V2)))))))))))
(TFINITE_SUBSETS_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (V1 @ V3))) @ V3))))))))))))
(TCARD_LE_SUBPOWERSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<=_c @ V0) @ V2)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (V1 @ V5)) @ (V3 @ ((cIMAGE @ V4) @ V5))))))))) @ ((c<=_c @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cSUBSET @ V5) @ V0)) @ (V1 @ V5))) @ V5)))))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cSUBSET @ V5) @ V2)) @ (V3 @ V5))) @ V5))))))))))))))))
(THULL_UNION_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chull @ V1) @ ((cUNION @ V0) @ V2))) @ ((chull @ V1) @ ((cUNION @ V0) @ ((chull @ V1) @ V2)))))))))))
(TSUM_OVER_PERMUTATIONS_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((cIN @ V2) @ V0)))) @ ((c= @ ((csum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cpermutes @ V4) @ ((cINSERT @ V2) @ V0))) @ V4)))))) @ V1)) @ ((csum @ ((cINSERT @ V2) @ V0)) @ (^[V3]: ((csum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cpermutes @ V5) @ V0)) @ V5)))))) @ (^[V4]: (V1 @ ((co @ (cswap @ ((c__comma__ @ V2) @ V3))) @ V4)))))))))))))))
(TPERMUTES_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (V1 @ cI)) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (V1 @ V5)) @ (cpermutation @ V5))))) @ (V1 @ ((co @ (cswap @ ((c__comma__ @ V3) @ V4))) @ V5)))))))))))) @ ((c==> @ ((cpermutes @ V2) @ V0)) @ (V1 @ V2))))))))))
(TCONTINUOUS_ON_LIFT_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((ccontinuous_on @ (^[V4]: (clift @ ((V1 @ V4) @ V3)))) @ V2)))))) @ ((ccontinuous_on @ (^[V3]: (clift @ ((cproduct @ V0) @ (V1 @ V3))))) @ V2)))))))))
(TINTEGRAL_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cintegrable_on @ (V2 @ V3)) @ V1)))))) @ ((c= @ ((cintegral @ V1) @ (^[V3]: ((cvsum @ V0) @ (^[V4]: ((V2 @ V4) @ V3)))))) @ ((cvsum @ V0) @ (^[V3]: ((cintegral @ V1) @ (V2 @ V3)))))))))))))
(TPASTING_LEMMA_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ (cUNIONS @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ V0)) @ (V2 @ V5))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V1)) @ (V2 @ V4))) @ ((ccontinuous_on @ (V3 @ V4)) @ (V2 @ V4))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ V6) @ ((cINTER @ V1) @ ((cINTER @ (V2 @ V4)) @ (V2 @ V5))))))) @ ((c= @ ((V3 @ V4) @ V6)) @ ((V3 @ V5) @ V6)))))))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ V1)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((cIN @ V5) @ ((cINTER @ V1) @ (V2 @ V6))))) @ ((c= @ (V4 @ V5)) @ ((V3 @ V6) @ V5))))))))))))))))))))
(TPASTING_LEMMA_EXISTS_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ (cUNIONS @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ V0)) @ (V2 @ V5))))))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ (V2 @ V4))) @ ((ccontinuous_on @ (V3 @ V4)) @ (V2 @ V4))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ V6) @ ((cINTER @ V1) @ ((cINTER @ (V2 @ V4)) @ (V2 @ V5))))))) @ ((c= @ ((V3 @ V4) @ V6)) @ ((V3 @ V5) @ V6))))))))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ V1)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((cIN @ V5) @ ((cINTER @ V1) @ (V2 @ V6))))) @ ((c= @ (V4 @ V5)) @ ((V3 @ V6) @ V5))))))))))))))))))))
(TCARD_ADD_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c=_c @ V0) @ V2)) @ ((c=_c @ V1) @ V3))) @ ((c=_c @ ((c+_c @ V0) @ V1)) @ ((c+_c @ V2) @ V3))))))))))))
(TCARD_MUL_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c=_c @ V0) @ V2)) @ ((c=_c @ V1) @ V3))) @ ((c=_c @ ((c*_c @ V0) @ V1)) @ ((c*_c @ V2) @ V3))))))))))))
(TCARD_EQ_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c=_c @ V0) @ V2)) @ ((c=_c @ V1) @ V3))) @ ((c= @ ((c=_c @ V0) @ V1)) @ ((c=_c @ V2) @ V3))))))))))))
(TCARD_LT_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c=_c @ V0) @ V2)) @ ((c=_c @ V1) @ V3))) @ ((c= @ ((c<_c @ V0) @ V1)) @ ((c<_c @ V2) @ V3))))))))))))
(TCARD_LE_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c=_c @ V0) @ V2)) @ ((c=_c @ V1) @ V3))) @ ((c= @ ((c<=_c @ V0) @ V1)) @ ((c<=_c @ V2) @ V3))))))))))))
(TCARD_LT_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<_c @ V0) @ V2)) @ ((c<_c @ V1) @ V3))) @ ((c<_c @ ((c+_c @ V0) @ V1)) @ ((c+_c @ V2) @ V3))))))))))))
(TCARD_LE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<=_c @ V0) @ V2)) @ ((c<=_c @ V1) @ V3))) @ ((c<=_c @ ((c+_c @ V0) @ V1)) @ ((c+_c @ V2) @ V3))))))))))))
(TCARD_LE_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<=_c @ V0) @ V2)) @ ((c<=_c @ V1) @ V3))) @ ((c<=_c @ ((c*_c @ V0) @ V1)) @ ((c*_c @ V2) @ V3))))))))))))
(TSUM_IMAGE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ (V2 @ V3)))))))) @ ((creal_le @ ((csum @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((csum @ V0) @ ((co @ V1) @ V2)))))))))))
(TSUM_IMAGE_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V4))) @ ((c= @ (V2 @ V3)) @ (V2 @ V4)))))) @ ((c= @ (V1 @ (V2 @ V3))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))) @ ((c= @ ((csum @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((csum @ V0) @ ((co @ V1) @ V2)))))))))))
(TNSUM_IMAGE_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V4))) @ ((c= @ (V2 @ V3)) @ (V2 @ V4)))))) @ ((c= @ (V1 @ (V2 @ V3))) @ (cNUMERAL @ c_0))))))))) @ ((c= @ ((cnsum @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((cnsum @ V0) @ ((co @ V1) @ V2)))))))))))
(TITERATE_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (c~ @ ((cIN @ V4) @ V2)))) @ ((c= @ (V3 @ V4)) @ (cneutral @ V1))))))) @ ((c= @ (((citerate @ V1) @ V0) @ V3)) @ (((citerate @ V1) @ V2) @ V3)))))))))))))
(TITERATE_DIFF_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ (((csupport @ V1) @ V3) @ V2))) @ ((cSUBSET @ (((csupport @ V1) @ V3) @ V0)) @ (((csupport @ V1) @ V3) @ V2)))) @ ((c= @ ((V1 @ (((citerate @ V1) @ ((cDIFF @ V2) @ V0)) @ V3)) @ (((citerate @ V1) @ V0) @ V3))) @ (((citerate @ V1) @ V2) @ V3)))))))))))))
(TITERATE_UNION_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ (((csupport @ V1) @ V3) @ V0))) @ ((c/__caret__ @ (cFINITE @ (((csupport @ V1) @ V3) @ V2))) @ ((cDISJOINT @ (((csupport @ V1) @ V3) @ V0)) @ (((csupport @ V1) @ V3) @ V2))))) @ ((c= @ (((citerate @ V1) @ ((cUNION @ V0) @ V2)) @ V3)) @ ((V1 @ (((citerate @ V1) @ V0) @ V3)) @ (((citerate @ V1) @ V2) @ V3))))))))))))))
(TITERATE_UNION_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V2)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ ((cINTER @ V0) @ V2))) @ ((c= @ (V3 @ V4)) @ (cneutral @ V1)))))))) @ ((c= @ (((citerate @ V1) @ ((cUNION @ V0) @ V2)) @ V3)) @ ((V1 @ (((citerate @ V1) @ V0) @ V3)) @ (((citerate @ V1) @ V2) @ V3))))))))))))))
(TVSUM_IMAGE_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V4))) @ ((c= @ (V2 @ V3)) @ (V2 @ V4)))))) @ ((c= @ (V1 @ (V2 @ V3))) @ (cvec @ (cNUMERAL @ c_0)))))))))) @ ((c= @ ((cvsum @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((cvsum @ V0) @ ((co @ V1) @ V2)))))))))))
(TCARD_INFINITE_CONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c=_c @ V0) @ V1)) @ ((c= @ (cINFINITE @ V0)) @ (cINFINITE @ V1))))))))
(TCARD_FINITE_CONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c=_c @ V0) @ V1)) @ ((c= @ (cFINITE @ V0)) @ (cFINITE @ V1))))))))
(TCARD_LE_LIST,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<=_c @ V0) @ V1)) @ ((c<=_c @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c! @ (^[V4]: ((c==> @ ((cMEM @ V4) @ V3)) @ ((cIN @ V4) @ V0))))) @ V3)))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c! @ (^[V4]: ((c==> @ ((cMEM @ V4) @ V3)) @ ((cIN @ V4) @ V1))))) @ V3))))))))))))
(TCARD_LE_POWERSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<=_c @ V0) @ V1)) @ ((c<=_c @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cSUBSET @ V3) @ V0)) @ V3)))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cSUBSET @ V3) @ V1)) @ V3))))))))))))
(TCARD_LE_FINITE_SUBSETS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<=_c @ V0) @ V1)) @ ((c<=_c @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (cFINITE @ V3))) @ V3)))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V1)) @ (cFINITE @ V3))) @ V3))))))))))))
(TCARD_LE_COUNTABLE_SUBSETS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<=_c @ V0) @ V1)) @ ((c<=_c @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (cCOUNTABLE @ V3))) @ V3)))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V1)) @ (cCOUNTABLE @ V3))) @ V3))))))))))))
(TCARD_ADD_ABSORB,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V1)) @ ((c<=_c @ V0) @ V1))) @ ((c=_c @ ((c+_c @ V0) @ V1)) @ V1)))))))
(TCARD_ADD_ABSORB_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V1)) @ ((c<=_c @ V0) @ V1))) @ ((c<=_c @ ((c+_c @ V0) @ V1)) @ V1)))))))
(TCARD_MUL_ABSORB_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V1)) @ ((c<=_c @ V0) @ V1))) @ ((c<=_c @ ((c*_c @ V0) @ V1)) @ V1)))))))
(TCARD_MUL_ABSORB,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ ((c<=_c @ V0) @ V1)))) @ ((c=_c @ ((c*_c @ V0) @ V1)) @ V1)))))))
(TCARD_LE_INFINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V0)) @ ((c<=_c @ V0) @ V1))) @ (cINFINITE @ V1)))))))
(TCARD_EQ_CARD_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c=_c @ V0) @ V1))) @ ((c= @ (cCARD @ V0)) @ (cCARD @ V1))))))))
(TCARD_LE_CARD_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c<=_c @ V0) @ V1))) @ ((c<= @ (cCARD @ V0)) @ (cCARD @ V1))))))))
(TCARD_LT_FINITE_INFINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cINFINITE @ V1))) @ ((c<_c @ V0) @ V1)))))))
(TCARD_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ (cCARD @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((c__comma__ @ V3) @ V4)))))))))) @ ((c* @ (cCARD @ V0)) @ (cCARD @ V1)))))))))
(TCARD_EQ_CARD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ ((c=_c @ V0) @ V1)) @ ((c= @ (cCARD @ V0)) @ (cCARD @ V1)))))))))
(TCARD_LT_CARD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ ((c<_c @ V0) @ V1)) @ ((c< @ (cCARD @ V0)) @ (cCARD @ V1)))))))))
(TCARD_LE_CARD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ ((c<=_c @ V0) @ V1)) @ ((c<= @ (cCARD @ V0)) @ (cCARD @ V1)))))))))
(TFINITE_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((c__comma__ @ V3) @ V4)))))))))))))))
(TCOUNTABLE_CARD_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (cCOUNTABLE @ V1))) @ (cCOUNTABLE @ ((c*_c @ V0) @ V1))))))))
(TCARD_LE_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((c<=_c @ V0) @ V1)) @ ((c<=_c @ V1) @ V0))) @ ((c=_c @ V0) @ V1)))))))
(TCARD_ADD_FINITE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cFINITE @ ((c+_c @ V0) @ V1))) @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))))))))
(TCOUNTABLE_CARD_MUL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cCOUNTABLE @ ((c*_c @ V0) @ V1))) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (cCOUNTABLE @ V1))))))))))
(TCARD_LE_ADDL,(c! @ (^[V0]: (c! @ (^[V1]: ((c<=_c @ V1) @ ((c+_c @ V0) @ V1)))))))
(TCARD_LE_ADDR,(c! @ (^[V0]: (c! @ (^[V1]: ((c<=_c @ V0) @ ((c+_c @ V0) @ V1)))))))
(TCARD_HAS_SIZE_CONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V0) @ V2)) @ ((c=_c @ V0) @ V1))) @ ((cHAS_SIZE @ V1) @ V2)))))))))
(THAS_SIZE_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V0) @ V2)) @ ((cHAS_SIZE @ V1) @ V3))) @ ((cHAS_SIZE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ V6) @ V1))) @ ((c__comma__ @ V5) @ V6))))))))) @ ((c* @ V2) @ V3))))))))))))
(TCARD_ADD_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c=_c @ ((c+_c @ V0) @ ((c+_c @ V1) @ V2))) @ ((c+_c @ ((c+_c @ V0) @ V1)) @ V2)))))))))
(TCARD_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c=_c @ ((c*_c @ ((c+_c @ V0) @ V1)) @ V2)) @ ((c+_c @ ((c*_c @ V0) @ V2)) @ ((c*_c @ V1) @ V2))))))))))
(TCARD_MUL_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c=_c @ ((c*_c @ V0) @ ((c*_c @ V1) @ V2))) @ ((c*_c @ ((c*_c @ V0) @ V1)) @ V2)))))))))
(TCARD_ADD2_ABSORB_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V2)) @ ((c/__caret__ @ ((c<_c @ V0) @ V2)) @ ((c<_c @ V1) @ V2)))) @ ((c<_c @ ((c+_c @ V0) @ V1)) @ V2)))))))))
(TCARD_ADD2_ABSORB_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V2)) @ ((c/__caret__ @ ((c<=_c @ V0) @ V2)) @ ((c<=_c @ V1) @ V2)))) @ ((c<=_c @ ((c+_c @ V0) @ V1)) @ V2)))))))))
(TCARD_MUL2_ABSORB_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V2)) @ ((c/__caret__ @ ((c<=_c @ V0) @ V2)) @ ((c<=_c @ V1) @ V2)))) @ ((c<=_c @ ((c*_c @ V0) @ V1)) @ V2)))))))))
(TMULT_NSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ ((c* @ ((cnsum @ V0) @ V2)) @ ((cnsum @ V1) @ V3))) @ ((cnsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ V6) @ V1))) @ ((c__comma__ @ V5) @ V6))))))))) @ (cGABS @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((cGEQ @ (V4 @ ((c__comma__ @ V5) @ V6))) @ ((c* @ (V2 @ V5)) @ (V3 @ V6)))))))))))))))))))))
(TBOUNDED_SUMS_IMAGES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (cbounded @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ V0)) @ ((V2 @ V5) @ V3)))))))))))) @ (cbounded @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ V0)) @ ((cvsum @ V1) @ (V2 @ V4))))))))))))))))
(TFINITE_SUBCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((V2 @ V4) @ V5)))) @ ((c__comma__ @ V4) @ V5)))))))))))))))))
(TFINITE_SUBSET_IMAGE_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cSUBSET @ V1) @ ((cIMAGE @ V2) @ V0)))) @ (c? @ (^[V3]: ((c/__caret__ @ (cFINITE @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((cSUBSET @ V1) @ ((cIMAGE @ V2) @ V3))))))))))))))
(TSUBSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cSUBSET @ V1) @ ((cIMAGE @ V2) @ V0))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c= @ V1) @ ((cIMAGE @ V2) @ V3)))))))))))))
(TFINITE_SUBSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cSUBSET @ V1) @ ((cIMAGE @ V2) @ V0)))) @ (c? @ (^[V3]: ((c/__caret__ @ (cFINITE @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c= @ V1) @ ((cIMAGE @ V2) @ V3))))))))))))))
(TCOUNTABLE_SUBSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((cSUBSET @ V1) @ ((cIMAGE @ V2) @ V0)))) @ (c? @ (^[V3]: ((c/__caret__ @ (cCOUNTABLE @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c= @ V1) @ ((cIMAGE @ V2) @ V3))))))))))))))
(TCARD_MUL_LT_INFINITE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<_c @ V0) @ V2)) @ ((c/__caret__ @ ((c<_c @ V1) @ V2)) @ (cINFINITE @ V2)))) @ ((c<_c @ ((c*_c @ V0) @ V1)) @ V2)))))))))
(TSUM_ZERO_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c__caret__/ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((creal_lt @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((creal_gt @ (V1 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))))
(TRADON_S_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((csum @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V3)))) @ V3)))))) @ V1)) @ (creal_neg @ ((csum @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((creal_lt @ (V1 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ V3)))))) @ V1)))))))))
(TSUM_POS_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V2)))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V2)))))))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((csum @ V0) @ V1))))))))
(TPRODUCT_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cproduct @ V0) @ (^[V2]: (creal_neg @ (V1 @ V2))))) @ ((creal_mul @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ V0))) @ ((cproduct @ V0) @ V1)))))))))
(TUPPER_BOUND_FINITE_SET_REAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (V1 @ V3)) @ V2))))))))))))
(TLOWER_BOUND_FINITE_SET_REAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ V2) @ (V1 @ V3)))))))))))))
(TSUM_POS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V2)))))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((csum @ V0) @ V1))))))))
(TPRODUCT_EQ_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((c= @ ((cproduct @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TINTEGER_SUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cinteger @ (V1 @ V2)))))) @ (cinteger @ ((csum @ V0) @ V1))))))))
(TSUM_BOUND_LT_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_lt @ (V1 @ V3)) @ ((creal_div @ V2) @ (creal_of_num @ (cCARD @ V0)))))))))) @ ((creal_lt @ ((csum @ V0) @ V1)) @ V2)))))))))
(TSUM_BOUND_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (V1 @ V3)) @ ((creal_div @ V2) @ (creal_of_num @ (cCARD @ V0)))))))))) @ ((creal_le @ ((csum @ V0) @ V1)) @ V2)))))))))
(TSUM_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((csum @ V0) @ (^[V3]: ((creal_mul @ (V1 @ V3)) @ V2)))) @ ((creal_mul @ ((csum @ V0) @ V1)) @ V2)))))))))
(TRADON_V_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((c= @ ((cvsum @ V0) @ V2)) @ (cvec @ (cNUMERAL @ c_0)))) @ (c! @ (^[V3]: ((c==> @ ((c= @ (V1 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ (V2 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))))))) @ ((c= @ ((cvsum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V4)))) @ V4)))))) @ V2)) @ (cvector_neg @ ((cvsum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((creal_lt @ (V1 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ V4)))))) @ V2)))))))))))
(TCONVEX_VSUM_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cconvex @ V3)) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V4))) @ ((c__caret__/ @ ((c= @ (V1 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((cIN @ (V2 @ V4)) @ V3))))))))) @ ((cIN @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V1 @ V4)) @ (V2 @ V4))))) @ V3)))))))))))
(TAFFINE_VSUM_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (caffine @ V3)) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c__caret__/ @ ((c= @ (V1 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((cIN @ (V2 @ V4)) @ V3)))))))) @ ((cIN @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V1 @ V4)) @ (V2 @ V4))))) @ V3)))))))))))
(TCONVEX_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cconvex @ V3)) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V4))) @ ((cIN @ (V2 @ V4)) @ V3))))))))) @ ((cIN @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V1 @ V4)) @ (V2 @ V4))))) @ V3)))))))))))
(TAFFINE_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (caffine @ V3)) @ ((c/__caret__ @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((cIN @ (V2 @ V4)) @ V3)))))))) @ ((cIN @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V1 @ V4)) @ (V2 @ V4))))) @ V3)))))))))))
(TSUM_EQ_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((c= @ (V1 @ V4)) @ (V3 @ V4)))))) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (c~ @ ((cIN @ V4) @ V2)))) @ ((c= @ (V1 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))) @ ((c= @ ((csum @ V0) @ V1)) @ ((csum @ V2) @ V3))))))))))))
(TSUM_BIJECTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c?! @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V4)) @ V3))))))))) @ ((c= @ ((csum @ V0) @ V1)) @ ((csum @ V0) @ ((co @ V1) @ V2)))))))))))
(TSUM_POS_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V4)))))) @ ((creal_le @ ((csum @ V0) @ V1)) @ V3)))) @ ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (V1 @ V2)) @ V3))))))))))))
(TNSUM_POS_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c< @ (cNUMERAL @ c_0)) @ (V1 @ V2))))))) @ ((c< @ (cNUMERAL @ c_0)) @ ((cnsum @ V0) @ V1))))))))
(TREAL_OF_NUM_NPRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (creal_of_num @ ((cnproduct @ V0) @ V1))) @ ((cproduct @ V0) @ (^[V2]: (creal_of_num @ (V1 @ V2)))))))))))
(TUPPER_BOUND_FINITE_SET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c<= @ (V1 @ V3)) @ V2))))))))))))
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(TNSUM_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (cNUMERAL @ c_0)))))) @ ((c= @ ((cnsum @ V0) @ V1)) @ (cNUMERAL @ c_0))))))))
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(TNSUM_BOUND_LT_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c< @ (V1 @ V3)) @ ((cDIV @ V2) @ (cCARD @ V0))))))))) @ ((c< @ ((cnsum @ V0) @ V1)) @ V2)))))))))
(TNPRODUCT_MOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0))))) @ (((c== @ (((citerate @ c*) @ V0) @ (^[V3]: ((cMOD @ (V1 @ V3)) @ V2)))) @ (((citerate @ c*) @ V0) @ V1)) @ (cnum_mod @ V2))))))))))
(TMOD_NSUM_MOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c~ @ ((c= @ V2) @ (cNUMERAL @ c_0))))) @ ((c= @ ((cMOD @ ((cnsum @ V0) @ V1)) @ V2)) @ ((cMOD @ ((cnsum @ V0) @ (^[V3]: ((cMOD @ (V1 @ V3)) @ V2)))) @ V2))))))))))
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(TNSUM_BIJECTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c?! @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V4)) @ V3))))))))) @ ((c= @ ((cnsum @ V0) @ V1)) @ ((cnsum @ V0) @ ((co @ V1) @ V2)))))))))))
(TNSUM_POS_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c<= @ ((cnsum @ V0) @ V1)) @ V3))) @ ((c==> @ ((cIN @ V2) @ V0)) @ ((c<= @ (V1 @ V2)) @ V3))))))))))))
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(TMEASURE_DISJOINT_UNIONS_IMAGE_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ (V1 @ V3)) @ cEMPTY)))) @ V3))))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cmeasurable @ (V1 @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((cDISJOINT @ (V1 @ V2)) @ (V1 @ V3)))))))))) @ ((c= @ (cmeasure @ (cUNIONS @ ((cIMAGE @ V1) @ V0)))) @ ((csum @ V0) @ (^[V2]: (cmeasure @ (V1 @ V2)))))))))))
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(TMEASURE_NEGLIGIBLE_UNIONS_IMAGE_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ (V1 @ V3)) @ cEMPTY)))) @ V3))))))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cmeasurable @ (V1 @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ (cnegligible @ ((cINTER @ (V1 @ V2)) @ (V1 @ V3))))))))))) @ ((c= @ (cmeasure @ (cUNIONS @ ((cIMAGE @ V1) @ V0)))) @ ((csum @ V0) @ (^[V2]: (cmeasure @ (V1 @ V2)))))))))))
(THAS_MEASURE_DISJOINT_UNIONS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cmeasurable @ (V1 @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((cDISJOINT @ (V1 @ V2)) @ (V1 @ V3)))))))))) @ ((chas_measure @ (cUNIONS @ ((cIMAGE @ V1) @ V0))) @ ((csum @ V0) @ (^[V2]: (cmeasure @ (V1 @ V2)))))))))))
(TMEASURE_DISJOINT_UNIONS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cmeasurable @ (V1 @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((cDISJOINT @ (V1 @ V2)) @ (V1 @ V3)))))))))) @ ((c= @ (cmeasure @ (cUNIONS @ ((cIMAGE @ V1) @ V0)))) @ ((csum @ V0) @ (^[V2]: (cmeasure @ (V1 @ V2)))))))))))
(THAS_MEASURE_NEGLIGIBLE_UNIONS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cmeasurable @ (V1 @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ (cnegligible @ ((cINTER @ (V1 @ V2)) @ (V1 @ V3))))))))))) @ ((chas_measure @ (cUNIONS @ ((cIMAGE @ V1) @ V0))) @ ((csum @ V0) @ (^[V2]: (cmeasure @ (V1 @ V2)))))))))))
(TMEASURE_NEGLIGIBLE_UNIONS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cmeasurable @ (V1 @ V2)))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ (cnegligible @ ((cINTER @ (V1 @ V2)) @ (V1 @ V3))))))))))) @ ((c= @ (cmeasure @ (cUNIONS @ ((cIMAGE @ V1) @ V0)))) @ ((csum @ V0) @ (^[V2]: (cmeasure @ (V1 @ V2)))))))))))
(TMEASURE_UNIONS_LE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cmeasurable @ (V1 @ V2))))))) @ ((creal_le @ (cmeasure @ (cUNIONS @ ((cIMAGE @ V1) @ V0)))) @ ((csum @ V0) @ (^[V2]: (cmeasure @ (V1 @ V2)))))))))))
(TOPEN_EXISTS_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (copen @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((V1 @ V2) @ V4)) @ V4)))))))))) @ (copen @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c/__caret__ @ (V0 @ V4)) @ ((V1 @ V4) @ V3))))) @ V3))))))))))))
(TCLOSED_FORALL_IN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (cclosed @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((V1 @ V2) @ V4)) @ V4)))))))))) @ (cclosed @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c! @ (^[V4]: ((c==> @ (V0 @ V4)) @ ((V1 @ V4) @ V3))))) @ V3))))))))))))
(TMEASURABLE_ON_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cmeasurable_on @ (V1 @ V3)) @ V2)))))) @ ((cmeasurable_on @ (^[V3]: ((cvsum @ V0) @ (^[V4]: ((V1 @ V4) @ V3))))) @ V2)))))))))
(TINTEGRABLE_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cintegrable_on @ (V1 @ V3)) @ V2)))))) @ ((cintegrable_on @ (^[V3]: ((cvsum @ V0) @ (^[V4]: ((V1 @ V4) @ V3))))) @ V2)))))))))
(TABSOLUTELY_INTEGRABLE_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cabsolutely_integrable_on @ (V1 @ V3)) @ V2)))))) @ ((cabsolutely_integrable_on @ (^[V3]: ((cvsum @ V0) @ (^[V4]: ((V1 @ V4) @ V3))))) @ V2)))))))))
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(TPASTING_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ ((copen_in @ ((csubtopology @ ceuclidean) @ V4)) @ (V1 @ V5))) @ ((ccontinuous_on @ (V2 @ V5)) @ (V1 @ V5))))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((cIN @ V7) @ ((cINTER @ V4) @ ((cINTER @ (V1 @ V5)) @ (V1 @ V6))))))) @ ((c= @ ((V2 @ V5) @ V7)) @ ((V2 @ V6) @ V7)))))))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V4)) @ (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ (V1 @ V6))) @ ((c= @ (V3 @ V5)) @ ((V2 @ V6) @ V5)))))))))))) @ ((ccontinuous_on @ V3) @ V4)))))))))))))
(TFINREC_FUN_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (c? @ (^[V3]: (c? @ (^[V4]: (((V1 @ V2) @ V3) @ V4))))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (((V1 @ V4) @ V5) @ V2)) @ (((V1 @ V4) @ V6) @ V3))) @ ((c/__caret__ @ ((c= @ V5) @ V6)) @ ((c= @ V2) @ V3))))))))))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (V0 @ V3)) @ ((c= @ (c? @ (^[V5]: (((V1 @ V3) @ V4) @ V5)))) @ ((c= @ (V2 @ V3)) @ V4)))))))))))))))
(THAS_SIZE_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V0) @ V2)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((cHAS_SIZE @ (V1 @ V4)) @ V3))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ (c~ @ ((c= @ V4) @ V5))))) @ ((cDISJOINT @ (V1 @ V4)) @ (V1 @ V5)))))))))) @ ((cHAS_SIZE @ (cUNIONS @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ V0)) @ (V1 @ V5)))))))) @ ((c* @ V2) @ V3))))))))))))
(THAS_SIZE_PRODUCT_DEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V0) @ V2)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((cHAS_SIZE @ (V1 @ V4)) @ V3)))))) @ ((cHAS_SIZE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((cIN @ V6) @ (V1 @ V5)))) @ ((c__comma__ @ V5) @ V6))))))))) @ ((c* @ V2) @ V3))))))))))))
(TCARD_UNIONS_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V0) @ V2)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ (cFINITE @ (V1 @ V4))) @ ((c<= @ (cCARD @ (V1 @ V4))) @ V3))))))) @ ((c<= @ (cCARD @ (cUNIONS @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ V0)) @ (V1 @ V5))))))))) @ ((c* @ V2) @ V3))))))))))))
(TSUM_MULTICOUNT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V3)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((c= @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((V1 @ V6) @ V4))) @ V6))))))) @ V2))))))) @ ((c= @ ((csum @ V0) @ (^[V4]: (creal_of_num @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V3)) @ ((V1 @ V4) @ V6))) @ V6)))))))))) @ (creal_of_num @ ((c* @ V2) @ (cCARD @ V3))))))))))))))
(TNSUM_MULTICOUNT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V3)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((c= @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((V1 @ V6) @ V4))) @ V6))))))) @ V2))))))) @ ((c= @ ((cnsum @ V0) @ (^[V4]: (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V3)) @ ((V1 @ V4) @ V6))) @ V6))))))))) @ ((c* @ V2) @ (cCARD @ V3)))))))))))))
(TSUM_MULTICOUNT_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V2)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((c= @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((V1 @ V6) @ V4))) @ V6))))))) @ (V3 @ V4)))))))) @ ((c= @ ((csum @ V0) @ (^[V4]: (creal_of_num @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ ((V1 @ V4) @ V6))) @ V6)))))))))) @ ((csum @ V2) @ (^[V4]: (creal_of_num @ (V3 @ V4)))))))))))))))
(TNSUM_MULTICOUNT_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V2)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((c= @ (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((V1 @ V6) @ V4))) @ V6))))))) @ (V3 @ V4)))))))) @ ((c= @ ((cnsum @ V0) @ (^[V4]: (cCARD @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ ((V1 @ V4) @ V6))) @ V6))))))))) @ ((cnsum @ V2) @ (^[V4]: (V3 @ V4))))))))))))))
(TSUM_SUM_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (cFINITE @ (V1 @ V3))))))) @ ((c= @ ((csum @ V0) @ (^[V3]: ((csum @ (V1 @ V3)) @ (V2 @ V3))))) @ ((csum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ (V1 @ V4)))) @ ((c__comma__ @ V4) @ V5))))))))) @ (cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ ((V2 @ V4) @ V5))))))))))))))))))
(TNSUM_NSUM_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (cFINITE @ (V1 @ V3))))))) @ ((c= @ ((cnsum @ V0) @ (^[V3]: ((cnsum @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cnsum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ (V1 @ V4)))) @ ((c__comma__ @ V4) @ V5))))))))) @ (cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ ((V2 @ V4) @ V5))))))))))))))))))
(TVSUM_VSUM_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (cFINITE @ (V1 @ V3))))))) @ ((c= @ ((cvsum @ V0) @ (^[V3]: ((cvsum @ (V1 @ V3)) @ (V2 @ V3))))) @ ((cvsum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ (V1 @ V4)))) @ ((c__comma__ @ V4) @ V5))))))))) @ (cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ ((V2 @ V4) @ V5))))))))))))))))))
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(TCOUNTABLE_PRODUCT_DEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (cCOUNTABLE @ (V1 @ V3))))))) @ (cCOUNTABLE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V5) @ (V1 @ V4)))) @ ((V2 @ V4) @ V5)))))))))))))))))
(TMULTIVECTOR_VSUM_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$$ @ ((cvsum @ V0) @ V1)) @ V2)) @ ((csum @ V0) @ (^[V3]: ((c$$ @ (V1 @ V3)) @ V2))))))))))))
(TNORM_VSUM_PYTHAGOREAN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cpairwise @ (^[V2]: (^[V3]: ((corthogonal @ (V1 @ V2)) @ (V1 @ V3))))) @ V0))) @ ((c= @ ((creal_pow @ (cvector_norm @ ((cvsum @ V0) @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((csum @ V0) @ (^[V2]: ((creal_pow @ (cvector_norm @ (V1 @ V2))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))
(TVSUM_SUPPORT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ (V1 @ V3)) @ (cvec @ (cNUMERAL @ c_0)))))) @ V3)))))) @ V1)) @ ((cvsum @ V0) @ V1)))))))
(Tvsum,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ V0) @ V1)) @ (clambda @ (^[V2]: ((csum @ V0) @ (^[V3]: ((c$ @ (V1 @ V3)) @ V2)))))))))))
(TVSUM_NORM_ALLSUBSETS_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V0)) @ ((creal_le @ (cvector_norm @ ((cvsum @ V3) @ V1))) @ V2)))))) @ ((creal_le @ ((csum @ V0) @ (^[V3]: (cvector_norm @ (V1 @ V3))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ (creal_of_num @ (cdimindex @ cUNIV))) @ V2)))))))))))
(TVSUM_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ ((cvsum @ V0) @ V1)) @ V2)) @ ((csum @ V0) @ (^[V3]: ((c$ @ (V1 @ V3)) @ V2))))))))))))
(TRIGID_TRANSFORMATION_BETWEEN_CONGRUENT_SETS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V0))) @ ((c= @ (cdistance @ ((c__comma__ @ (V2 @ V3)) @ (V2 @ V4)))) @ (cdistance @ ((c__comma__ @ (V1 @ V3)) @ (V1 @ V4)))))))))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (corthogonal_transformation @ V4)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V0)) @ ((c= @ (V1 @ V5)) @ ((cvector_add @ V3) @ (V4 @ (V2 @ V5))))))))))))))))))))
(TVSUM_BIJECTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c?! @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V4)) @ V3))))))))) @ ((c= @ ((cvsum @ V0) @ V1)) @ ((cvsum @ V0) @ ((co @ V1) @ V2)))))))))))
(TORTHOGONAL_LVSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((corthogonal @ (V1 @ V3)) @ V2)))))) @ ((corthogonal @ ((cvsum @ V0) @ V1)) @ V2)))))))))
(TVSUM_EQ_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((c= @ (V1 @ V4)) @ (V3 @ V4)))))) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (c~ @ ((cIN @ V4) @ V2)))) @ ((c= @ (V1 @ V4)) @ (cvec @ (cNUMERAL @ c_0)))))))))) @ ((c= @ ((cvsum @ V0) @ V1)) @ ((cvsum @ V2) @ V3))))))))))))
(TVSUM_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((c= @ ((cvsum @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TMSUM_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cmsum @ V0) @ (^[V2]: (cmatrix_neg @ (V1 @ V2))))) @ (cmatrix_neg @ ((cmsum @ V0) @ V1)))))))))
(TMSUM_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ (cFINITE @ V0)))))) @ ((c= @ ((c$ @ ((c$ @ ((cmsum @ V0) @ V1)) @ V2)) @ V3)) @ ((csum @ V0) @ (^[V4]: ((c$ @ ((c$ @ (V1 @ V4)) @ V2)) @ V3))))))))))))))
(TMSUM_MATRIX_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cmsum @ V0) @ (^[V3]: ((cmatrix_mul @ (V1 @ V3)) @ V2)))) @ ((cmatrix_mul @ ((cmsum @ V0) @ V1)) @ V2))))))))))
(TINTER_SUBSET_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ ((cINTER @ V1) @ V0)) @ V0))))))
(TINTER_SUBSET_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ ((cINTER @ V0) @ V1)) @ V0))))))
(TSUBSET_UNION_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ V0) @ ((cUNION @ V1) @ V0)))))))
(TSUBSET_UNION_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ V0) @ ((cUNION @ V0) @ V1)))))))
(TFINITE_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c__caret__/ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ (cFINITE @ ((cINTER @ V0) @ V1))))))))
(TCARD_LE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cSUBSET @ V0) @ V1)) @ ((c<=_c @ V0) @ V1)))))))
(TCARD_DISJOINT_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)) @ ((c=_c @ ((cUNION @ V0) @ V1)) @ ((c+_c @ V0) @ V1))))))))
(TSUBSET_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((cSUBSET @ V1) @ V0))) @ ((c= @ V0) @ V1)))))))
(TCARD_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ (cFINITE @ V1))) @ ((c<= @ (cCARD @ V0)) @ (cCARD @ V1))))))))
(TCARD_PSUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cPSUBSET @ V0) @ V1)) @ (cFINITE @ V1))) @ ((c< @ (cCARD @ V0)) @ (cCARD @ V1))))))))
(TINFINITE_DIFF_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V0)) @ (cFINITE @ V1))) @ (cINFINITE @ ((cDIFF @ V0) @ V1))))))))
(TCARD_SUBSET_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c= @ (cCARD @ V0)) @ (cCARD @ V1))))) @ ((c= @ V0) @ V1)))))))
(TCARD_SUBSET_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c<= @ (cCARD @ V1)) @ (cCARD @ V0))))) @ ((c= @ V0) @ V1)))))))
(TFINITE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cSUBSET @ V1) @ V0))) @ (cFINITE @ V1)))))))
(TCARD_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)))) @ ((c= @ (cCARD @ ((cUNION @ V0) @ V1))) @ ((c+ @ (cCARD @ V0)) @ (cCARD @ V1)))))))))
(TCARD_ADD_SYMDIFF_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ ((c+ @ (cCARD @ V0)) @ (cCARD @ V1))) @ ((c+ @ (cCARD @ ((cUNION @ ((cDIFF @ V0) @ V1)) @ ((cDIFF @ V1) @ V0)))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cCARD @ ((cINTER @ V0) @ V1)))))))))))
(TCARD_UNION_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c<= @ (cCARD @ ((cUNION @ V0) @ V1))) @ ((c+ @ (cCARD @ V0)) @ (cCARD @ V1)))))))))
(TFINITE_UNION_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ (cFINITE @ ((cUNION @ V0) @ V1))))))))
(TCOUNTABLE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ ((cSUBSET @ V1) @ V0))) @ (cCOUNTABLE @ V1)))))))
(TCOUNTABLE_UNION_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (cCOUNTABLE @ V1))) @ (cCOUNTABLE @ ((cUNION @ V0) @ V1))))))))
(TFINITE_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (V1 @ V3))) @ V3))))))))))))
(TMONO_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c? @ (^[V2]: (V0 @ V2)))) @ ((c==> @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))) @ (c? @ (^[V2]: (V1 @ V2))))))))))
(Tre_union,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cre_union @ V0) @ V1)) @ (^[V2]: ((c__caret__/ @ (V0 @ V2)) @ (V1 @ V2)))))))))
(Tre_intersect,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cre_intersect @ V0) @ V1)) @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ (V1 @ V2)))))))))
(TUNION_COMM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cUNION @ V1) @ V0)) @ ((cUNION @ V0) @ V1)))))))
(TUNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cUNION @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c__caret__/ @ ((cIN @ V3) @ V0)) @ ((cIN @ V3) @ V1))) @ V3)))))))))))
(TINTER_COMM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINTER @ V1) @ V0)) @ ((cINTER @ V0) @ V1)))))))
(TINTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINTER @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V3) @ V1))) @ V3)))))))))))
(TDIFF_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDIFF @ ((cDIFF @ V0) @ V1)) @ V1)) @ ((cDIFF @ V0) @ V1)))))))
(TDIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDIFF @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V1)))) @ V3)))))))))))
(Tre_subset,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cre_subset @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TOR_EXISTS_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c__caret__/ @ (c? @ (^[V2]: (V0 @ V2)))) @ (c? @ (^[V2]: (V1 @ V2))))) @ (c? @ (^[V2]: ((c__caret__/ @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TSUBSET_INTER_ABSORPTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cSUBSET @ V1) @ V0)) @ ((c= @ ((cINTER @ V1) @ V0)) @ V1)))))))
(TSUBSET_UNION_ABSORPTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cSUBSET @ V0) @ V1)) @ ((c= @ ((cUNION @ V0) @ V1)) @ V1)))))))
(TSUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cSUBSET @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((cIN @ V2) @ V1))))))))))
(TPSUBSET_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cPSUBSET @ V1) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c~ @ ((cIN @ V2) @ V1))))))))))))
(TPSUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cPSUBSET @ V0) @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ (c~ @ ((c= @ V0) @ V1)))))))))
(TPSUBSET_INSERT_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cPSUBSET @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((cIN @ V2) @ V0))) @ ((cSUBSET @ ((cINSERT @ V2) @ V0)) @ V1))))))))))
(TDISJOINT_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDISJOINT @ V1) @ V0)) @ ((cDISJOINT @ V0) @ V1)))))))
(TDISJOINT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDISJOINT @ V0) @ V1)) @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)))))))
(TIN_DISJOINT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDISJOINT @ V0) @ V1)) @ (c~ @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((cIN @ V2) @ V1)))))))))))
(TEMPTY_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cUNION @ V0) @ V1)) @ cEMPTY)) @ ((c/__caret__ @ ((c= @ V0) @ cEMPTY)) @ ((c= @ V1) @ cEMPTY))))))))
(TEXTENSION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ ((cIN @ V2) @ V0)) @ ((cIN @ V2) @ V1))))))))))
(TSUBSETA_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cre_subset @ V0) @ V1)) @ ((cre_subset @ V1) @ V0))) @ ((c= @ V0) @ V1)))))))
(TSUBSET_ANTISYM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((cSUBSET @ V1) @ V0))) @ ((c= @ V0) @ V1)))))))
(TAND_FORALL_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ V2)))) @ (c! @ (^[V2]: (V1 @ V2))))) @ (c! @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TNOT_EQUAL_SETS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c= @ V1) @ V0))) @ (c? @ (^[V2]: ((c= @ ((cIN @ V2) @ V0)) @ (c~ @ ((cIN @ V2) @ V1)))))))))))
(TFINITE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cFINITE @ ((cUNION @ V0) @ V1))) @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))))))))
(TCOUNTABLE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cCOUNTABLE @ ((cUNION @ V0) @ V1))) @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (cCOUNTABLE @ V1))))))))
(TEXISTS_OR_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c__caret__/ @ (V0 @ V2)) @ (V1 @ V2))))) @ ((c__caret__/ @ (c? @ (^[V2]: (V0 @ V2)))) @ (c? @ (^[V2]: (V1 @ V2))))))))))
(TFORALL_AND_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ (V1 @ V2))))) @ ((c/__caret__ @ (c! @ (^[V2]: (V0 @ V2)))) @ (c! @ (^[V2]: (V1 @ V2))))))))))
(TUNION_LE_ADD_C,(c! @ (^[V0]: (c! @ (^[V1]: ((c<=_c @ ((cUNION @ V0) @ V1)) @ ((c+_c @ V0) @ V1)))))))
(TCHOOSE_SUBSET_BETWEEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((c<= @ (cCARD @ V0)) @ V2)) @ ((c==> @ (cFINITE @ V1)) @ ((c<= @ V2) @ (cCARD @ V1))))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V0) @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V1)) @ ((cHAS_SIZE @ V3) @ V2)))))))))))))
(THAS_SIZE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V0) @ V2)) @ ((c/__caret__ @ ((cHAS_SIZE @ V1) @ V3)) @ ((cSUBSET @ V0) @ V1)))) @ ((c<= @ V2) @ V3)))))))))))
(TEVENTUALLY_MP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ceventually @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((ceventually @ V0) @ V2))) @ ((ceventually @ V1) @ V2)))))))))
(TEVENTUALLY_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V1 @ V3))))) @ ((ceventually @ V0) @ V2))) @ ((ceventually @ V1) @ V2)))))))))
(TEVENTUALLY_AND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ceventually @ (^[V3]: ((c/__caret__ @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((c/__caret__ @ ((ceventually @ V0) @ V2)) @ ((ceventually @ V1) @ V2))))))))))
(TMONO_ALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cALL @ V0) @ V2)) @ ((c==> @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V1 @ V3))))) @ ((cALL @ V1) @ V2))))))))))
(TALL_FILTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cALL @ V1) @ ((cFILTER @ V0) @ V2))) @ ((cALL @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TEXISTS_SUBSET_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ ((cUNION @ V0) @ V1))) @ (V2 @ V3))))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V4) @ V1)) @ (V2 @ ((cUNION @ V3) @ V4))))))))))))))))
(TFORALL_SUBSET_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ ((cUNION @ V0) @ V1))) @ (V2 @ V3))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((cSUBSET @ V4) @ V1))) @ (V2 @ ((cUNION @ V3) @ V4)))))))))))))))
(TSUM_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V1)))) @ ((c= @ (V2 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((csum @ V0) @ V2)) @ ((csum @ V1) @ V2))))))))))
(TSUM_SUBSET_SIMPLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cDIFF @ V1) @ V0))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V2 @ V3)))))))) @ ((creal_le @ ((csum @ V0) @ V2)) @ ((csum @ V1) @ V2))))))))))
(TSUM_UNION_RZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V1)))) @ ((c= @ (V2 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((csum @ ((cUNION @ V1) @ V0)) @ V2)) @ ((csum @ V1) @ V2))))))))))
(TSUM_UNION_LZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V1)))) @ ((c= @ (V2 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((csum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((csum @ V1) @ V2))))))))))
(TSUM_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cDIFF @ V0) @ V1))) @ ((creal_le @ (V2 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cDIFF @ V1) @ V0))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V2 @ V3))))))))) @ ((creal_le @ ((csum @ V0) @ V2)) @ ((csum @ V1) @ V2))))))))))
(TSUM_INCL_EXCL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ ((creal_add @ ((csum @ V0) @ V2)) @ ((csum @ V1) @ V2))) @ ((creal_add @ ((csum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((csum @ ((cINTER @ V0) @ V1)) @ V2)))))))))))
(TNSUM_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V1)))) @ ((c= @ (V2 @ V3)) @ (cNUMERAL @ c_0))))))) @ ((c= @ ((cnsum @ V0) @ V2)) @ ((cnsum @ V1) @ V2))))))))))
(TNSUM_UNION_RZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V1)))) @ ((c= @ (V2 @ V3)) @ (cNUMERAL @ c_0))))))) @ ((c= @ ((cnsum @ ((cUNION @ V1) @ V0)) @ V2)) @ ((cnsum @ V1) @ V2))))))))))
(TNSUM_UNION_LZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V1)))) @ ((c= @ (V2 @ V3)) @ (cNUMERAL @ c_0))))))) @ ((c= @ ((cnsum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cnsum @ V1) @ V2))))))))))
(TNSUM_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cDIFF @ V0) @ V1))) @ ((c= @ (V2 @ V3)) @ (cNUMERAL @ c_0)))))))) @ ((c<= @ ((cnsum @ V0) @ V2)) @ ((cnsum @ V1) @ V2))))))))))
(TNSUM_INCL_EXCL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ ((c+ @ ((cnsum @ V0) @ V2)) @ ((cnsum @ V1) @ V2))) @ ((c+ @ ((cnsum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cnsum @ ((cINTER @ V0) @ V1)) @ V2)))))))))))
(TNSUM_RESTRICT_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cnsum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (V1 @ V4))) @ V4)))))) @ V2)) @ ((cnsum @ V0) @ (^[V3]: (((cCOND @ (V1 @ V3)) @ (V2 @ V3)) @ (cNUMERAL @ c_0))))))))))))
(TVSUM_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V1)))) @ ((c= @ (V2 @ V3)) @ (cvec @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((cvsum @ V0) @ V2)) @ ((cvsum @ V1) @ V2))))))))))
(TVSUM_INCL_EXCL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ ((cvector_add @ ((cvsum @ V0) @ V2)) @ ((cvsum @ V1) @ V2))) @ ((cvector_add @ ((cvsum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cvsum @ ((cINTER @ V0) @ V1)) @ V2)))))))))))
(TVSUM_UNION_RZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V1)))) @ ((c= @ (V2 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((c= @ ((cvsum @ ((cUNION @ V1) @ V0)) @ V2)) @ ((cvsum @ V1) @ V2))))))))))
(TVSUM_UNION_LZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((cIN @ V3) @ V1)))) @ ((c= @ (V2 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((c= @ ((cvsum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cvsum @ V1) @ V2))))))))))
(TRIGID_TRANSFORMATION_BETWEEN_CONGRUENT_SETS_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V0) @ V1)) @ ((c/__caret__ @ ((c= @ ((chull @ caffine) @ ((cIMAGE @ V2) @ V0))) @ ((chull @ caffine) @ ((cIMAGE @ V2) @ V1)))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((cIN @ V5) @ V0))) @ ((c= @ (cdistance @ ((c__comma__ @ (V3 @ V4)) @ (V3 @ V5)))) @ (cdistance @ ((c__comma__ @ (V2 @ V4)) @ (V2 @ V5)))))))))))) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ (corthogonal_transformation @ V5)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V1)) @ ((c= @ (V2 @ V6)) @ ((cvector_add @ V4) @ (V5 @ (V3 @ V6))))))))))))))))))))))
(TMSUM_RESTRICT_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmsum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (V1 @ V4))) @ V4)))))) @ V2)) @ ((cmsum @ V0) @ (^[V3]: (((cCOND @ (V1 @ V3)) @ (V2 @ V3)) @ (cmat @ (cNUMERAL @ c_0)))))))))))))
(TSUBSETA_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cre_subset @ V1) @ V0)) @ ((cre_subset @ V0) @ V2))) @ ((cre_subset @ V1) @ V2)))))))))
(TSUBSET_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((cSUBSET @ V0) @ V2))) @ ((cSUBSET @ V1) @ V2)))))))))
(TSUBSET_PSUBSET_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((cPSUBSET @ V0) @ V2))) @ ((cPSUBSET @ V1) @ V2)))))))))
(TPSUBSET_SUBSET_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cPSUBSET @ V1) @ V0)) @ ((cSUBSET @ V0) @ V2))) @ ((cPSUBSET @ V1) @ V2)))))))))
(TPSUBSET_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cPSUBSET @ V1) @ V0)) @ ((cPSUBSET @ V0) @ V2))) @ ((cPSUBSET @ V1) @ V2)))))))))
(TUNION_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cUNION @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cUNION @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TINTER_OVER_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cUNION @ V1) @ ((cINTER @ V0) @ V2))) @ ((cINTER @ ((cUNION @ V1) @ V0)) @ ((cUNION @ V1) @ V2))))))))))
(TINTER_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cINTER @ ((cINTER @ V0) @ V1)) @ V2)) @ ((cINTER @ V0) @ ((cINTER @ V1) @ V2))))))))))
(TUNION_OVER_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cINTER @ V1) @ ((cUNION @ V0) @ V2))) @ ((cUNION @ ((cINTER @ V1) @ V0)) @ ((cINTER @ V1) @ V2))))))))))
(TDISJOINT_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cDISJOINT @ ((cUNION @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((cDISJOINT @ V0) @ V2)) @ ((cDISJOINT @ V1) @ V2))))))))))
(TEXISTS_IN_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ ((cUNION @ V0) @ V1))) @ (V2 @ V3))))) @ ((c__caret__/ @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (V2 @ V3))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ (V2 @ V3)))))))))))))
(TFORALL_IN_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cUNION @ V0) @ V1))) @ (V2 @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (V2 @ V3))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (V2 @ V3)))))))))))))
(TMONO_FORALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V1 @ V3))))) @ ((c==> @ (c! @ (^[V3]: (V0 @ V3)))) @ (V1 @ V2))))))))))
(TDELETE_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cINTER @ ((cDELETE @ V0) @ V2)) @ V1)) @ ((cDELETE @ ((cINTER @ V0) @ V1)) @ V2)))))))))
(TSUBSET_INSERT_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cSUBSET @ V1) @ ((cINSERT @ V2) @ V0))) @ ((c__caret__/ @ ((cSUBSET @ V1) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c= @ V1) @ ((cINSERT @ V2) @ V3))))))))))))))
(TCARD_IMAGE_EQ_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((c= @ (cCARD @ ((cIMAGE @ V1) @ V0))) @ (cCARD @ V0))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3)))))))))))))
(TFINITE_IMAGE_EXPAND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ V3) @ (V1 @ V4)))))) @ V3))))))))))))
(TIMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIMAGE @ V1) @ V0)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ V3) @ (V1 @ V4)))))) @ V3)))))))))))
(TINJECTIVE_ON_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ ((c= @ ((cIMAGE @ V1) @ V2)) @ ((cIMAGE @ V1) @ V3))))) @ ((c= @ V2) @ V3))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))))))))
(TIMAGE_INJECTIVE_IMAGE_OF_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((cSUBSET @ V2) @ V0)) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ V0)) @ ((cIMAGE @ V1) @ V2))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((c= @ (V1 @ V3)) @ (V1 @ V4))))) @ ((c= @ V3) @ V4)))))))))))))))
(TITERATE_EQ_NEUTRAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cmonoidal @ V2)) @ ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ (cneutral @ V2)))))) @ ((c= @ (((citerate @ V2) @ V0) @ V1)) @ (cneutral @ V2)))))))))))
(Tsupport,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((csupport @ V2) @ V1) @ V0)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (c~ @ ((c= @ (V1 @ V4)) @ (cneutral @ V2))))) @ V4)))))))))))))
(TFINITE_FINITE_PREIMAGE_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (cFINITE @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c= @ (V1 @ V5)) @ V3))) @ V5))))))))))) @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TFINITE_IMAGE_INJ_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V3)) @ (V1 @ V4))))) @ ((c= @ V3) @ V4))))))) @ (cFINITE @ V2))) @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TCOUNTABLE_IMAGE_INJ_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V3)) @ (V1 @ V4))))) @ ((c= @ V3) @ V4))))))) @ (cCOUNTABLE @ V2))) @ (cCOUNTABLE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ (V1 @ V4)) @ V2))) @ V4))))))))))))))
(TIMAGE_LEMMA_2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((c= @ (cCARD @ V0)) @ (cCARD @ V2))) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ ((cIMAGE @ V1) @ V0)) @ V2))) @ ((cIN @ V3) @ V2))))))) @ ((c__caret__/ @ ((c= @ (cCARD @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c/__caret__ @ ((c= @ V5) @ ((cDELETE @ V0) @ V6))) @ ((c= @ ((cIMAGE @ V1) @ V5)) @ ((cDELETE @ V2) @ V3))))))) @ V5))))))) @ (cNUMERAL @ c_0))) @ ((c= @ (cCARD @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c/__caret__ @ ((c= @ V5) @ ((cDELETE @ V0) @ V6))) @ ((c= @ ((cIMAGE @ V1) @ V5)) @ ((cDELETE @ V2) @ V3))))))) @ V5))))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))
(TIMAGE_LEMMA_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((c= @ (cCARD @ V0)) @ (cCARD @ V2))) @ ((c/__caret__ @ ((c= @ ((cIMAGE @ V1) @ V0)) @ V2)) @ ((cIN @ V3) @ V2)))))) @ ((c= @ (cCARD @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c/__caret__ @ ((c= @ V5) @ ((cDELETE @ V0) @ V6))) @ ((c= @ ((cIMAGE @ V1) @ V5)) @ ((cDELETE @ V2) @ V3))))))) @ V5))))))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TIMAGE_LEMMA_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cHAS_SIZE @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((c= @ ((cIMAGE @ V1) @ ((cDELETE @ V0) @ V6))) @ ((cDELETE @ V2) @ V3)))) @ V6)))))) @ V4)) @ ((cHAS_SIZE @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ (c? @ (^[V7]: ((c/__caret__ @ ((cIN @ V7) @ V0)) @ ((c/__caret__ @ ((c= @ V6) @ ((cDELETE @ V0) @ V7))) @ ((c= @ ((cIMAGE @ V1) @ V6)) @ ((cDELETE @ V2) @ V3))))))) @ V6)))))) @ V4)))))))))))))
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(TNSUM_IMAGE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cnsum @ V0) @ V2)) @ ((cnsum @ ((cIMAGE @ V1) @ V0)) @ (^[V3]: ((cnsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c= @ (V1 @ V5)) @ V3))) @ V5)))))) @ V2))))))))))))
(TVSUM_IMAGE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cvsum @ V0) @ V2)) @ ((cvsum @ ((cIMAGE @ V1) @ V0)) @ (^[V3]: ((cvsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V0)) @ ((c= @ (V1 @ V5)) @ V3))) @ V5)))))) @ V2))))))))))))
(TSURJECTIVE_IFF_INJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ V0))) @ ((c= @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V3)) @ V2)))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3)))))))))))))
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(TLEFT_OR_EXISTS_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c__caret__/ @ (c? @ (^[V2]: (V0 @ V2)))) @ V1)) @ (c? @ (^[V2]: ((c__caret__/ @ (V0 @ V2)) @ V1)))))))))
(TLEFT_OR_FORALL_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c__caret__/ @ (c! @ (^[V2]: (V0 @ V2)))) @ V1)) @ (c! @ (^[V2]: ((c__caret__/ @ (V0 @ V2)) @ V1)))))))))
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(TFINITE_DELETE_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ ((cDELETE @ V0) @ V1))))))))
(TSELECT_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c= @ (V0 @ V2)) @ ((c= @ V2) @ V1))))) @ ((c= @ (c__at__ @ V0)) @ V1)))))))
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(TINSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINSERT @ V1) @ V0)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c__caret__/ @ ((cIN @ V3) @ V0)) @ ((c= @ V3) @ V1))) @ V3)))))))))))
(TDELETE_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDELETE @ ((cDELETE @ V0) @ V1)) @ V1)) @ ((cDELETE @ V0) @ V1)))))))
(TDELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDELETE @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V3) @ V1)))) @ V3)))))))))))
(TDECOMPOSITION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ V0) @ ((cINSERT @ V1) @ V2))) @ (c~ @ ((cIN @ V1) @ V2)))))))))))
(TIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V1) @ V0)) @ (V0 @ V1)))))))
(TUNWIND_THM2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ V2) @ V1)) @ (V0 @ V2))))) @ (V0 @ V1)))))))
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(TCOMPL_MEM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (V0 @ V1)) @ (c~ @ ((cre_compl @ V0) @ V1))))))))
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(TIN_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ V1) @ ((cDIFF @ V0) @ V2))) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c~ @ ((cIN @ V1) @ V2)))))))))))
(TDISJOINT_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cDISJOINT @ ((cINSERT @ V1) @ V0)) @ V2)) @ ((c/__caret__ @ ((cDISJOINT @ V0) @ V2)) @ (c~ @ ((cIN @ V1) @ V2)))))))))))
(TDISJOINT_DELETE_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cDISJOINT @ ((cDELETE @ V2) @ V1)) @ V0)) @ ((cDISJOINT @ ((cDELETE @ V0) @ V1)) @ V2)))))))))
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(TDELETE_COMM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cDELETE @ ((cDELETE @ V0) @ V2)) @ V1)) @ ((cDELETE @ ((cDELETE @ V0) @ V1)) @ V2)))))))))
(TIN_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ V1) @ ((cDELETE @ V0) @ V2))) @ ((c/__caret__ @ ((cIN @ V1) @ V0)) @ (c~ @ ((c= @ V1) @ V2)))))))))))
(Tone_axiom,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ V0) @ V1))))))
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(TQUANTIFY_SURJECTION_HIGHER_THM_conjunct9,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (V1 @ V2)))) @ (c? @ (^[V2]: (V1 @ ((co @ V0) @ V2)))))))))))
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(TQUANTIFY_SURJECTION_HIGHER_THM_conjunct4,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (V1 @ V2)))) @ (c! @ (^[V2]: (V1 @ ((cIMAGE @ (cIMAGE @ V0)) @ V2)))))))))))
(TQUANTIFY_SURJECTION_HIGHER_THM_conjunct7,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (V1 @ V2)))) @ (c? @ (^[V2]: (V1 @ ((co @ V0) @ V2)))))))))))
(TQUANTIFY_SURJECTION_HIGHER_THM_conjunct6,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (V1 @ V2)))) @ (c! @ (^[V2]: (V1 @ ((co @ V0) @ V2)))))))))))
(TQUANTIFY_SURJECTION_HIGHER_THM_conjunct13,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V1 @ V3)) @ V3)))))) @ ((cIMAGE @ (cIMAGE @ V0)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V1 @ ((cIMAGE @ V0) @ V3))) @ V3)))))))))))))
(TQUANTIFY_SURJECTION_HIGHER_THM_conjunct3,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (V1 @ V2)))) @ (c? @ (^[V2]: (V1 @ ((cIMAGE @ V0) @ V2)))))))))))
(TQUANTIFY_SURJECTION_HIGHER_THM_conjunct2,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (V1 @ V2)))) @ (c! @ (^[V2]: (V1 @ ((cIMAGE @ V0) @ V2)))))))))))
(TQUANTIFY_SURJECTION_HIGHER_THM_conjunct12,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V1 @ V3)) @ V3)))))) @ ((cIMAGE @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V1 @ (V0 @ V3))) @ V3)))))))))))))
(TQUANTIFY_SURJECTION_HIGHER_THM_conjunct1,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (V1 @ V2)))) @ (c? @ (^[V2]: (V1 @ (V0 @ V2)))))))))))
(TQUANTIFY_SURJECTION_HIGHER_THM_conjunct0,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (V1 @ V2)))) @ (c! @ (^[V2]: (V1 @ (V0 @ V2)))))))))))
(TMAP_conjunct0,(c! @ (^[V0]: ((c= @ ((cMAP @ V0) @ cNIL)) @ cNIL))))
(TETA_AX,(c! @ (^[V0]: ((c= @ (^[V1]: (V0 @ V1))) @ V0))))
(TI_O_ID_conjunct0,(c! @ (^[V0]: ((c= @ ((co @ cI) @ V0)) @ V0))))
(TI_O_ID_conjunct1,(c! @ (^[V0]: ((c= @ ((co @ V0) @ cI)) @ V0))))
(TBIJECTIVE_LEFT_RIGHT_INVERSE,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1))))))) @ (c? @ (^[V1]: ((c/__caret__ @ (c! @ (^[V2]: ((c= @ (V0 @ (V1 @ V2))) @ V2)))) @ (c! @ (^[V2]: ((c= @ (V1 @ (V0 @ V2))) @ V2))))))))))
(TONTO,(c! @ (^[V0]: ((c= @ (cONTO @ V0)) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ V1) @ (V0 @ V2))))))))))
(TONE_ONE,(c! @ (^[V0]: ((c= @ (cONE_ONE @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))))
(TSURJECTIVE_MAP,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ ((cMAP @ V0) @ V2)) @ V1)))))) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))))))
(TINJECTIVE_MAP,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ ((cMAP @ V0) @ V1)) @ ((cMAP @ V0) @ V2))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))))
(TSURJECTIVE_IMAGE,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ ((cIMAGE @ V0) @ V2)) @ V1)))))) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))))))
(TINJECTIVE_IMAGE,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ ((cIMAGE @ V0) @ V1)) @ ((cIMAGE @ V0) @ V2))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))))
(TSURJECTIVE_IMAGE_THM,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ ((cIMAGE @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V1 @ (V0 @ V3))) @ V3))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V1 @ V3)) @ V3))))))))))))
(TSURJECTIVE_EXISTS_THM,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (V1 @ (V0 @ V2))))) @ (c? @ (^[V2]: (V1 @ V2))))))))))
(TSURJECTIVE_FORALL_THM,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (V1 @ (V0 @ V2))))) @ (c! @ (^[V2]: (V1 @ V2))))))))))
(TLENGTH_MAP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cLENGTH @ ((cMAP @ V0) @ V1))) @ (cLENGTH @ V1)))))))
(TITERATE_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ (cFINITE @ V2)) @ ((c= @ (((citerate @ V1) @ V2) @ (^[V5]: (((cCOND @ (V3 @ V5)) @ (V0 @ V5)) @ (V4 @ V5))))) @ ((V1 @ (((citerate @ V1) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ (V3 @ V6))) @ V6)))))) @ V0)) @ (((citerate @ V1) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ (c~ @ (V3 @ V6)))) @ V6)))))) @ V4))))))))))))))))
(TITERATE_OP_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ (((csupport @ V1) @ V0) @ V2))) @ (cFINITE @ (((csupport @ V1) @ V3) @ V2)))) @ ((c= @ (((citerate @ V1) @ V2) @ (^[V4]: ((V1 @ (V0 @ V4)) @ (V3 @ V4))))) @ ((V1 @ (((citerate @ V1) @ V2) @ V0)) @ (((citerate @ V1) @ V2) @ V3))))))))))))))
(TITERATE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((c= @ (V0 @ V4)) @ (V3 @ V4)))))) @ ((c= @ (((citerate @ V1) @ V2) @ V0)) @ (((citerate @ V1) @ V2) @ V3)))))))))))))
(TFINITE_FINITE_PREIMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ (V0 @ V4)) @ V2)) @ V4))))))))))) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ (V0 @ V3)) @ V1)) @ V3))))))))))))
(TFINITE_IMAGE_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))) @ (cFINITE @ V1))) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ (V0 @ V3)) @ V1)) @ V3))))))))))))
(TCOUNTABLE_IMAGE_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))) @ (cCOUNTABLE @ V1))) @ (cCOUNTABLE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ (V0 @ V3)) @ V1)) @ V3))))))))))))
(TCARD_LE_IMAGE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V1) @ ((cIMAGE @ V0) @ V2))) @ ((c<=_c @ V1) @ V2)))))))))
(TCARD_IMAGE_INJ_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((cIN @ (V0 @ V3)) @ V1))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (c?! @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((c= @ (V0 @ V4)) @ V3)))))))))) @ ((c= @ (cCARD @ V1)) @ (cCARD @ V2))))))))))
(TBIJECTIONS_CARD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c__caret__/ @ (cFINITE @ V2)) @ (cFINITE @ V3))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((c/__caret__ @ ((cIN @ (V0 @ V4)) @ V3)) @ ((c= @ (V1 @ (V0 @ V4))) @ V4)))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((c/__caret__ @ ((cIN @ (V1 @ V4)) @ V2)) @ ((c= @ (V0 @ (V1 @ V4))) @ V4)))))))) @ ((c= @ (cCARD @ V2)) @ (cCARD @ V3))))))))))))
(TCARD_EQ_LEMMA_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ (cFINITE @ V3)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((cIN @ (V0 @ V4)) @ V3))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((cIN @ (V1 @ V4)) @ V2))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((c= @ (V1 @ (V0 @ V4))) @ V4))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((c= @ (V0 @ (V1 @ V4))) @ V4)))))))))) @ ((c= @ (cCARD @ V2)) @ (cCARD @ V3))))))))))))
(TBIJECTIONS_HAS_SIZE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((cIN @ (V0 @ V5)) @ V3)) @ ((c= @ (V1 @ (V0 @ V5))) @ V5)))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((c/__caret__ @ ((cIN @ (V1 @ V5)) @ V2)) @ ((c= @ (V0 @ (V1 @ V5))) @ V5)))))) @ ((cHAS_SIZE @ V2) @ V4)))) @ ((cHAS_SIZE @ V3) @ V4)))))))))))))
(TBIJECTIONS_HAS_SIZE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((cIN @ (V0 @ V5)) @ V3)) @ ((c= @ (V1 @ (V0 @ V5))) @ V5)))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ ((c/__caret__ @ ((cIN @ (V1 @ V5)) @ V2)) @ ((c= @ (V0 @ (V1 @ V5))) @ V5))))))) @ ((c= @ ((cHAS_SIZE @ V2) @ V4)) @ ((cHAS_SIZE @ V3) @ V4))))))))))))))
(TCARD_IMAGE_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V2)) @ (V0 @ V3))))) @ ((c= @ V2) @ V3))))))) @ (cFINITE @ V1))) @ ((c= @ (cCARD @ ((cIMAGE @ V0) @ V1))) @ (cCARD @ V1))))))))
(TCARD_IMAGE_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ ((c<= @ (cCARD @ ((cIMAGE @ V0) @ V1))) @ (cCARD @ V1))))))))
(TFINITE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ (cFINITE @ ((cIMAGE @ V0) @ V1))))))))
(TCOUNTABLE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cCOUNTABLE @ V1)) @ (cCOUNTABLE @ ((cIMAGE @ V0) @ V1))))))))
(TINFINITE_IMAGE_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))) @ ((c==> @ (cINFINITE @ V1)) @ (cINFINITE @ ((cIMAGE @ V0) @ V1)))))))))
(TINJECTIVE_SURJECTIVE_PREIMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ V2) @ V3))))))) @ (c? @ (^[V2]: ((c= @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ (V0 @ V4)) @ V2)) @ V4)))))) @ V1)))))))))
(TCARD_EQ_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V2)) @ (V0 @ V3))))) @ ((c= @ V2) @ V3))))))) @ ((c=_c @ ((cIMAGE @ V0) @ V1)) @ V1)))))))
(TFINITE_IMAGE_INJ_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V2)) @ (V0 @ V3))))) @ ((c= @ V2) @ V3))))))) @ ((c= @ (cFINITE @ ((cIMAGE @ V0) @ V1))) @ (cFINITE @ V1))))))))
(TCOUNTABLE_IMAGE_INJ_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V2)) @ (V0 @ V3))))) @ ((c= @ V2) @ V3))))))) @ ((c= @ (cCOUNTABLE @ ((cIMAGE @ V0) @ V1))) @ (cCOUNTABLE @ V1))))))))
(THAS_SIZE_IMAGE_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V0 @ V3)) @ (V0 @ V4))))) @ ((c= @ V3) @ V4))))))) @ ((cHAS_SIZE @ V1) @ V2))) @ ((cHAS_SIZE @ ((cIMAGE @ V0) @ V1)) @ V2)))))))))
(TBIJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cBIJ @ V0) @ V1) @ V2)) @ ((c/__caret__ @ (((cINJ @ V0) @ V1) @ V2)) @ (((cSURJ @ V0) @ V1) @ V2))))))))))
(TSUM_EQ_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ (c?! @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((c= @ (V0 @ V6)) @ V5)))))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ ((cIN @ (V0 @ V5)) @ V3)) @ ((c= @ (V4 @ (V0 @ V5))) @ (V2 @ V5)))))))) @ ((c= @ ((csum @ V1) @ V2)) @ ((csum @ V3) @ V4))))))))))))))
(TNSUM_EQ_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ (c?! @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((c= @ (V0 @ V6)) @ V5)))))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ ((cIN @ (V0 @ V5)) @ V3)) @ ((c= @ (V4 @ (V0 @ V5))) @ (V2 @ V5)))))))) @ ((c= @ ((cnsum @ V1) @ V2)) @ ((cnsum @ V3) @ V4))))))))))))))
(TVSUM_EQ_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V3)) @ (c?! @ (^[V6]: ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((c= @ (V0 @ V6)) @ V5)))))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ ((cIN @ (V0 @ V5)) @ V3)) @ ((c= @ (V4 @ (V0 @ V5))) @ (V2 @ V5)))))))) @ ((c= @ ((cvsum @ V1) @ V2)) @ ((cvsum @ V3) @ V4))))))))))))))
(TITERATE_EQ_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (cmonoidal @ V3)) @ ((c==> @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V4)) @ (c?! @ (^[V7]: ((c/__caret__ @ ((cIN @ V7) @ V1)) @ ((c= @ (V0 @ V7)) @ V6)))))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V1)) @ ((c/__caret__ @ ((cIN @ (V0 @ V6)) @ V4)) @ ((c= @ (V5 @ (V0 @ V6))) @ (V2 @ V6)))))))) @ ((c= @ (((citerate @ V3) @ V1) @ V2)) @ (((citerate @ V3) @ V4) @ V5)))))))))))))))))
(TEQ_EXT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c= @ (V0 @ V2)) @ (V1 @ V2))))) @ ((c= @ V0) @ V1)))))))
(TFUN_EQ_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TBETA_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((^[V2]: (V0 @ V2)) @ V1)) @ (V0 @ V1)))))))
(TLET_DEF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cLET @ V0) @ V1)) @ (V0 @ V1)))))))
(TMAP_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMAP @ V0) @ ((cCONS @ V1) @ V2))) @ ((cCONS @ (V0 @ V1)) @ ((cMAP @ V0) @ V2))))))))))
(TPERMUTATION_FINITE_SUPPORT,(c! @ (^[V0]: ((c==> @ (cpermutation @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ (c~ @ ((c= @ (V0 @ V2)) @ V2))) @ V2))))))))))
(TPERMUTES_UNIV,(c! @ (^[V0]: ((c= @ ((cpermutes @ V0) @ cUNIV)) @ (c! @ (^[V1]: (c?! @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))))))
(TPERMUTATION_PERMUTES,(c! @ (^[V0]: ((c= @ (cpermutation @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (cFINITE @ V1)) @ ((cpermutes @ V0) @ V1))))))))
(TSWAPSEQ_EVEN_EVEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cswapseq @ V1) @ V0)) @ ((cswapseq @ V2) @ V0))) @ ((c= @ (cEVEN @ V1)) @ (cEVEN @ V2))))))))))
(THULL_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (V1 @ ((chull @ V1) @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c= @ (V1 @ ((cIMAGE @ V0) @ V3))) @ (V1 @ V3))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V0 @ V3)) @ (V0 @ V4))) @ ((c= @ V3) @ V4))))))) @ (c! @ (^[V3]: (c? @ (^[V4]: ((c= @ (V0 @ V4)) @ V3))))))))) @ ((c= @ ((chull @ V1) @ ((cIMAGE @ V0) @ V2))) @ ((cIMAGE @ V0) @ ((chull @ V1) @ V2)))))))))))
(TITERATE_INJECTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((cIN @ (V0 @ V4)) @ V2))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V2)) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c= @ (V0 @ V4)) @ (V0 @ V5))))) @ ((c= @ V4) @ V5))))))))) @ ((c= @ (((citerate @ V1) @ V2) @ ((co @ V3) @ V0))) @ (((citerate @ V1) @ V2) @ V3)))))))))))))
(TIMAGE_COMPOSE_PERMUTATIONS_R,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V0) @ V1)) @ ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cpermutes @ V3) @ V1)) @ ((co @ V3) @ V0))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cpermutes @ V3) @ V1)) @ V3))))))))))))
(TIMAGE_COMPOSE_PERMUTATIONS_L,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V0) @ V1)) @ ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cpermutes @ V3) @ V1)) @ ((co @ V0) @ V3))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cpermutes @ V3) @ V1)) @ V3))))))))))))
(TINVOLUTION_FIX_ODD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((cinvolution @ V0) @ V1)) @ (c?! @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c= @ (V0 @ V2)) @ V2))))))) @ (cODD @ (cCARD @ V1))))))))
(TINVOLUTION_EVEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((cinvolution @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c~ @ ((c= @ (V0 @ V2)) @ V2)))))))) @ (cEVEN @ (cCARD @ V1))))))))
(TPERMUTATION_COMPOSE_EQ_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cpermutation @ V1)) @ ((c= @ (cpermutation @ ((co @ V0) @ V1))) @ (cpermutation @ V0))))))))
(TPERMUTATION_COMPOSE_EQ_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cpermutation @ V0)) @ ((c= @ (cpermutation @ ((co @ V0) @ V1))) @ (cpermutation @ V1))))))))
(TLEFT_RIGHT_INVERSE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c= @ ((co @ V1) @ V0)) @ cI)) @ ((c= @ ((co @ V0) @ V2)) @ cI))) @ ((c= @ V1) @ V2)))))))))
(TPERMUTATION_COMPOSE_SWAP_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cpermutation @ ((co @ (cswap @ ((c__comma__ @ V1) @ V2))) @ V0))) @ (cpermutation @ V0)))))))))
(TPERMUTATION_COMPOSE_SWAP_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cpermutation @ ((co @ V0) @ (cswap @ ((c__comma__ @ V1) @ V2))))) @ (cpermutation @ V0)))))))))
(Titerate,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((citerate @ V2) @ V1) @ V0)) @ (((cCOND @ (cFINITE @ (((csupport @ V2) @ V0) @ V1))) @ (((cITSET @ (^[V3]: (^[V4]: ((V2 @ (V0 @ V3)) @ V4)))) @ (((csupport @ V2) @ V0) @ V1)) @ (cneutral @ V2))) @ (cneutral @ V2))))))))))
(TCARD_PERMUTATIONS,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cCARD @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cpermutes @ V2) @ V0)) @ V2))))))) @ (cFACT @ (cCARD @ V0)))))))
(TFINITE_PERMUTATIONS,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cpermutes @ V2) @ V0)) @ V2))))))))))
(TPERMUTES_INVERSE_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V1) @ V0)) @ ((c= @ (cinverse @ (cinverse @ V1))) @ V1)))))))
(TPERMUTES_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V0) @ V1)) @ ((cpermutes @ (cinverse @ V0)) @ V1)))))))
(TPERMUTES_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpermutes @ V1) @ V2)) @ ((cpermutes @ V0) @ V2))) @ ((cpermutes @ ((co @ V0) @ V1)) @ V2)))))))))
(TPERMUTES_I,(c! @ (^[V0]: ((cpermutes @ cI) @ V0))))
(TPERMUTES_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpermutes @ V1) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cDIFF @ V0) @ V2))) @ ((c= @ (V1 @ V3)) @ V3)))))) @ ((cpermutes @ V1) @ V2)))))))))
(TPERMUTES_INVERSE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cpermutes @ V1) @ V0)) @ ((c= @ ((c= @ ((cinverse @ V1) @ V3)) @ V2)) @ ((c= @ (V1 @ V2)) @ V3))))))))))))
(TPERMUTES_EMPTY,(c! @ (^[V0]: ((c= @ ((cpermutes @ V0) @ cEMPTY)) @ ((c= @ V0) @ cI)))))
(TPERMUTES_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpermutes @ V1) @ V0)) @ ((cSUBSET @ V0) @ V2))) @ ((cpermutes @ V1) @ V2)))))))))
(TPERMUTES_INVERSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V1) @ V0)) @ (c! @ (^[V2]: ((c= @ ((cinverse @ V1) @ (V1 @ V2))) @ V2)))))))))
(TPERMUTES_INVERSES_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V1) @ V0)) @ (c! @ (^[V2]: ((c= @ (V1 @ ((cinverse @ V1) @ V2))) @ V2)))))))))
(TPERMUTES_INVERSES_o_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V1) @ V0)) @ ((c= @ ((co @ (cinverse @ V1)) @ V1)) @ cI)))))))
(TPERMUTES_INVERSES_o_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V1) @ V0)) @ ((c= @ ((co @ V1) @ (cinverse @ V1))) @ cI)))))))
(TPERMUTES_SURJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cpermutes @ V1) @ V0)) @ (c? @ (^[V3]: ((c= @ (V1 @ V3)) @ V2)))))))))))
(TPERMUTES_INJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cpermutes @ V1) @ V0)) @ ((c= @ ((c= @ (V1 @ V2)) @ (V1 @ V3))) @ ((c= @ V2) @ V3))))))))))))
(TPERMUTES_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cpermutes @ V0) @ V1)) @ ((c= @ ((cIMAGE @ V0) @ V1)) @ V1)))))))
(TPERMUTES_IN_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cpermutes @ V0) @ V2)) @ ((c= @ ((cIN @ (V0 @ V1)) @ V2)) @ ((cIN @ V1) @ V2))))))))))
(TINVERSE_UNIQUE_o,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ ((co @ V0) @ V1)) @ cI)) @ ((c= @ ((co @ V1) @ V0)) @ cI))) @ ((c= @ (cinverse @ V0)) @ V1)))))))
(TINJECTIVE_INVERSE_o,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))) @ ((c= @ ((co @ (cinverse @ V0)) @ V0)) @ cI)))))
(TINJECTIVE_INVERSE,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: ((c= @ ((cinverse @ V0) @ (V0 @ V1))) @ V1)))))))
(TSURJECTIVE_INVERSE_o,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ ((c= @ ((co @ V0) @ (cinverse @ V0))) @ cI)))))
(TSURJECTIVE_INVERSE,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c! @ (^[V1]: ((c= @ (V0 @ ((cinverse @ V0) @ V1))) @ V1)))))))
(Tinverse,(c! @ (^[V0]: ((c= @ (cinverse @ V0)) @ (^[V1]: (c__at__ @ (^[V2]: ((c= @ (V0 @ V2)) @ V1))))))))
(Tpermutes,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpermutes @ V1) @ V0)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ (c~ @ ((cIN @ V2) @ V0))) @ ((c= @ (V1 @ V2)) @ V2))))) @ (c! @ (^[V2]: (c?! @ (^[V3]: ((c= @ (V1 @ V3)) @ V2))))))))))))
(TSUBSET_PRED,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cSUBSET @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (V1 @ V2))))))))))
(TSUPERADMISSIBLE_T,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((((csuperadmissible @ V0) @ (^[V3]: (^[V4]: cT))) @ V1) @ V2)) @ ((((ctailadmissible @ V0) @ (^[V3]: (^[V4]: cT))) @ V1) @ V2)))))))))
(TWF_REC_TAIL_GENERAL',(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cWF @ V0)) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ (c! @ (^[V8]: ((c==> @ ((V0 @ V8) @ V7)) @ ((c= @ (V5 @ V8)) @ (V6 @ V8)))))) @ ((c/__caret__ @ ((c= @ ((V1 @ V5) @ V7)) @ ((V1 @ V6) @ V7))) @ ((c/__caret__ @ ((c= @ ((V2 @ V5) @ V7)) @ ((V2 @ V6) @ V7))) @ ((c= @ ((V3 @ V5) @ V7)) @ ((V3 @ V6) @ V7)))))))))))) @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((V1 @ V5) @ V6)) @ ((V0 @ V7) @ ((V2 @ V5) @ V6)))) @ ((V0 @ V7) @ V6))))))))) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c= @ ((V4 @ V5) @ V6)) @ (((cCOND @ ((V1 @ V5) @ V6)) @ (V5 @ ((V2 @ V5) @ V6))) @ ((V3 @ V5) @ V6))))))))))) @ (c? @ (^[V5]: (c! @ (^[V6]: ((c= @ (V5 @ V6)) @ ((V4 @ V5) @ V6))))))))))))))))))
(TSUPERADMISSIBLE_MATCH_SEQPATTERN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: (c? @ (^[V8]: ((((V4 @ V6) @ V7) @ ((V3 @ V6) @ V7)) @ V8))))))) @ ((c/__caret__ @ ((((csuperadmissible @ V0) @ (^[V6]: (^[V7]: ((c/__caret__ @ ((V1 @ V6) @ V7)) @ (c? @ (^[V8]: ((((V4 @ V6) @ V7) @ ((V3 @ V6) @ V7)) @ V8))))))) @ V2) @ (^[V6]: (^[V7]: ((c_MATCH @ ((V3 @ V6) @ V7)) @ ((V4 @ V6) @ V7)))))) @ ((((csuperadmissible @ V0) @ (^[V6]: (^[V7]: ((c/__caret__ @ ((V1 @ V6) @ V7)) @ (c~ @ (c? @ (^[V8]: ((((V4 @ V6) @ V7) @ ((V3 @ V6) @ V7)) @ V8)))))))) @ V2) @ (^[V6]: (^[V7]: ((c_MATCH @ ((V3 @ V6) @ V7)) @ ((V5 @ V6) @ V7)))))))) @ ((((csuperadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: ((c_MATCH @ ((V3 @ V6) @ V7)) @ ((c_SEQPATTERN @ ((V4 @ V6) @ V7)) @ ((V5 @ V6) @ V7))))))))))))))))))))
(TSUPERADMISSIBLE_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((((csuperadmissible @ V0) @ V1) @ V2) @ (^[V4]: V3)))))))))))
(TVC_SEQ_ASSIGN_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((ccorrect @ V0) @ V1) @ ((co @ V3) @ V2))) @ (((ccorrect @ V0) @ ((cSeq @ V1) @ (cAssign @ V2))) @ V3)))))))))))
(TVC_SEQ_ASSERT_MIDDLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((ccorrect @ V0) @ V1) @ V2)) @ (((ccorrect @ V2) @ V3) @ V4))) @ (((ccorrect @ V0) @ ((cSeq @ V1) @ ((cSeq @ (cASSERT @ V2)) @ V3))) @ V4)))))))))))))
(TVC_SEQ_ASSERT_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((ccorrect @ V0) @ V1) @ V2)) @ ((cIMPLIES @ V2) @ V3))) @ (((ccorrect @ V0) @ ((cSeq @ V1) @ (cASSERT @ V2))) @ V3)))))))))))
(TVC_SEQ_ASSERT_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIMPLIES @ V0) @ V1)) @ (((ccorrect @ V1) @ V2) @ V3))) @ (((ccorrect @ V0) @ ((cSeq @ (cASSERT @ V1)) @ V2)) @ V3)))))))))))
(TVC_ADO_VARIANT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cWF @ V2)) @ ((c/__caret__ @ ((cIMPLIES @ ((cAND @ V4) @ V1)) @ V0)) @ ((c/__caret__ @ ((cIMPLIES @ ((cAND @ (cNOT @ V4)) @ V1)) @ V5)) @ (c! @ (^[V6]: (((ccorrect @ ((cAND @ V0) @ (^[V7]: ((c= @ V6) @ V7)))) @ V3) @ ((cAND @ V1) @ (^[V7]: ((V2 @ V7) @ V6)))))))))) @ (((ccorrect @ V0) @ ((((cADO @ V1) @ V2) @ V3) @ V4)) @ V5)))))))))))))))
(TVC_AWHILE_VARIANT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cWF @ V2)) @ ((c/__caret__ @ ((cIMPLIES @ V0) @ V1)) @ ((c/__caret__ @ ((cIMPLIES @ ((cAND @ (cNOT @ V3)) @ V1)) @ V5)) @ (c! @ (^[V6]: (((ccorrect @ ((cAND @ V1) @ ((cAND @ V3) @ (^[V7]: ((c= @ V6) @ V7))))) @ V4) @ ((cAND @ V1) @ (^[V7]: ((V2 @ V7) @ V6)))))))))) @ (((ccorrect @ V0) @ ((((cAWHILE @ V1) @ V2) @ V3) @ V4)) @ V5)))))))))))))))
(TVC_IF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((ccorrect @ ((cAND @ V0) @ V1)) @ V2) @ V3)) @ ((cIMPLIES @ ((cAND @ V0) @ (cNOT @ V1))) @ V3))) @ (((ccorrect @ V0) @ ((cIF @ V1) @ V2)) @ V3)))))))))))
(TVC_ITE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((ccorrect @ ((cAND @ V0) @ V1)) @ V2) @ V4)) @ (((ccorrect @ ((cAND @ V0) @ (cNOT @ V1))) @ V3) @ V4))) @ (((ccorrect @ V0) @ (((cIte @ V1) @ V2) @ V3)) @ V4)))))))))))))
(TVC_ASSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIMPLIES @ V0) @ ((cAND @ V1) @ V2))) @ (((ccorrect @ V0) @ (cASSERT @ V1)) @ V2)))))))))
(TVC_ABORT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ cF) @ (((ccorrect @ V0) @ cABORT) @ V1)))))))
(TVC_SKIP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIMPLIES @ V0) @ V1)) @ (((ccorrect @ V0) @ cSKIP) @ V1)))))))
(TVC_ASSIGN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIMPLIES @ V0) @ ((co @ V2) @ V1))) @ (((ccorrect @ V0) @ (cAssign @ V1)) @ V2)))))))))
(TCORRECT_ASSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIMPLIES @ V0) @ ((cAND @ V1) @ V2))) @ (((ccorrect @ V0) @ (cASSERT @ V1)) @ V2)))))))))
(TCORRECT_IF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((ccorrect @ ((cAND @ V0) @ V1)) @ V2) @ V3)) @ ((cIMPLIES @ ((cAND @ V0) @ (cNOT @ V1))) @ V3))) @ (((ccorrect @ V0) @ ((cIF @ V1) @ V2)) @ V3)))))))))))
(TCORRECT_ABORT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ cF) @ (((ccorrect @ V0) @ cABORT) @ V1)))))))
(TCORRECT_SKIP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIMPLIES @ V0) @ V1)) @ (((ccorrect @ V0) @ cSKIP) @ V1)))))))
(TCORRECT_ITE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((ccorrect @ ((cAND @ V0) @ V1)) @ V2) @ V4)) @ (((ccorrect @ ((cAND @ V0) @ (cNOT @ V1))) @ V3) @ V4))) @ (((ccorrect @ V0) @ (((cIte @ V1) @ V2) @ V3)) @ V4)))))))))))))
(TCORRECT_SEQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((ccorrect @ V1) @ V2) @ V0)) @ (((ccorrect @ V0) @ V3) @ V4))) @ (((ccorrect @ V1) @ ((cSeq @ V2) @ V3)) @ V4)))))))))))))
(TCORRECT_ASSIGN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIMPLIES @ V0) @ (^[V3]: (V2 @ (V1 @ V3))))) @ (((ccorrect @ V0) @ (cAssign @ V1)) @ V2)))))))))
(TCORRECT_POSTWEAK,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((ccorrect @ V1) @ V2) @ V0)) @ ((cIMPLIES @ V0) @ V3))) @ (((ccorrect @ V1) @ V2) @ V3)))))))))))
(TCORRECT_PRESTRENGTH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIMPLIES @ V1) @ V0)) @ (((ccorrect @ V0) @ V2) @ V3))) @ (((ccorrect @ V1) @ V2) @ V3)))))))))))
(Tcorrect,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((ccorrect @ V0) @ V1) @ V2)) @ ((cIMPLIES @ V0) @ ((cwp @ V1) @ V2))))))))))
(TWP_ASSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cwp @ (cASSERT @ V0)) @ V1)) @ ((cAND @ V0) @ V1)))))))
(TWP_ABORT,(c! @ (^[V0]: ((c= @ ((cwp @ cABORT) @ V0)) @ cFALSE))))
(TWP_SKIP,(c! @ (^[V0]: ((c= @ ((cwp @ cSKIP) @ V0)) @ V0))))
(TWP_WHILE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cwp @ ((cIF @ V0) @ ((cSeq @ V1) @ ((cWhile @ V0) @ V1)))) @ V2)) @ ((cwp @ ((cWhile @ V0) @ V1)) @ V2)))))))))
(TWP_ASSIGN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cwp @ (cAssign @ V1)) @ V0)) @ ((co @ V0) @ V1)))))))
(TWP_MONOTONIC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIMPLIES @ V0) @ V2)) @ ((cIMPLIES @ ((cwp @ V1) @ V0)) @ ((cwp @ V1) @ V2))))))))))
(TADMISSIBLE_MATCH_SEQPATTERN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: (c? @ (^[V8]: ((((V4 @ V6) @ V7) @ ((V3 @ V6) @ V7)) @ V8))))))) @ ((c/__caret__ @ ((((cadmissible @ V0) @ (^[V6]: (^[V7]: ((c/__caret__ @ ((V1 @ V6) @ V7)) @ (c? @ (^[V8]: ((((V4 @ V6) @ V7) @ ((V3 @ V6) @ V7)) @ V8))))))) @ V2) @ (^[V6]: (^[V7]: ((c_MATCH @ ((V3 @ V6) @ V7)) @ ((V4 @ V6) @ V7)))))) @ ((((cadmissible @ V0) @ (^[V6]: (^[V7]: ((c/__caret__ @ ((V1 @ V6) @ V7)) @ (c~ @ (c? @ (^[V8]: ((((V4 @ V6) @ V7) @ ((V3 @ V6) @ V7)) @ V8)))))))) @ V2) @ (^[V6]: (^[V7]: ((c_MATCH @ ((V3 @ V6) @ V7)) @ ((V5 @ V6) @ V7)))))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: ((c_MATCH @ ((V3 @ V6) @ V7)) @ ((c_SEQPATTERN @ ((V4 @ V6) @ V7)) @ ((V5 @ V6) @ V7))))))))))))))))))))
(Tdeterministic,(c! @ (^[V0]: ((c= @ (cdeterministic @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V0 @ V1) @ V2)) @ ((V0 @ V1) @ V3))) @ ((c= @ V2) @ V3))))))))))))
(TSEM_ASSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((csem @ (cASSERT @ V0)) @ V2) @ V1)) @ ((c/__caret__ @ (V0 @ V2)) @ ((c= @ V1) @ V2))))))))))
(TSEM_WHILE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csem @ ((cWhile @ V0) @ V1)) @ V2) @ V3)) @ (((csem @ ((cIF @ V0) @ ((cSeq @ V1) @ ((cWhile @ V0) @ V1)))) @ V2) @ V3)))))))))))
(Tsem_RULES_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ (V0 @ V3))) @ (((csem @ V2) @ V3) @ V4))) @ (((csem @ (((cIte @ V0) @ V1) @ V2)) @ V3) @ V4)))))))))))))
(Tsem_RULES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ (((csem @ V1) @ V3) @ V4))) @ (((csem @ (((cIte @ V0) @ V1) @ V2)) @ V3) @ V4)))))))))))))
(Tsem_RULES_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ (V0 @ V2))) @ (((csem @ ((cWhile @ V0) @ V1)) @ V2) @ V2)))))))))
(Tsem_RULES_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((c/__caret__ @ (((csem @ V1) @ V2) @ V3)) @ (((csem @ ((cWhile @ V0) @ V1)) @ V3) @ V4)))) @ (((csem @ ((cWhile @ V0) @ V1)) @ V2) @ V4)))))))))))))
(Tsem_RULES_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (((csem @ (cAssign @ V0)) @ V1) @ (V0 @ V1)))))))
(TASSERT,(c! @ (^[V0]: ((c= @ (cASSERT @ V0)) @ (((cIte @ V0) @ cSKIP) @ cABORT)))))
(TDO,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDO @ V1) @ V0)) @ ((cSeq @ V1) @ ((cWhile @ V0) @ V1))))))))
(TIF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIF @ V0) @ V1)) @ (((cIte @ V0) @ V1) @ cSKIP)))))))
(TIMPLIES_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIMPLIES @ V1) @ V0)) @ ((cIMPLIES @ V0) @ V2))) @ ((cIMPLIES @ V1) @ V2)))))))))
(TMORDER_WF,(c! @ (^[V0]: ((c==> @ (cWF @ V0)) @ (cWF @ (cmorder @ V0))))))
(TWFP_INDUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((V0 @ V4) @ V3)) @ (V1 @ V4))))) @ (V1 @ V3))))) @ ((c==> @ ((cWFP @ V0) @ V2)) @ (V1 @ V2))))))))))
(TWFP_RULES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((V0 @ V2) @ V1)) @ ((cWFP @ V0) @ V2))))) @ ((cWFP @ V0) @ V1)))))))
(TMULTIPLICITY_MULTISET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ (c~ @ ((c= @ (V0 @ V4)) @ (cNUMERAL @ c_0)))) @ V4))))))) @ ((c= @ (V0 @ V1)) @ V2))) @ ((c= @ ((cmultiplicity @ (cmultiset @ V0)) @ V1)) @ V2)))))))))
(TUNION_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c~ @ ((c= @ ((c+ @ (V0 @ V3)) @ (V1 @ V3))) @ (cNUMERAL @ c_0)))) @ V3)))))) @ ((cUNION @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c~ @ ((c= @ (V0 @ V3)) @ (cNUMERAL @ c_0)))) @ V3)))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c~ @ ((c= @ (V1 @ V3)) @ (cNUMERAL @ c_0)))) @ V3))))))))))))
(TEMPTY_IS_FINITE,(c! @ (^[V0]: ((c==> @ ((c= @ V0) @ cEMPTY)) @ (cFINITE @ V0)))))
(TADMISSIBLE_GUARDED_PATTERN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V3)) @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V4)) @ ((c/__caret__ @ ((((cadmissible @ V0) @ (^[V8]: (^[V9]: ((c/__caret__ @ ((V1 @ V8) @ V9)) @ ((c/__caret__ @ ((c= @ ((V3 @ V8) @ V9)) @ ((V4 @ V8) @ V9))) @ ((V5 @ V8) @ V9)))))) @ V2) @ V6)) @ ((c/__caret__ @ ((((cadmissible @ V0) @ (^[V8]: (^[V9]: ((c/__caret__ @ ((V1 @ V8) @ V9)) @ ((c= @ ((V3 @ V8) @ V9)) @ ((V4 @ V8) @ V9)))))) @ V2) @ V5)) @ ((((cadmissible @ V0) @ (^[V8]: (^[V9]: ((c/__caret__ @ ((V1 @ V8) @ V9)) @ ((c/__caret__ @ ((c= @ ((V3 @ V8) @ V9)) @ ((V4 @ V8) @ V9))) @ ((V5 @ V8) @ V9)))))) @ V2) @ V7)))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V8]: (^[V9]: (((c_GUARDED_PATTERN @ ((cGEQ @ ((V3 @ V8) @ V9)) @ ((V4 @ V8) @ V9))) @ ((V5 @ V8) @ V9)) @ ((cGEQ @ ((V6 @ V8) @ V9)) @ ((V7 @ V8) @ V9))))))))))))))))))))))))
(TADMISSIBLE_UNGUARDED_PATTERN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V3)) @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V4)) @ ((c/__caret__ @ ((((cadmissible @ V0) @ (^[V7]: (^[V8]: ((c/__caret__ @ ((V1 @ V7) @ V8)) @ ((c= @ ((V3 @ V7) @ V8)) @ ((V4 @ V7) @ V8)))))) @ V2) @ V5)) @ ((((cadmissible @ V0) @ (^[V7]: (^[V8]: ((c/__caret__ @ ((V1 @ V7) @ V8)) @ ((c= @ ((V3 @ V7) @ V8)) @ ((V4 @ V7) @ V8)))))) @ V2) @ V6))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V7]: (^[V8]: ((c_UNGUARDED_PATTERN @ ((cGEQ @ ((V3 @ V7) @ V8)) @ ((V4 @ V7) @ V8))) @ ((cGEQ @ ((V5 @ V7) @ V8)) @ ((V6 @ V7) @ V8))))))))))))))))))))))
(Tconfluent_diamond_RTC,(c! @ (^[V0]: ((c= @ (cconfluent @ V0)) @ (cCR @ (cRTC @ V0))))))
(Tconfluent,(c! @ (^[V0]: ((c= @ (cconfluent @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cRTC @ V0) @ V1) @ V2)) @ (((cRTC @ V0) @ V1) @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ (((cRTC @ V0) @ V2) @ V4)) @ (((cRTC @ V0) @ V3) @ V4)))))))))))))))
(TJOINABLE_TRANS,(c! @ (^[V0]: ((c= @ (cCR @ (cRTC @ V0))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cJOINABLE @ V0) @ V1) @ V2)) @ (((cJOINABLE @ V0) @ V2) @ V3))) @ (((cJOINABLE @ V0) @ V1) @ V3))))))))))))
(TJOINABLE_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cJOINABLE @ V0) @ V2) @ V1)) @ (((cJOINABLE @ V0) @ V1) @ V2)))))))))
(TJOINABLE_REFL,(c! @ (^[V0]: (c! @ (^[V1]: (((cJOINABLE @ V0) @ V1) @ V1))))))
(TADMISSIBLE_SEQPATTERN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: (c? @ (^[V8]: ((((V3 @ V6) @ V7) @ ((V5 @ V6) @ V7)) @ V8))))))) @ ((c/__caret__ @ ((((cadmissible @ V0) @ (^[V6]: (^[V7]: ((c/__caret__ @ ((V1 @ V6) @ V7)) @ (c? @ (^[V8]: ((((V3 @ V6) @ V7) @ ((V5 @ V6) @ V7)) @ V8))))))) @ V2) @ (^[V6]: (^[V7]: (((V3 @ V6) @ V7) @ ((V5 @ V6) @ V7)))))) @ ((((cadmissible @ V0) @ (^[V6]: (^[V7]: ((c/__caret__ @ ((V1 @ V6) @ V7)) @ (c~ @ (c? @ (^[V8]: ((((V3 @ V6) @ V7) @ ((V5 @ V6) @ V7)) @ V8)))))))) @ V2) @ (^[V6]: (^[V7]: (((V4 @ V6) @ V7) @ ((V5 @ V6) @ V7)))))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: (((c_SEQPATTERN @ ((V3 @ V6) @ V7)) @ ((V4 @ V6) @ V7)) @ ((V5 @ V6) @ V7)))))))))))))))))))
(TADMISSIBLE_MATCH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V3)) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V5]: (^[V6]: (((V4 @ V5) @ V6) @ ((V3 @ V5) @ V6))))))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V5]: (^[V6]: ((c_MATCH @ ((V3 @ V5) @ V6)) @ ((V4 @ V5) @ V6)))))))))))))))))
(TADMISSIBLE_COND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((((cadmissible @ V0) @ V1) @ V2) @ V3)) @ ((c/__caret__ @ ((((cadmissible @ V0) @ (^[V6]: (^[V7]: ((c/__caret__ @ ((V1 @ V6) @ V7)) @ ((V3 @ V6) @ V7))))) @ V2) @ V4)) @ ((((cadmissible @ V0) @ (^[V6]: (^[V7]: ((c/__caret__ @ ((V1 @ V6) @ V7)) @ (c~ @ ((V3 @ V6) @ V7)))))) @ V2) @ V5)))) @ ((((cadmissible @ V0) @ V1) @ V2) @ (^[V6]: (^[V7]: (((cCOND @ ((V3 @ V6) @ V7)) @ ((V4 @ V6) @ V7)) @ ((V5 @ V6) @ V7)))))))))))))))))))
(TIN_TRIPLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cIN @ ((c__comma__ @ V1) @ ((c__comma__ @ V2) @ V3))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V4) @ (((V0 @ V5) @ V6) @ V7)) @ ((c__comma__ @ V5) @ ((c__comma__ @ V6) @ V7))))))))))))) @ (((V0 @ V1) @ V2) @ V3)))))))))))
(TINVOLUTION_FIX_FIX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((cinvolution @ V0) @ V1)) @ ((c/__caret__ @ ((cinvolution @ V2) @ V1)) @ (c?! @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ V3)))))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ V3))))))))))))
(TINVOLUTION_ODD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((cinvolution @ V1) @ V0)) @ (cODD @ (cCARD @ V0))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ V2))))))))))
(TINVOLUTION_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cinvolution @ V1) @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((cIN @ (V1 @ V3)) @ V2))))) @ ((cSUBSET @ V2) @ V0)))) @ ((cinvolution @ V1) @ V2)))))))))
(TINVOLUTION_NOFIXES,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cinvolution @ V1) @ V0)) @ ((cinvolution @ V1) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ (V1 @ V3)) @ V3)))) @ V3))))))))))))
(TINVOLUTION_STEPDOWN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cinvolution @ V1) @ V0)) @ ((cIN @ V2) @ V0))) @ ((cinvolution @ V1) @ ((cDIFF @ V0) @ ((cINSERT @ V2) @ ((cINSERT @ (V1 @ V2)) @ cEMPTY))))))))))))
(TINVOLUTION_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cinvolution @ V0) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c= @ (V0 @ V2)) @ V2)))) @ ((cinvolution @ V0) @ ((cDELETE @ V1) @ V2))))))))))
(TINVOLUTION_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cinvolution @ V0) @ V1)) @ ((c= @ ((cIMAGE @ V0) @ V1)) @ V1)))))))
(Tinvolution,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinvolution @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ (V1 @ V2)) @ V0)) @ ((c= @ (V1 @ (V1 @ V2))) @ V2)))))))))))
(Tlemma,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ V1) @ (cUNIONS @ ((cIMAGE @ (^[V2]: (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V0 @ V4)) @ V2))) @ V4))))))) @ ((cIMAGE @ V0) @ V1)))))))))
(TADMISSIBLE_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((((cadmissible @ V0) @ V1) @ V2) @ (^[V4]: V3)))))))))))
(Tcountable,(c! @ (^[V0]: ((c= @ (ccountable @ V0)) @ ((c<=_c @ V0) @ cUNIV)))))
(TMATCH_SEQPATTERN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c_MATCH @ V1) @ ((c_SEQPATTERN @ V0) @ V2))) @ (((cCOND @ (c? @ (^[V3]: ((V0 @ V1) @ V3)))) @ ((c_MATCH @ V1) @ V0)) @ ((c_MATCH @ V1) @ V2))))))))))
(Tsuperadmissible,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((csuperadmissible @ V0) @ V1) @ V2) @ V3)) @ ((c==> @ ((((cadmissible @ V0) @ (^[V4]: (^[V5]: cT))) @ V2) @ V1)) @ ((((ctailadmissible @ V0) @ V1) @ V2) @ V3))))))))))))
(TCASEWISE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((cCASEWISE @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ V2)) @ V3) @ V4)) @ (((cCOND @ (c? @ (^[V5]: ((c= @ (V1 @ V5)) @ V4)))) @ ((V0 @ V3) @ (c__at__ @ (^[V5]: ((c= @ (V1 @ V5)) @ V4))))) @ (((cCASEWISE @ V2) @ V3) @ V4))))))))))))))
(Tdelete_edge,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cdelete_edge @ V1) @ ((c__comma__ @ V0) @ ((c__comma__ @ V2) @ V3)))) @ ((c__comma__ @ ((cDELETE @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))))))))))))
(TPRIME_DIVIDES_NPRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cprime @ V1)) @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cnum_divides @ V1) @ ((cnproduct @ V0) @ V2))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cnum_divides @ V1) @ (V2 @ V3)))))))))))))
(TNPRODUCT_EQ_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((c= @ V0) @ V2)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V1 @ V4)) @ (V3 @ V4)))))))) @ ((c= @ ((cnproduct @ V0) @ V1)) @ ((cnproduct @ V2) @ V3))))))))))))
(TNPRODUCT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3))))))) @ ((c= @ ((cnproduct @ V1) @ V0)) @ ((cnproduct @ V1) @ V2))))))))))
(TNPRODUCT_EQ_1_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((c= @ ((cnproduct @ V0) @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TNPRODUCT_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((cnproduct @ cEMPTY) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(Tcycle,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((ccycle @ V0) @ V1) @ V2)) @ ((c/__caret__ @ (c! @ (^[V3]: ((V0 @ (V2 @ V3)) @ (V2 @ ((c+ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ (c! @ (^[V3]: ((c= @ (V2 @ ((c+ @ V3) @ V1))) @ (V2 @ V3)))))))))))))
(TEVEN_NSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cEVEN @ (V1 @ V2))))))) @ (cEVEN @ ((cnsum @ V0) @ V1))))))))
(TVARIATION_SET_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((V1 @ V3) @ V4)))) @ ((c__comma__ @ V3) @ V4)))))))))))))))
(TPAIR_BETA_THM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cGABS @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((cGEQ @ (V3 @ ((c__comma__ @ V4) @ V5))) @ ((V0 @ V4) @ V5)))))))) @ ((c__comma__ @ V1) @ V2))) @ ((V0 @ V1) @ V2)))))))))
(TSUM_CASES_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cIN @ V3) @ V0))) @ ((c= @ ((csum @ V0) @ (^[V4]: (((cCOND @ ((c= @ V4) @ V3)) @ V1) @ (V2 @ V4))))) @ ((creal_add @ ((csum @ V0) @ V2)) @ ((creal_sub @ V1) @ (V2 @ V3))))))))))))))
(TSUM_UNION_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cINTER @ V0) @ V1))) @ ((c= @ (V2 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ ((c= @ ((csum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((creal_add @ ((csum @ V0) @ V2)) @ ((csum @ V1) @ V2)))))))))))
(TSUM_INJECTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cIN @ (V0 @ V3)) @ V1))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V0 @ V3)) @ (V0 @ V4))))) @ ((c= @ V3) @ V4))))))))) @ ((c= @ ((csum @ V1) @ ((co @ V2) @ V0))) @ ((csum @ V1) @ V2))))))))))
(TREAL_TENDSTO,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c--> @ V0) @ V1)) @ ((c---> @ ((co @ cdrop) @ V0)) @ (cdrop @ V1))))))))
(TTENDSTO_REAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c---> @ V0) @ V1)) @ ((c--> @ ((co @ clift) @ V0)) @ (clift @ V1))))))))
(Treallim,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creallim @ V1) @ V0)) @ (c__at__ @ (^[V2]: (((c---> @ V0) @ V2) @ V1)))))))))
(Ttendsto_real,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c---> @ V0) @ V1) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((ceventually @ (^[V4]: ((creal_lt @ (creal_abs @ ((creal_sub @ (V0 @ V4)) @ V1))) @ V3))) @ V2))))))))))))
(TITER_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cITER @ (cNUMERAL @ (cBIT1 @ c_0))) @ V0) @ V1)) @ (V0 @ V1)))))))
(TITER_ALT_POINTLESS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cITER @ (cSUC @ V1)) @ V0)) @ ((co @ ((cITER @ V1) @ V0)) @ V0)))))))
(TITER_ALT_POINTLESS_conjunct0,(c! @ (^[V0]: ((c= @ ((cITER @ (cNUMERAL @ c_0)) @ V0)) @ cI))))
(TITER_ALT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cITER @ (cSUC @ V1)) @ V0) @ V2)) @ (((cITER @ V1) @ V0) @ (V0 @ V2))))))))))
(TITER_ALT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cITER @ (cNUMERAL @ c_0)) @ V0) @ V1)) @ V1))))))
(TITER_POINTLESS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cITER @ (cSUC @ V1)) @ V0)) @ ((co @ V0) @ ((cITER @ V1) @ V0))))))))
(TITER_POINTLESS_conjunct0,(c! @ (^[V0]: ((c= @ ((cITER @ (cNUMERAL @ c_0)) @ V0)) @ cI))))
(TPOLYFUN_N_SUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: (c! @ (^[V5]: ((c= @ ((V1 @ V5) @ V3)) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V6]: ((creal_mul @ (V4 @ V6)) @ ((creal_pow @ V5) @ V6)))))))))))))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c= @ ((csum @ V0) @ (V1 @ V4))) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ V2)) @ (^[V5]: ((creal_mul @ (V3 @ V5)) @ ((creal_pow @ V4) @ V5)))))))))))))))))
(TMSUM_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ ((c= @ ((cmsum @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((cmsum @ V0) @ ((co @ V1) @ V2)))))))))))
(TMSUM_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmsum @ ((cINSERT @ V1) @ cEMPTY)) @ V0)) @ (V0 @ V1)))))))
(TMSUM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3)))))) @ ((c= @ ((cmsum @ V1) @ V0)) @ ((cmsum @ V1) @ V2))))))))))
(TMSUM_SUPPORT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmsum @ (((csupport @ cmatrix_add) @ V1) @ V0)) @ V1)) @ ((cmsum @ V0) @ V1)))))))
(TMSUM_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cmsum @ V1) @ (^[V3]: ((cmatrix_sub @ (V0 @ V3)) @ (V2 @ V3))))) @ ((cmatrix_sub @ ((cmsum @ V1) @ V0)) @ ((cmsum @ V1) @ V2)))))))))))
(TMSUM_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cmsum @ V1) @ (^[V3]: ((cmatrix_add @ (V0 @ V3)) @ (V2 @ V3))))) @ ((cmatrix_add @ ((cmsum @ V1) @ V0)) @ ((cmsum @ V1) @ V2)))))))))))
(TSURJECTIVE_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: (c? @ (^[V4]: ((c= @ (V1 @ V4)) @ V3)))))) @ (c! @ (^[V3]: (c? @ (^[V4]: ((c= @ (V0 @ V4)) @ V3))))))) @ (c? @ (^[V3]: ((c= @ (((co @ V0) @ V1) @ V3)) @ V2)))))))))))
(TREAL_OF_NUM_SUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (creal_of_num @ ((cnsum @ V0) @ V1))) @ ((csum @ V0) @ (^[V2]: (creal_of_num @ (V1 @ V2)))))))))))
(TCARD_EQ_SUM,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (creal_of_num @ (cCARD @ V0))) @ ((csum @ V0) @ (^[V1]: (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TSUM_SUM_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (cFINITE @ V0))) @ ((c= @ ((csum @ V1) @ (^[V4]: ((csum @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((V2 @ V4) @ V6))) @ V6)))))) @ (^[V5]: ((V3 @ V4) @ V5)))))) @ ((csum @ V0) @ (^[V4]: ((csum @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((V2 @ V6) @ V4))) @ V6)))))) @ (^[V5]: ((V3 @ V5) @ V4))))))))))))))))
(TSUM_RESTRICT_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((csum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (V1 @ V4))) @ V4)))))) @ V2)) @ ((csum @ V0) @ (^[V3]: (((cCOND @ (V1 @ V3)) @ (V2 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))
(TSUM_UNION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)) @ ((c= @ ((cUNION @ V0) @ V1)) @ V2)))) @ ((c= @ ((creal_add @ ((csum @ V0) @ V3)) @ ((csum @ V1) @ V3))) @ ((csum @ V2) @ V3))))))))))))
(TSUM_BOUND_LT_ALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_lt @ (V0 @ V3)) @ V2))))))) @ ((creal_lt @ ((csum @ V1) @ V0)) @ ((creal_mul @ (creal_of_num @ (cCARD @ V1))) @ V2))))))))))
(TSUM_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((csum @ V0) @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V0)) @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((csum @ V0) @ V1))))))))
(TSUM_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ ((c= @ ((csum @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((csum @ V0) @ ((co @ V1) @ V2)))))))))))
(TSUM_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((csum @ ((cINSERT @ V1) @ cEMPTY)) @ V0)) @ (V0 @ V1)))))))
(TSUM_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cIN @ V2) @ V0))) @ ((c= @ ((csum @ ((cDELETE @ V0) @ V2)) @ V1)) @ ((creal_sub @ ((csum @ V0) @ V1)) @ (V1 @ V2)))))))))))
(TSUM_POS_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V3)))))) @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))
(TSUM_LT_ALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_lt @ (V0 @ V3)) @ (V2 @ V3)))))))) @ ((creal_lt @ ((csum @ V1) @ V0)) @ ((csum @ V1) @ V2))))))))))
(TVALMOD_BASIC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((((c|-> @ V1) @ V2) @ V0) @ V1)) @ V2))))))))
(TINJ_LEMMA,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))))
(Tletlemma,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cLET @ (^[V2]: (cLET_END @ (V0 @ V2)))) @ V1)) @ (V0 @ V1)))))))
(TSUM_ADD_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (c~ @ ((c= @ (V0 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ V4))))))) @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (c~ @ ((c= @ (V2 @ V4)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ V4)))))))) @ ((c= @ ((csum @ V1) @ (^[V3]: ((creal_add @ (V0 @ V3)) @ (V2 @ V3))))) @ ((creal_add @ ((csum @ V1) @ V0)) @ ((csum @ V1) @ V2)))))))))))
(TCARD_EQ_REAL_IMP_UNCOUNTABLE,(c! @ (^[V0]: ((c==> @ ((c=_c @ V0) @ cUNIV)) @ (c~ @ (cCOUNTABLE @ V0))))))
(TSUM_SUPPORT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((csum @ (((csupport @ creal_add) @ V1) @ V0)) @ V1)) @ ((csum @ V0) @ V1)))))))
(TFORALL_COUNTABLE_SUBSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V3)) @ ((cSUBSET @ V3) @ ((cIMAGE @ V2) @ V0)))) @ (V1 @ V3))))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V3)) @ ((cSUBSET @ V3) @ V0))) @ (V1 @ ((cIMAGE @ V2) @ V3)))))))))))))
(TEXISTS_COUNTABLE_SUBSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ (cCOUNTABLE @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ ((cIMAGE @ V2) @ V0))) @ (V1 @ V3)))))) @ (c? @ (^[V3]: ((c/__caret__ @ (cCOUNTABLE @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (V1 @ ((cIMAGE @ V2) @ V3))))))))))))))
(TSUM_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cDISJOINT @ V0) @ V1)))) @ ((c= @ ((csum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((creal_add @ ((csum @ V0) @ V2)) @ ((csum @ V1) @ V2)))))))))))
(TCOUNTABLE_AS_INJECTIVE_IMAGE,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (cINFINITE @ V0))) @ (c? @ (^[V1]: ((c/__caret__ @ ((c= @ V0) @ ((cIMAGE @ V1) @ cUNIV))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V1 @ V2)) @ (V1 @ V3))) @ ((c= @ V2) @ V3)))))))))))))
(TCOUNTABLE_AS_IMAGE_SUBSET,(c! @ (^[V0]: ((c==> @ (cCOUNTABLE @ V0)) @ (c? @ (^[V1]: ((cSUBSET @ V0) @ ((cIMAGE @ V1) @ cUNIV))))))))
(TCOUNTABLE_CROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cCOUNTABLE @ V0)) @ (cCOUNTABLE @ V1))) @ (cCOUNTABLE @ ((cCROSS @ V0) @ V1))))))))
(TCOUNTABLE_DIFF_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cCOUNTABLE @ ((cDIFF @ V1) @ V0))) @ (cCOUNTABLE @ V1))))))))
(TCOUNTABLE_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c__caret__/ @ (cCOUNTABLE @ V0)) @ (cCOUNTABLE @ V1))) @ (cCOUNTABLE @ ((cINTER @ V0) @ V1))))))))
(TFINITE_IMP_COUNTABLE,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cCOUNTABLE @ V0)))))
(TSUM_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((csum @ cEMPTY) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TCOUNTABLE_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cCOUNTABLE @ V0)) @ (cCOUNTABLE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (V1 @ V3))) @ V3))))))))))))
(TCARD_COUNTABLE_CONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c=_c @ V0) @ V1)) @ ((c= @ (cCOUNTABLE @ V0)) @ (cCOUNTABLE @ V1))))))))
(TCOUNTABLE_CASES,(c! @ (^[V0]: ((c= @ (cCOUNTABLE @ V0)) @ ((c__caret__/ @ (cFINITE @ V0)) @ ((c=_c @ V0) @ cUNIV))))))
(TCOUNTABLE_ALT,(c! @ (^[V0]: ((c= @ (cCOUNTABLE @ V0)) @ ((c<=_c @ V0) @ cUNIV)))))
(TCARD_MUL_LT_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<=_c @ V0) @ V1)) @ ((c/__caret__ @ ((c<_c @ V1) @ V2)) @ (cINFINITE @ V2)))) @ ((c<_c @ ((c*_c @ V0) @ V1)) @ V2)))))))))
(TSUM_DEGENERATE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ (V1 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ V3)))))))) @ ((c= @ ((csum @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TCARD_MUL_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ (cFINITE @ ((c*_c @ V0) @ V1))))))))
(TCARD_ADD_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ (cFINITE @ ((c+_c @ V0) @ V1))))))))
(TCARD_ADD_C,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ (cCARD @ ((c+_c @ V0) @ V1))) @ ((c+ @ (cCARD @ V0)) @ (cCARD @ V1)))))))))
(TIN_CARD_ADD_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ (cINL @ V2)) @ ((c+_c @ V1) @ V0))) @ ((cIN @ V2) @ V1)))))))))
(TIN_CARD_ADD_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ (cINR @ V2)) @ ((c+_c @ V0) @ V1))) @ ((cIN @ V2) @ V1)))))))))
(Tmul_c,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c*_c @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((c__comma__ @ V3) @ V4))))))))))))))
(Tadd_c,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c+_c @ V0) @ V1)) @ ((cUNION @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V0)) @ (cINL @ V3))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ (cINR @ V3)))))))))))))
(TCARD_LE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c<=_c @ ((cIMAGE @ V0) @ V1)) @ V1))))))
(TCARD_LE_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<=_c @ V0) @ V1)) @ ((c__caret__/ @ ((c<_c @ V0) @ V1)) @ ((c=_c @ V0) @ V1))))))))
(TCARD_LT_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<_c @ V0) @ V1)) @ ((c/__caret__ @ ((c<=_c @ V0) @ V1)) @ (c~ @ ((c=_c @ V0) @ V1)))))))))
(TCARD_EQ_EMPTY,(c! @ (^[V0]: ((c= @ ((c=_c @ V0) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TCARD_LE_EMPTY,(c! @ (^[V0]: ((c= @ ((c<=_c @ V0) @ cEMPTY)) @ ((c= @ V0) @ cEMPTY)))))
(TCARD_LT_IMP_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c<_c @ V0) @ V1)) @ ((c<=_c @ V0) @ V1)))))))
(TCARD_EQ_IMP_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c=_c @ V0) @ V1)) @ ((c<=_c @ V0) @ V1)))))))
(TCARD_EQ_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c=_c @ V1) @ V0)) @ ((c=_c @ V0) @ V1)))))))
(TBIJECTIVE_INVERSES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c?! @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V4)) @ V3))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((cIN @ (V3 @ V4)) @ V1))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ (V3 @ V4))) @ V4))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V3 @ (V2 @ V4))) @ V4)))))))))))))))))
(TBIJECTIVE_INJECTIVE_SURJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c?! @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V4)) @ V3))))))))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V4)) @ V3)))))))))))))))))
(TINJECTIVE_LEFT_INVERSE_NONEMPTY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c? @ (^[V3]: ((cIN @ V3) @ V1)))) @ ((c= @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((cIN @ (V3 @ V4)) @ V1))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V3 @ (V2 @ V4))) @ V4))))))))))))))))
(TFLATTEN_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V2 @ (V1 @ V3))) @ V3))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ V3) @ (V1 @ V4)))) @ ((c= @ (V2 @ V3)) @ V4))))))))))))))
(TMEM_QSORT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMEM @ V1) @ ((cQSORT @ V0) @ V2))) @ ((cMEM @ V1) @ V2)))))))))
(TLENGTH_QSORT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cLENGTH @ ((cQSORT @ V0) @ V1))) @ (cLENGTH @ V1)))))))
(TALL_QSORT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cALL @ V1) @ ((cQSORT @ V0) @ V2))) @ ((cALL @ V1) @ V2)))))))))
(TCOUNT_QSORT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cCOUNT @ V1) @ ((cQSORT @ V0) @ V2))) @ ((cCOUNT @ V1) @ V2)))))))))
(TORDERED_RULES_conjunct0,(c! @ (^[V0]: ((cORDERED @ V0) @ cNIL))))
(TORDERED_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cORDERED @ V0) @ V2)) @ ((cALL @ (V0 @ V1)) @ V2))) @ ((cORDERED @ V0) @ ((cCONS @ V1) @ V2))))))))))
(TLIST_UNIQ_LIST_OF_SET,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ (cLIST_UNIQ @ (clist_of_set @ V0))))))
(TCOUNT_FILTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cCOUNT @ V1) @ ((cFILTER @ V0) @ V2))) @ (((cCOND @ (V0 @ V1)) @ ((cCOUNT @ V1) @ V2)) @ (cNUMERAL @ c_0))))))))))
(TNSUM_UNION_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cINTER @ V0) @ V1))) @ ((c= @ (V2 @ V3)) @ (cNUMERAL @ c_0)))))))) @ ((c= @ ((cnsum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((c+ @ ((cnsum @ V0) @ V2)) @ ((cnsum @ V1) @ V2)))))))))))
(TNSUM_INJECTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cIN @ (V0 @ V3)) @ V1))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V0 @ V3)) @ (V0 @ V4))))) @ ((c= @ V3) @ V4))))))))) @ ((c= @ ((cnsum @ V1) @ ((co @ V2) @ V0))) @ ((cnsum @ V1) @ V2))))))))))
(TNSUM_SUBSET_SIMPLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cSUBSET @ V0) @ V1))) @ ((c<= @ ((cnsum @ V0) @ V2)) @ ((cnsum @ V1) @ V2))))))))))
(TRSTC_INV,(c! @ (^[V0]: ((c= @ (cRSTC @ (cINV @ V0))) @ (cINV @ (cRSTC @ V0))))))
(TSTC_INV,(c! @ (^[V0]: ((c= @ (cSTC @ (cINV @ V0))) @ (cINV @ (cSTC @ V0))))))
(TRTC_INV,(c! @ (^[V0]: ((c= @ (cRTC @ (cINV @ V0))) @ (cINV @ (cRTC @ V0))))))
(TRSC_INV,(c! @ (^[V0]: ((c= @ (cRSC @ (cINV @ V0))) @ (cINV @ (cRSC @ V0))))))
(TTC_INV,(c! @ (^[V0]: ((c= @ (cTC @ (cINV @ V0))) @ (cINV @ (cTC @ V0))))))
(TSC_INV_STRONG,(c! @ (^[V0]: ((c= @ (cSC @ (cINV @ V0))) @ (cSC @ V0)))))
(TSC_INV,(c! @ (^[V0]: ((c= @ (cSC @ (cINV @ V0))) @ (cINV @ (cSC @ V0))))))
(TRC_INV,(c! @ (^[V0]: ((c= @ (cRC @ (cINV @ V0))) @ (cINV @ (cRC @ V0))))))
(TRTC_NE_IMP_TC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((cRTC @ V0) @ V1) @ V2)) @ (c~ @ ((c= @ V1) @ V2)))) @ (((cTC @ V0) @ V1) @ V2)))))))))
(TRTC_STUTTER,(c! @ (^[V0]: ((c= @ (cRTC @ V0)) @ (cRTC @ (^[V1]: (^[V2]: ((c/__caret__ @ ((V0 @ V1) @ V2)) @ (c~ @ ((c= @ V1) @ V2))))))))))
(TCARD_EQ_NSUM,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cCARD @ V0)) @ ((cnsum @ V0) @ (^[V1]: (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TNSUM_NSUM_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (cFINITE @ V0))) @ ((c= @ ((cnsum @ V1) @ (^[V4]: ((cnsum @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V0)) @ ((V2 @ V4) @ V6))) @ V6)))))) @ (^[V5]: ((V3 @ V4) @ V5)))))) @ ((cnsum @ V0) @ (^[V4]: ((cnsum @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((V2 @ V6) @ V4))) @ V6)))))) @ (^[V5]: ((V3 @ V5) @ V4))))))))))))))))
(TNSUM_UNION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)) @ ((c= @ ((cUNION @ V0) @ V1)) @ V2)))) @ ((c= @ ((c+ @ ((cnsum @ V0) @ V3)) @ ((cnsum @ V1) @ V3))) @ ((cnsum @ V2) @ V3))))))))))))
(TNSUM_BOUND_LT_ALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c< @ (V0 @ V3)) @ V2))))))) @ ((c< @ ((cnsum @ V1) @ V0)) @ ((c* @ (cCARD @ V1)) @ V2))))))))))
(TNSUM_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cnsum @ V0) @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V0)) @ (V1 @ V2)) @ (cNUMERAL @ c_0))))) @ ((cnsum @ V0) @ V1))))))))
(TNSUM_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ ((c= @ ((cnsum @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((cnsum @ V0) @ ((co @ V1) @ V2)))))))))))
(TNSUM_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnsum @ ((cINSERT @ V1) @ cEMPTY)) @ V0)) @ (V0 @ V1)))))))
(TNSUM_EQ_0_IFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((c= @ ((cnsum @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (cNUMERAL @ c_0))))))))))))
(TNSUM_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cnsum @ V0) @ (^[V2]: V1))) @ ((c* @ (cCARD @ V0)) @ V1))))))))
(TNSUM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3)))))) @ ((c= @ ((cnsum @ V1) @ V0)) @ ((cnsum @ V1) @ V2))))))))))
(TNSUM_LT_ALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c< @ (V0 @ V3)) @ (V2 @ V3)))))))) @ ((c< @ ((cnsum @ V1) @ V0)) @ ((cnsum @ V1) @ V2))))))))))
(TNSUM_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c<= @ (V0 @ V3)) @ (V2 @ V3))))))) @ ((c<= @ ((cnsum @ V1) @ V0)) @ ((cnsum @ V1) @ V2))))))))))
(TNSUM_ADD_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (c~ @ ((c= @ (V0 @ V4)) @ (cNUMERAL @ c_0))))) @ V4))))))) @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (c~ @ ((c= @ (V2 @ V4)) @ (cNUMERAL @ c_0))))) @ V4)))))))) @ ((c= @ ((cnsum @ V1) @ (^[V3]: ((c+ @ (V0 @ V3)) @ (V2 @ V3))))) @ ((c+ @ ((cnsum @ V1) @ V0)) @ ((cnsum @ V1) @ V2)))))))))))
(TNSUM_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cnsum @ V1) @ (^[V3]: ((c+ @ (V0 @ V3)) @ (V2 @ V3))))) @ ((c+ @ ((cnsum @ V1) @ V0)) @ ((cnsum @ V1) @ V2)))))))))))
(TNSUM_SUPPORT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnsum @ (((csupport @ c+) @ V1) @ V0)) @ V1)) @ ((cnsum @ V0) @ V1)))))))
(TNSUM_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cSUBSET @ V1) @ V0))) @ ((c= @ ((cnsum @ ((cDIFF @ V0) @ V1)) @ V2)) @ ((c- @ ((cnsum @ V0) @ V2)) @ ((cnsum @ V1) @ V2)))))))))))
(TNSUM_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cDISJOINT @ V0) @ V1)))) @ ((c= @ ((cnsum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((c+ @ ((cnsum @ V0) @ V2)) @ ((cnsum @ V1) @ V2)))))))))))
(TNSUM_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((cnsum @ cEMPTY) @ V0)) @ (cNUMERAL @ c_0)))))
(TNSUM_DEGENERATE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (cFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ (V1 @ V3)) @ (cNUMERAL @ c_0))))) @ V3)))))))) @ ((c= @ ((cnsum @ V0) @ V1)) @ (cNUMERAL @ c_0))))))))
(TITERATE_CLAUSES_NUMSEG_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmonoidal @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((citerate @ V0) @ ((c.. @ V2) @ (cSUC @ V3))) @ V1)) @ (((cCOND @ ((c<= @ V2) @ (cSUC @ V3))) @ ((V0 @ (((citerate @ V0) @ ((c.. @ V2) @ V3)) @ V1)) @ (V1 @ (cSUC @ V3)))) @ (((citerate @ V0) @ ((c.. @ V2) @ V3)) @ V1)))))))))))))
(TITERATE_OP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ (cFINITE @ V2)) @ ((c= @ (((citerate @ V1) @ V2) @ (^[V4]: ((V1 @ (V0 @ V4)) @ (V3 @ V4))))) @ ((V1 @ (((citerate @ V1) @ V2) @ V0)) @ (((citerate @ V1) @ V2) @ V3))))))))))))))
(TITERATE_DELTA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V3)) @ ((c= @ (((citerate @ V3) @ V0) @ (^[V4]: (((cCOND @ ((c= @ V4) @ V2)) @ (V1 @ V4)) @ (cneutral @ V3))))) @ (((cCOND @ ((cIN @ V2) @ V0)) @ (V1 @ V2)) @ (cneutral @ V3)))))))))))))
(TITERATE_INCL_EXCL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V0)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (cFINITE @ V2))) @ ((c= @ ((V0 @ (((citerate @ V0) @ V1) @ V3)) @ (((citerate @ V0) @ V2) @ V3))) @ ((V0 @ (((citerate @ V0) @ ((cUNION @ V1) @ V2)) @ V3)) @ (((citerate @ V0) @ ((cINTER @ V1) @ V2)) @ V3))))))))))))))
(TITERATE_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((cSUBSET @ V0) @ V2))) @ ((c= @ ((V1 @ (((citerate @ V1) @ ((cDIFF @ V2) @ V0)) @ V3)) @ (((citerate @ V1) @ V0) @ V3))) @ (((citerate @ V1) @ V2) @ V3)))))))))))))
(TITERATE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V2)) @ ((cDISJOINT @ V0) @ V2)))) @ ((c= @ (((citerate @ V1) @ ((cUNION @ V0) @ V2)) @ V3)) @ ((V1 @ (((citerate @ V1) @ V0) @ V3)) @ (((citerate @ V1) @ V2) @ V3))))))))))))))
(TITERATE_CLAUSES_conjunct1,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cFINITE @ V3)) @ ((c= @ (((citerate @ V0) @ ((cINSERT @ V2) @ V3)) @ V1)) @ (((cCOND @ ((cIN @ V2) @ V3)) @ (((citerate @ V0) @ V3) @ V1)) @ ((V0 @ (V1 @ V2)) @ (((citerate @ V0) @ V3) @ V1)))))))))))))))
(TITERATE_CLAUSES_conjunct0,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ (c! @ (^[V1]: ((c= @ (((citerate @ V0) @ cEMPTY) @ V1)) @ (cneutral @ V0))))))))
(TITERATE_EXPAND_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((citerate @ V2) @ V0) @ V1)) @ (((cCOND @ (cFINITE @ (((csupport @ V2) @ V1) @ V0))) @ (((citerate @ V2) @ (((csupport @ V2) @ V1) @ V0)) @ V1)) @ (cneutral @ V2))))))))))
(TITERATE_SUPPORT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((citerate @ V0) @ (((csupport @ V0) @ V2) @ V1)) @ V2)) @ (((citerate @ V0) @ V1) @ V2)))))))))
(TSUPPORT_DELTA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csupport @ V1) @ (^[V4]: (((cCOND @ ((c= @ V4) @ V3)) @ (V2 @ V4)) @ (cneutral @ V1)))) @ V0)) @ (((cCOND @ ((cIN @ V3) @ V0)) @ (((csupport @ V1) @ V2) @ ((cINSERT @ V3) @ cEMPTY))) @ cEMPTY)))))))))))
(TSUPPORT_CLAUSES_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csupport @ V0) @ V2) @ ((cIMAGE @ V1) @ V3))) @ ((cIMAGE @ V1) @ (((csupport @ V0) @ ((co @ V2) @ V1)) @ V3))))))))))))
(TSUPPORT_CLAUSES_conjunct5,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csupport @ V0) @ V1) @ ((cDIFF @ V2) @ V3))) @ ((cDIFF @ (((csupport @ V0) @ V1) @ V2)) @ (((csupport @ V0) @ V1) @ V3))))))))))))
(TSUPPORT_CLAUSES_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csupport @ V0) @ V1) @ ((cINTER @ V2) @ V3))) @ ((cINTER @ (((csupport @ V0) @ V1) @ V2)) @ (((csupport @ V0) @ V1) @ V3))))))))))))
(TSUPPORT_CLAUSES_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csupport @ V0) @ V1) @ ((cUNION @ V2) @ V3))) @ ((cUNION @ (((csupport @ V0) @ V1) @ V2)) @ (((csupport @ V0) @ V1) @ V3))))))))))))
(TSUPPORT_CLAUSES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csupport @ V0) @ V1) @ ((cDELETE @ V3) @ V2))) @ ((cDELETE @ (((csupport @ V0) @ V1) @ V3)) @ V2)))))))))))
(TSUPPORT_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csupport @ V0) @ V1) @ ((cINSERT @ V2) @ V3))) @ (((cCOND @ ((c= @ (V1 @ V2)) @ (cneutral @ V0))) @ (((csupport @ V0) @ V1) @ V3)) @ ((cINSERT @ V2) @ (((csupport @ V0) @ V1) @ V3)))))))))))))
(TSUPPORT_CLAUSES_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((csupport @ V0) @ V1) @ cEMPTY)) @ cEMPTY))))))
(TFINITE_SUPPORT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V2)) @ (cFINITE @ (((csupport @ V0) @ V1) @ V2))))))))))
(TSUPPORT_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((cSUBSET @ (((csupport @ V0) @ V1) @ V2)) @ V2))))))))
(TSUPPORT_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((c= @ (V1 @ V3)) @ (cneutral @ V0)))))) @ ((c= @ (((csupport @ V0) @ V1) @ V2)) @ cEMPTY)))))))))
(TSUPPORT_SUPPORT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((csupport @ V0) @ V1) @ (((csupport @ V0) @ V1) @ V2))) @ (((csupport @ V0) @ V1) @ V2)))))))))
(TIN_SUPPORT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cIN @ V2) @ (((csupport @ V3) @ V1) @ V0))) @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ (c~ @ ((c= @ (V1 @ V2)) @ (cneutral @ V3))))))))))))))
(TMONOIDAL_AC_conjunct0,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ (c! @ (^[V1]: ((c= @ ((V0 @ (cneutral @ V0)) @ V1)) @ V1)))))))
(TMONOIDAL_AC_conjunct1,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ (c! @ (^[V1]: ((c= @ ((V0 @ V1) @ (cneutral @ V0))) @ V1)))))))
(TMONOIDAL_AC_conjunct2,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((V0 @ V1) @ V2)) @ ((V0 @ V2) @ V1))))))))))
(TMONOIDAL_AC_conjunct3,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((V0 @ ((V0 @ V1) @ V2)) @ V3)) @ ((V0 @ V1) @ ((V0 @ V2) @ V3)))))))))))))
(TMONOIDAL_AC_conjunct4,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((V0 @ V1) @ ((V0 @ V2) @ V3))) @ ((V0 @ V2) @ ((V0 @ V1) @ V3)))))))))))))
(Tneutral,(c! @ (^[V0]: ((c= @ (cneutral @ V0)) @ (c__at__ @ (^[V1]: (c! @ (^[V2]: ((c/__caret__ @ ((c= @ ((V0 @ V1) @ V2)) @ V2)) @ ((c= @ ((V0 @ V2) @ V1)) @ V2))))))))))
(TCOUNTABLE,(c! @ (^[V0]: ((c= @ (cCOUNTABLE @ V0)) @ ((c>=_c @ cUNIV) @ V0)))))
(TGE_C,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c>=_c @ V1) @ V0)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ V3) @ (V2 @ V4))))))))))))))))
(TLE_C,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<=_c @ V0) @ V1)) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V4)) @ V3)))))))))))))))
(Tgt_c,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c>_c @ V1) @ V0)) @ ((c<_c @ V0) @ V1)))))))
(Tge_c,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c>=_c @ V1) @ V0)) @ ((c<=_c @ V0) @ V1)))))))
(Teq_c,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c=_c @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c?! @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V4)) @ V3))))))))))))))))
(Tlt_c,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<_c @ V1) @ V0)) @ ((c/__caret__ @ ((c<=_c @ V1) @ V0)) @ (c~ @ ((c<=_c @ V0) @ V1)))))))))
(Tle_c,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c<=_c @ V1) @ V0)) @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4)))))))))))))))
(TEXISTS_IN_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ ((cINSERT @ V1) @ V2))) @ (V0 @ V3))))) @ ((c__caret__/ @ (V0 @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V2)) @ (V0 @ V3)))))))))))))
(TEXISTS_IN_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ cEMPTY)) @ (V0 @ V1))))) @ cF))))
(TFORALL_IN_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cINSERT @ V1) @ V2))) @ (V0 @ V3))))) @ ((c/__caret__ @ (V0 @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (V0 @ V3)))))))))))))
(TFORALL_IN_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c==> @ ((cIN @ V1) @ cEMPTY)) @ (V0 @ V1))))) @ cT))))
(TIMAGE_IMP_INJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c= @ ((cIMAGE @ V1) @ V0)) @ V0))) @ ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))))))))
(TPAIRWISE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpairwise @ V0) @ ((cIMAGE @ V1) @ V2))) @ ((cpairwise @ (^[V3]: (^[V4]: ((c==> @ (c~ @ ((c= @ (V1 @ V3)) @ (V1 @ V4)))) @ ((V0 @ (V1 @ V3)) @ (V1 @ V4)))))) @ V2)))))))))
(TPAIRWISE_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpairwise @ V1) @ V0)) @ ((cSUBSET @ V2) @ V0))) @ ((cpairwise @ V1) @ V2)))))))))
(TPAIRWISE_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpairwise @ V0) @ ((cINSERT @ V1) @ cEMPTY))) @ cT))))))
(TPAIRWISE_EMPTY,(c! @ (^[V0]: ((c= @ ((cpairwise @ V0) @ cEMPTY)) @ cT))))
(Tpairwise,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpairwise @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (c~ @ ((c= @ V2) @ V3))))) @ ((V1 @ V2) @ V3))))))))))))
(TSET_OF_LIST_MAP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cset_of_list @ ((cMAP @ V0) @ V1))) @ ((cIMAGE @ V0) @ (cset_of_list @ V1))))))))
(TLENGTH_LIST_OF_SET,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cLENGTH @ (clist_of_set @ V0))) @ (cCARD @ V0))))))
(TSET_OF_LIST_OF_SET,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cset_of_list @ (clist_of_set @ V0))) @ V0)))))
(Tlist_of_set,(c! @ (^[V0]: ((c= @ (clist_of_set @ V0)) @ (c__at__ @ (^[V1]: ((c/__caret__ @ ((c= @ (cset_of_list @ V1)) @ V0)) @ ((c= @ (cLENGTH @ V1)) @ (cCARD @ V0)))))))))
(TOPERATIVE_1_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmonoidal @ V0)) @ ((c= @ ((coperative @ V0) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V2))) @ ((c= @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (cneutral @ V0)))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_le @ (cdrop @ V2)) @ (cdrop @ V4))) @ ((creal_le @ (cdrop @ V4)) @ (cdrop @ V3)))) @ ((c= @ ((V0 @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL)))) @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V3)) @ cNIL))))) @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))))))))
(TOPERATIVE_1_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmonoidal @ V0)) @ ((c= @ ((coperative @ V0) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V2))) @ ((c= @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ (cneutral @ V0)))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (cdrop @ V2)) @ (cdrop @ V4))) @ ((creal_lt @ (cdrop @ V4)) @ (cdrop @ V3)))) @ ((c= @ ((V0 @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL)))) @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V3)) @ cNIL))))) @ (V1 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))))))))
(TITERATE_AND,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (((citerate @ c/__caret__) @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (V1 @ V2)))))))))))
(TFINITE_FUNSPACE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (cFINITE @ V0))) @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((cIN @ (V4 @ V5)) @ V0))))) @ (c! @ (^[V5]: ((c==> @ (c~ @ ((cIN @ V5) @ V1))) @ ((c= @ (V4 @ V5)) @ V2)))))) @ V4))))))))))))))
(TITERATE_SOME,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cmonoidal @ V0)) @ ((c==> @ (cFINITE @ V1)) @ ((c= @ (((citerate @ (clifted @ V0)) @ V1) @ (^[V3]: (cSOME @ (V2 @ V3))))) @ (cSOME @ (((citerate @ V0) @ V1) @ V2))))))))))))
(TMONOIDAL_LIFTED,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ (cmonoidal @ (clifted @ V0))))))
(TNEUTRAL_LIFTED,(c! @ (^[V0]: ((c==> @ (cmonoidal @ V0)) @ ((c= @ (cneutral @ (clifted @ V0))) @ (cSOME @ (cneutral @ V0)))))))
(Tlifted_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((clifted @ V0) @ cNONE) @ V1)) @ cNONE))))))
(Tlifted_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((clifted @ V0) @ V1) @ cNONE)) @ cNONE))))))
(Tlifted_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((clifted @ V0) @ (cSOME @ V1)) @ (cSOME @ V2))) @ (cSOME @ ((V0 @ V1) @ V2))))))))))
(TCROSS_EQ_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cCROSS @ V0) @ V1)) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V0) @ cEMPTY)) @ ((c= @ V1) @ cEMPTY))))))))
(TCARD_CROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ (cCARD @ ((cCROSS @ V0) @ V1))) @ ((c* @ (cCARD @ V0)) @ (cCARD @ V1)))))))))
(TFINITE_CROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ (cFINITE @ ((cCROSS @ V0) @ V1))))))))
(THAS_SIZE_CROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V0) @ V2)) @ ((cHAS_SIZE @ V1) @ V3))) @ ((cHAS_SIZE @ ((cCROSS @ V0) @ V1)) @ ((c* @ V2) @ V3))))))))))))
(TCROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cCROSS @ V0) @ V1)) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((cIN @ V4) @ V1))) @ ((c__comma__ @ V3) @ V4))))))))))))))
(TFINE_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cfine @ V0) @ V2))))) @ ((cfine @ V0) @ (cUNIONS @ V1))))))))
(TFINE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cfine @ V0) @ V1)) @ ((cfine @ V0) @ V2))) @ ((cfine @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TFINE_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cfine @ (^[V3]: (cINTERS @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cIN @ V5) @ V0)) @ ((V1 @ V5) @ V3))))))))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cfine @ (V1 @ V3)) @ V2))))))))))))
(TFINE_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cfine @ (^[V3]: ((cINTER @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((c/__caret__ @ ((cfine @ V0) @ V2)) @ ((cfine @ V1) @ V2))))))))))
(THAS_SIZE_IMAGE_INJ_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V0 @ V3)) @ (V0 @ V4))))) @ ((c= @ V3) @ V4))))))) @ ((c= @ ((cHAS_SIZE @ ((cIMAGE @ V0) @ V1)) @ V2)) @ ((cHAS_SIZE @ V1) @ V2))))))))))
(TCARD_SUBSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((cSUBSET @ V1) @ ((cIMAGE @ V0) @ V2)))) @ ((c<= @ (cCARD @ V1)) @ (cCARD @ V2))))))))))
(TCARD_UNION_OVERLAP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c< @ (cCARD @ ((cUNION @ V0) @ V1))) @ ((c+ @ (cCARD @ V0)) @ (cCARD @ V1)))))) @ (c~ @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY))))))))
(TCARD_UNION_OVERLAP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ ((c= @ (cCARD @ ((cUNION @ V0) @ V1))) @ ((c+ @ (cCARD @ V0)) @ (cCARD @ V1)))) @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY))))))))
(TCARD_UNION_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ (cCARD @ ((cUNION @ V0) @ V1))) @ ((c- @ ((c+ @ (cCARD @ V0)) @ (cCARD @ V1))) @ (cCARD @ ((cINTER @ V0) @ V1))))))))))
(TGAUGE_EXISTENCE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (c? @ (^[V3]: ((c==> @ (V0 @ V2)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((V1 @ V3) @ V2)))))))) @ (c! @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c==> @ (V0 @ V2)) @ ((V1 @ V3) @ V2)))))))))))))
(TGAUGE_INTERS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cgauge @ (V1 @ V2))))))) @ (cgauge @ (^[V2]: (cINTERS @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ V0)) @ ((V1 @ V4) @ V2)))))))))))))))
(TSEQITERATE_ITERATE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cmonoidal @ V0)) @ (cFINITE @ V1))) @ ((c= @ (((cseqiterate @ V0) @ V1) @ V2)) @ (((citerate @ V0) @ V1) @ V2))))))))))
(TSEQITERATE_CLAUSES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V3)) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ cEMPTY))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((c< @ V2) @ V4))))))) @ ((c= @ (((cseqiterate @ V0) @ ((cINSERT @ V2) @ V3)) @ V1)) @ ((V0 @ (V1 @ V2)) @ (((cseqiterate @ V0) @ V3) @ V1)))))))))))))
(TSEQITERATE_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cseqiterate @ V0) @ ((cINSERT @ V2) @ cEMPTY)) @ V1)) @ (V1 @ V2)))))))))
(TSEQITERATE_CLAUSES_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cseqiterate @ V0) @ cEMPTY) @ V1)) @ (cneutral @ V0)))))))
(Tseqiterate_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: (c! @ (^[V3]: ((c= @ (V2 @ V3)) @ (((cCOND @ ((c__caret__/ @ (cINFINITE @ V3)) @ ((c= @ V3) @ cEMPTY))) @ (cneutral @ V0)) @ ((cLET @ (^[V4]: (cLET_END @ (((cCOND @ ((c= @ V3) @ ((cINSERT @ V4) @ cEMPTY))) @ (V1 @ V4)) @ ((V0 @ (V1 @ V4)) @ (V2 @ ((cDELETE @ V3) @ V4))))))) @ (cminimal @ (^[V4]: ((cIN @ V4) @ V3)))))))))))))))
(Tseqiterate,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cseqiterate @ V0) @ V2) @ V1)) @ (((cCOND @ ((c__caret__/ @ (cINFINITE @ V2)) @ ((c= @ V2) @ cEMPTY))) @ (cneutral @ V0)) @ ((cLET @ (^[V3]: (cLET_END @ (((cCOND @ ((c= @ V2) @ ((cINSERT @ V3) @ cEMPTY))) @ (V1 @ V3)) @ ((V0 @ (V1 @ V3)) @ (((cseqiterate @ V0) @ ((cDELETE @ V2) @ V3)) @ V1)))))) @ (cminimal @ (^[V3]: ((cIN @ V3) @ V2)))))))))))))
(TSUBSET_CARD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cSUBSET @ V0) @ V1))) @ ((c= @ ((c= @ (cCARD @ V0)) @ (cCARD @ V1))) @ ((c= @ V0) @ V1))))))))
(TMULTIVECTOR_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ V0) @ V1)) @ (clambdas @ (^[V2]: ((csum @ V0) @ (^[V3]: ((c$$ @ (V1 @ V3)) @ V2)))))))))))
(THAS_SIZE_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((cHAS_SIZE @ V0) @ (cNUMERAL @ c_0))) @ ((c= @ V0) @ cEMPTY)))))
(TSYMDIFF_PARITY_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c= @ ((cUNION @ ((cDIFF @ V1) @ V2)) @ ((cDIFF @ V2) @ V1))) @ V0)))) @ ((c= @ (cEVEN @ (cCARD @ V0))) @ ((c= @ (cEVEN @ (cCARD @ V1))) @ (cEVEN @ (cCARD @ V2))))))))))))
(TCARD_DIFF_INTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cCARD @ V0)) @ ((c+ @ (cCARD @ ((cDIFF @ V0) @ V1))) @ (cCARD @ ((cINTER @ V0) @ V1))))))))))
(TFINITE_HAS_SIZE,(c! @ (^[V0]: ((c= @ (cFINITE @ V0)) @ ((cHAS_SIZE @ V0) @ (cCARD @ V0))))))
(TCARD_UNION_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ (cFINITE @ V3)) @ ((c/__caret__ @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)) @ ((c/__caret__ @ ((c= @ ((cINTER @ V2) @ V3)) @ cEMPTY)) @ ((c= @ ((cUNION @ V0) @ V1)) @ ((cUNION @ V2) @ V3))))))))) @ ((c= @ ((c+ @ (cCARD @ V0)) @ (cCARD @ V1))) @ ((c+ @ (cCARD @ V2)) @ (cCARD @ V3)))))))))))))
(THAS_SIZE_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V0) @ V2)) @ ((c/__caret__ @ ((cHAS_SIZE @ V1) @ V3)) @ ((cSUBSET @ V1) @ V0)))) @ ((cHAS_SIZE @ ((cDIFF @ V0) @ V1)) @ ((c- @ V2) @ V3))))))))))))
(THAS_SIZE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cHAS_SIZE @ V0) @ V2)) @ ((c/__caret__ @ ((cHAS_SIZE @ V1) @ V3)) @ ((cDISJOINT @ V0) @ V1)))) @ ((cHAS_SIZE @ ((cUNION @ V0) @ V1)) @ ((c+ @ V2) @ V3))))))))))))
(THAS_SIZE_CARD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cHAS_SIZE @ V0) @ V1)) @ ((c= @ (cCARD @ V0)) @ V1)))))))
(THAS_SIZE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cHAS_SIZE @ V0) @ V1)) @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c= @ (cCARD @ V0)) @ V1))))))))
(TCARD_EQ_0,(c! @ (^[V0]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((c= @ (cCARD @ V0)) @ (cNUMERAL @ c_0))) @ ((c= @ V0) @ cEMPTY))))))
(TCARD_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cSUBSET @ V1) @ V0))) @ ((c= @ (cCARD @ ((cDIFF @ V0) @ V1))) @ ((c- @ (cCARD @ V0)) @ (cCARD @ V1)))))))))
(TCARD_UNION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((c= @ ((cINTER @ V0) @ V1)) @ cEMPTY)) @ ((c= @ ((cUNION @ V0) @ V1)) @ V2)))) @ ((c= @ ((c+ @ (cCARD @ V0)) @ (cCARD @ V1))) @ (cCARD @ V2))))))))))
(TCARD,(c! @ (^[V0]: ((c= @ (cCARD @ V0)) @ (((cITSET @ (^[V1]: (^[V2]: (cSUC @ V2)))) @ V0) @ (cNUMERAL @ c_0))))))
(TITSET_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((c= @ (V0 @ V4)) @ (V1 @ V4)))))) @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (c~ @ ((c= @ V4) @ V5))) @ ((c= @ ((V0 @ V4) @ ((V0 @ V5) @ V6))) @ ((V0 @ V5) @ ((V0 @ V4) @ V6))))))))))) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (c~ @ ((c= @ V4) @ V5))) @ ((c= @ ((V1 @ V4) @ ((V1 @ V5) @ V6))) @ ((V1 @ V5) @ ((V1 @ V4) @ V6)))))))))))))) @ ((c= @ (((cITSET @ V0) @ V2) @ V3)) @ (((cITSET @ V1) @ V2) @ V3))))))))))))
(TDIFFERENTIABLE_VSUM_NUMSEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ V1) @ V5)) @ ((c<= @ V5) @ V2))) @ ((cdifferentiable @ (V3 @ V5)) @ V4)))))) @ ((cdifferentiable @ (^[V5]: ((cvsum @ ((c.. @ V1) @ V2)) @ (^[V6]: ((V3 @ V6) @ V5))))) @ V4)))))))))))))
(TDIFFERENTIABLE_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cdifferentiable @ (V1 @ V3)) @ V2)))))) @ ((cdifferentiable @ (^[V3]: ((cvsum @ V0) @ (^[V4]: ((V1 @ V4) @ V3))))) @ V2)))))))))
(THAS_DERIVATIVE_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ (((chas_derivative @ (V0 @ V4)) @ (V2 @ V4)) @ V3)))))) @ (((chas_derivative @ (^[V4]: ((cvsum @ V1) @ (^[V5]: ((V0 @ V5) @ V4))))) @ (^[V4]: ((cvsum @ V1) @ (^[V5]: ((V2 @ V5) @ V4))))) @ V3)))))))))))
(TFINREC_1_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((((cFINREC @ V2) @ V3) @ V0) @ V1) @ (cSUC @ (cNUMERAL @ c_0)))) @ (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((cINSERT @ V4) @ cEMPTY))) @ ((c= @ V1) @ ((V2 @ V4) @ V3)))))))))))))))
(TINFINITE_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cINFINITE @ V0)) @ ((cSUBSET @ V0) @ V1))) @ (cINFINITE @ V1)))))))
(TFINITE_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ (cFINITE @ ((cDIFF @ V0) @ V1))))))))
(TFORALL_FINITE_SUBSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V3)) @ ((cSUBSET @ V3) @ ((cIMAGE @ V2) @ V0)))) @ (V1 @ V3))))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V3)) @ ((cSUBSET @ V3) @ V0))) @ (V1 @ ((cIMAGE @ V2) @ V3)))))))))))))
(TEXISTS_FINITE_SUBSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ (cFINITE @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ ((cIMAGE @ V2) @ V0))) @ (V1 @ V3)))))) @ (c? @ (^[V3]: ((c/__caret__ @ (cFINITE @ V3)) @ ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (V1 @ ((cIMAGE @ V2) @ V3))))))))))))))
(TINFINITE_NONEMPTY,(c! @ (^[V0]: ((c==> @ (cINFINITE @ V0)) @ (c~ @ ((c= @ V0) @ cEMPTY))))))
(TFUNCTION_FACTORS_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (c? @ (^[V3]: ((c= @ (V1 @ V3)) @ (V0 @ V2))))))) @ (c? @ (^[V2]: ((c= @ V0) @ ((co @ V1) @ V2))))))))))
(TFUNCTION_FACTORS_RIGHT_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ (c? @ (^[V4]: ((c= @ (V2 @ V4)) @ (V1 @ V3)))))))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ (V0 @ V4)) @ ((c= @ (V1 @ V4)) @ (V2 @ (V3 @ V4))))))))))))))))
(TFUNCTION_FACTORS_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c= @ (V1 @ V2)) @ (V1 @ V3))) @ ((c= @ (V0 @ V2)) @ (V0 @ V3)))))))) @ (c? @ (^[V2]: ((c= @ V0) @ ((co @ V2) @ V1))))))))))
(TFUNCTION_FACTORS_LEFT_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (V0 @ V3)) @ ((c/__caret__ @ (V0 @ V4)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ (V1 @ V3)) @ (V1 @ V4)))))))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ (V0 @ V4)) @ ((c= @ (V1 @ V4)) @ (V3 @ (V2 @ V4))))))))))))))))
(TINJECTIVE_LEFT_INVERSE,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c= @ (V1 @ (V0 @ V2))) @ V2)))))))))
(TSURJECTIVE_RIGHT_INVERSE,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))) @ (c? @ (^[V1]: (c! @ (^[V2]: ((c= @ (V0 @ (V1 @ V2))) @ V2)))))))))
(TBIJECTIVE_ON_LEFT_RIGHT_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cIN @ (V2 @ V3)) @ V0))))) @ ((c= @ ((c/__caret__ @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V4)) @ V3))))))))) @ (c? @ (^[V3]: ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((cIN @ (V3 @ V4)) @ V1))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ (V3 @ V4))) @ V4))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((c= @ (V3 @ (V2 @ V4))) @ V4)))))))))))))))))
(TINJECTIVE_ON_LEFT_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((c= @ (V2 @ (V1 @ V3))) @ V3))))))))))))
(TSURJECTIVE_ON_RIGHT_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V2 @ V4)) @ V3)))))))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((c/__caret__ @ ((cIN @ (V3 @ V4)) @ V1)) @ ((c= @ (V2 @ (V3 @ V4))) @ V4)))))))))))))))
(TINJECTIVE_ALT,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ (V0 @ V1)) @ (V0 @ V2))) @ ((c= @ V1) @ V2))))))))))
(TINJECTIVE_ON_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ ((c/__caret__ @ (V0 @ V3)) @ ((c= @ (V1 @ V2)) @ (V1 @ V3))))) @ ((c= @ V2) @ V3))))))) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (V0 @ V2)) @ (V0 @ V3))) @ ((c= @ ((c= @ (V1 @ V2)) @ (V1 @ V3))) @ ((c= @ V2) @ V3)))))))))))))
(TINTERS_GSPEC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cINTERS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V2) @ (((V0 @ V3) @ V4) @ V5)) @ (((V1 @ V3) @ V4) @ V5)))))))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ (((V0 @ V4) @ V5) @ V6)) @ ((cIN @ V3) @ (((V1 @ V4) @ V5) @ V6)))))))))) @ V3)))))))))))
(TINTERS_GSPEC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cINTERS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((V0 @ V3) @ V4)) @ ((V1 @ V3) @ V4)))))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((V0 @ V4) @ V5)) @ ((cIN @ V3) @ ((V1 @ V4) @ V5)))))))) @ V3)))))))))))
(TINTERS_GSPEC_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cINTERS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V0 @ V3)) @ (V1 @ V3)))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c! @ (^[V4]: ((c==> @ (V0 @ V4)) @ ((cIN @ V3) @ (V1 @ V4)))))) @ V3)))))))))))
(TUNIONS_GSPEC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V2) @ (((V0 @ V3) @ V4) @ V5)) @ (((V1 @ V3) @ V4) @ V5)))))))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ (((V0 @ V4) @ V5) @ V6)) @ ((cIN @ V3) @ (((V1 @ V4) @ V5) @ V6)))))))))) @ V3)))))))))))
(TUNIONS_GSPEC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((V0 @ V3) @ V4)) @ ((V1 @ V3) @ V4)))))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((V0 @ V4) @ V5)) @ ((cIN @ V3) @ ((V1 @ V4) @ V5)))))))) @ V3)))))))))))
(TUNIONS_GSPEC_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V0 @ V3)) @ (V1 @ V3)))))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c/__caret__ @ (V0 @ V4)) @ ((cIN @ V3) @ (V1 @ V4)))))) @ V3)))))))))))
(TINTERS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cINTERS @ ((cIMAGE @ V1) @ V0))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V0)) @ ((cIN @ V3) @ (V1 @ V4)))))) @ V3)))))))))))
(TUNIONS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cUNIONS @ ((cIMAGE @ V1) @ V0))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((cIN @ V3) @ (V1 @ V4)))))) @ V3)))))))))))
(THAS_SIZE_2_EXISTS,(c! @ (^[V0]: ((c= @ ((cHAS_SIZE @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ (c! @ (^[V3]: ((c= @ ((cIN @ V3) @ V0)) @ ((c__caret__/ @ ((c= @ V3) @ V1)) @ ((c= @ V3) @ V2))))))))))))))
(THAS_SIZE_1_EXISTS,(c! @ (^[V0]: ((c= @ ((cHAS_SIZE @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (c?! @ (^[V1]: ((cIN @ V1) @ V0)))))))
(TEXISTS_IN_GSPEC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V4) @ (((V1 @ V5) @ V6) @ V7)) @ (((V2 @ V5) @ V6) @ V7)))))))))))) @ (V0 @ V3))))) @ (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ (((V1 @ V3) @ V4) @ V5)) @ (V0 @ (((V2 @ V3) @ V4) @ V5)))))))))))))))))
(TEXISTS_IN_GSPEC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((V1 @ V5) @ V6)) @ ((V2 @ V5) @ V6)))))))))) @ (V0 @ V3))))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((V1 @ V3) @ V4)) @ (V0 @ ((V2 @ V3) @ V4)))))))))))))))
(TEXISTS_IN_GSPEC_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ (V1 @ V5)) @ (V2 @ V5)))))))) @ (V0 @ V3))))) @ (c? @ (^[V3]: ((c/__caret__ @ (V1 @ V3)) @ (V0 @ (V2 @ V3)))))))))))))
(TEXISTS_TRIPLED_THM,(c! @ (^[V0]: ((c= @ (c? @ (cGABS @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V1 @ ((c__comma__ @ V2) @ ((c__comma__ @ V3) @ V4)))) @ (((V0 @ V2) @ V3) @ V4)))))))))))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (((V0 @ V1) @ V2) @ V3)))))))))))
(TFORALL_IN_GSPEC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V4) @ (((V1 @ V5) @ V6) @ V7)) @ (((V2 @ V5) @ V6) @ V7)))))))))))) @ (V0 @ V3))))) @ (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (((V1 @ V3) @ V4) @ V5)) @ (V0 @ (((V2 @ V3) @ V4) @ V5)))))))))))))))))
(TFORALL_IN_GSPEC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((V1 @ V5) @ V6)) @ ((V2 @ V5) @ V6)))))))))) @ (V0 @ V3))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((V1 @ V3) @ V4)) @ (V0 @ ((V2 @ V3) @ V4)))))))))))))))
(TFORALL_IN_GSPEC_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ (V1 @ V5)) @ (V2 @ V5)))))))) @ (V0 @ V3))))) @ (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ (V0 @ (V2 @ V3)))))))))))))
(TIN_ELIM_PAIR_THM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ ((c__comma__ @ V1) @ V2)) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((V0 @ V4) @ V5)) @ ((c__comma__ @ V4) @ V5)))))))))) @ ((V0 @ V1) @ V2)))))))))
(TSURJECTIVE_IMAGE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (c? @ (^[V4]: ((c= @ (V0 @ V4)) @ V3))))))) @ (c! @ (^[V3]: ((c= @ ((cIN @ (V0 @ V3)) @ V2)) @ ((cIN @ V3) @ V1)))))) @ ((c= @ ((cIMAGE @ V0) @ V1)) @ V2)))))))))
(TIMAGE_UNIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIMAGE @ V0) @ (cUNIONS @ V1))) @ (cUNIONS @ ((cIMAGE @ (cIMAGE @ V0)) @ V1))))))))
(TFORALL_TRIPLED_THM,(c! @ (^[V0]: ((c= @ (c! @ (cGABS @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V1 @ ((c__comma__ @ V2) @ ((c__comma__ @ V3) @ V4)))) @ (((V0 @ V2) @ V3) @ V4)))))))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (((V0 @ V1) @ V2) @ V3)))))))))))
(TSIMPLE_IMAGE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V1 @ V3)) @ (V0 @ V3))))))) @ ((cIMAGE @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V1 @ V3)) @ V3))))))))))))
(TSIMPLE_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ (V0 @ V3))))))) @ ((cIMAGE @ V0) @ V1)))))))
(TIMAGE_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIMAGE @ (^[V2]: V1)) @ V0)) @ (((cCOND @ ((c= @ V0) @ cEMPTY)) @ cEMPTY) @ ((cINSERT @ V1) @ cEMPTY))))))))
(TEXISTS_SUBSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ ((cIMAGE @ V2) @ V0))) @ (V1 @ V3))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cSUBSET @ V3) @ V0)) @ (V1 @ ((cIMAGE @ V2) @ V3)))))))))))))
(TFORALL_SUBSET_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ ((cIMAGE @ V2) @ V0))) @ (V1 @ V3))))) @ (c! @ (^[V3]: ((c==> @ ((cSUBSET @ V3) @ V0)) @ (V1 @ ((cIMAGE @ V2) @ V3)))))))))))))
(TEXISTS_IN_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ ((cIMAGE @ V2) @ V0))) @ (V1 @ V3))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V0)) @ (V1 @ (V2 @ V3)))))))))))))
(TFORALL_IN_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cIMAGE @ V2) @ V0))) @ (V1 @ V3))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ (V1 @ (V2 @ V3)))))))))))))
(TIMAGE_EQ_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cIMAGE @ V0) @ V1)) @ cEMPTY)) @ ((c= @ V1) @ cEMPTY)))))))
(TIMAGE_DELETE_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((c= @ (V1 @ V3)) @ (V1 @ V2))) @ ((c= @ V3) @ V2))))) @ ((c= @ ((cIMAGE @ V1) @ ((cDELETE @ V0) @ V2))) @ ((cDELETE @ ((cIMAGE @ V1) @ V0)) @ (V1 @ V2)))))))))))
(TEXISTS_PAIRED_THM,(c! @ (^[V0]: ((c= @ (c? @ (cGABS @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((cGEQ @ (V1 @ ((c__comma__ @ V2) @ V3))) @ ((V0 @ V2) @ V3)))))))))) @ (c? @ (^[V1]: (c? @ (^[V2]: ((V0 @ V1) @ V2)))))))))
(TIMAGE_DIFF_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V1 @ V3)) @ (V1 @ V4))) @ ((c= @ V3) @ V4))))))) @ ((c= @ ((cIMAGE @ V1) @ ((cDIFF @ V0) @ V2))) @ ((cDIFF @ ((cIMAGE @ V1) @ V0)) @ ((cIMAGE @ V1) @ V2)))))))))))
(TIMAGE_INTER_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c= @ (V1 @ V3)) @ (V1 @ V4))) @ ((c= @ V3) @ V4))))))) @ ((c= @ ((cIMAGE @ V1) @ ((cINTER @ V0) @ V2))) @ ((cINTER @ ((cIMAGE @ V1) @ V0)) @ ((cIMAGE @ V1) @ V2)))))))))))
(TIMAGE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V0) @ V2)) @ ((cSUBSET @ ((cIMAGE @ V1) @ V0)) @ ((cIMAGE @ V1) @ V2))))))))))
(TIMAGE_o,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIMAGE @ ((co @ V0) @ V1)) @ V2)) @ ((cIMAGE @ V0) @ ((cIMAGE @ V1) @ V2))))))))))
(TIMAGE_I,(c! @ (^[V0]: ((c= @ ((cIMAGE @ cI) @ V0)) @ V0))))
(TIMAGE_ID,(c! @ (^[V0]: ((c= @ ((cIMAGE @ (^[V1]: V1)) @ V0)) @ V0))))
(TIMAGE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIMAGE @ V1) @ ((cUNION @ V0) @ V2))) @ ((cUNION @ ((cIMAGE @ V1) @ V0)) @ ((cIMAGE @ V1) @ V2))))))))))
(TIMAGE_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((cIMAGE @ V0) @ cEMPTY)) @ cEMPTY))))
(TINTERS_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cINTERS @ ((cINSERT @ V0) @ V1))) @ ((cINTER @ V0) @ (cINTERS @ V1))))))))
(TINTERS_2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cINTERS @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))) @ ((cINTER @ V0) @ V1)))))))
(TFORALL_PAIRED_THM,(c! @ (^[V0]: ((c= @ (c! @ (cGABS @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((cGEQ @ (V1 @ ((c__comma__ @ V2) @ V3))) @ ((V0 @ V2) @ V3)))))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((V0 @ V1) @ V2)))))))))
(TINTERS_1,(c! @ (^[V0]: ((c= @ (cINTERS @ ((cINSERT @ V0) @ cEMPTY))) @ V0))))
(TUNIONS_MONO_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((cSUBSET @ (V0 @ V3)) @ (V1 @ V3)))))) @ ((cSUBSET @ (cUNIONS @ ((cIMAGE @ V0) @ V2))) @ (cUNIONS @ ((cIMAGE @ V1) @ V2)))))))))))
(TUNIONS_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cUNIONS @ ((cINSERT @ V0) @ V1))) @ ((cUNION @ V0) @ (cUNIONS @ V1))))))))
(TUNIONS_2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cUNIONS @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))) @ ((cUNION @ V0) @ V1)))))))
(TUNIONS_1,(c! @ (^[V0]: ((c= @ (cUNIONS @ ((cINSERT @ V0) @ cEMPTY))) @ V0))))
(TUNION_ACI_conjunct3,(c! @ (^[V0]: ((c= @ ((cUNION @ V0) @ V0)) @ V0))))
(TUNION_ACI_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cUNION @ V1) @ V0)) @ ((cUNION @ V0) @ V1)))))))
(TUNION_ACI_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cUNION @ V0) @ ((cUNION @ V0) @ V1))) @ ((cUNION @ V0) @ V1)))))))
(TUNION_ACI_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cUNION @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cUNION @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TUNION_ACI_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cUNION @ V1) @ ((cUNION @ V0) @ V2))) @ ((cUNION @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TINTER_ACI_conjunct3,(c! @ (^[V0]: ((c= @ ((cINTER @ V0) @ V0)) @ V0))))
(TINTER_ACI_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINTER @ V1) @ V0)) @ ((cINTER @ V0) @ V1)))))))
(TINTER_ACI_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINTER @ V0) @ ((cINTER @ V0) @ V1))) @ ((cINTER @ V0) @ V1)))))))
(TINTER_ACI_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cINTER @ ((cINTER @ V0) @ V1)) @ V2)) @ ((cINTER @ V0) @ ((cINTER @ V1) @ V2))))))))))
(TINTER_ACI_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cINTER @ V1) @ ((cINTER @ V0) @ V2))) @ ((cINTER @ V0) @ ((cINTER @ V1) @ V2))))))))))
(TSUBSET_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ ((cDIFF @ V1) @ V0)) @ V1))))))
(TSUBSET_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cSUBSET @ V1) @ ((cINTER @ V0) @ V2))) @ ((c/__caret__ @ ((cSUBSET @ V1) @ V0)) @ ((cSUBSET @ V1) @ V2))))))))))
(TUNION_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cSUBSET @ ((cUNION @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ V0) @ V2)) @ ((cSUBSET @ V1) @ V2))))))))))
(TSUBSET_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ (V0 @ V3))) @ V3)))))) @ V1))))))
(TIN_ELIM_THM_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V1) @ (^[V2]: (V0 @ V2)))) @ (V0 @ V1)))))))
(TIN_ELIM_THM_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V0 @ V3)) @ V3))))) @ V1)) @ (V0 @ V1)))))))
(TIN_ELIM_THM_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V1) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (V0 @ V3)) @ V3))))))) @ (V0 @ V1)))))))
(TSKOLEM_THM_GEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ (V0 @ V2)) @ (c? @ (^[V3]: ((V1 @ V2) @ V3))))))) @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ (V0 @ V3)) @ ((V1 @ V3) @ (V2 @ V3)))))))))))))
(TCONTINUOUS_INV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ ((co @ clift) @ V0)) @ V1)) @ (c~ @ ((c= @ (V0 @ (cnetlimit @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((ccontinuous @ ((co @ clift) @ ((co @ creal_inv) @ V0))) @ V1)))))))
(TCONTINUOUS_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ ((co @ clift) @ V0)) @ V2)) @ ((ccontinuous @ V1) @ V2))) @ ((ccontinuous @ (^[V3]: ((c% @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TCONTINUOUS_VMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ccontinuous @ ((co @ clift) @ V0)) @ V2)) @ ((ccontinuous @ (^[V3]: ((c% @ (V0 @ V3)) @ V1))) @ V2)))))))))
(TUNIFORMLY_CONTINUOUS_ON_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cuniformly_continuous_on @ (V1 @ V3)) @ V2)))))) @ ((cuniformly_continuous_on @ (^[V3]: ((cvsum @ V0) @ (^[V4]: ((V1 @ V4) @ V3))))) @ V2)))))))))
(TCONTINUOUS_ON_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((ccontinuous_on @ (V1 @ V3)) @ V2)))))) @ ((ccontinuous_on @ (^[V3]: ((cvsum @ V0) @ (^[V4]: ((V1 @ V4) @ V3))))) @ V2)))))))))
(TCONTINUOUS_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((ccontinuous @ (V1 @ V3)) @ V2)))))) @ ((ccontinuous @ (^[V3]: ((cvsum @ V0) @ (^[V4]: ((V1 @ V4) @ V3))))) @ V2)))))))))
(TCONTINUOUS_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V0) @ V2)) @ ((ccontinuous @ V1) @ V2))) @ ((ccontinuous @ (^[V3]: ((cvector_sub @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TCONTINUOUS_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V0) @ V2)) @ ((ccontinuous @ V1) @ V2))) @ ((ccontinuous @ (^[V3]: ((cvector_add @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TCONTINUOUS_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((ccontinuous @ V0) @ V1)) @ ((ccontinuous @ (^[V2]: (cvector_neg @ (V0 @ V2)))) @ V1)))))))
(TLIM_CONTINUOUS_FUNCTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V1) @ (cat @ V2))) @ (((c--> @ V0) @ V2) @ V3))) @ (((c--> @ (^[V4]: (V1 @ (V0 @ V4)))) @ (V1 @ V2)) @ V3)))))))))))
(TCONTINUOUS_TRIVIAL_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (ctrivial_limit @ V1)) @ ((ccontinuous @ V0) @ V1)))))))
(Tcontinuous,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous @ V0) @ V1)) @ (((c--> @ V0) @ (V0 @ (cnetlimit @ V1))) @ V1)))))))
(TMAP_REVERSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cREVERSE @ ((cMAP @ V0) @ V1))) @ ((cMAP @ V0) @ (cREVERSE @ V1))))))))
(TEL_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c< @ V1) @ (cLENGTH @ V2))) @ ((c= @ ((cEL @ V1) @ ((cMAP @ V0) @ V2))) @ (V0 @ ((cEL @ V1) @ V2)))))))))))
(TMAP_EQ_NIL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cMAP @ V0) @ V1)) @ cNIL)) @ ((c= @ V1) @ cNIL)))))))
(TLENGTH_MAP2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (cLENGTH @ V1)) @ (cLENGTH @ V2))) @ ((c= @ (cLENGTH @ (((cMAP2 @ V0) @ V1) @ V2))) @ (cLENGTH @ V2))))))))))
(TALL2_ALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cALL2 @ V0) @ V1) @ V1)) @ ((cALL @ (^[V2]: ((V0 @ V2) @ V2))) @ V1)))))))
(TAND_ALL2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c/__caret__ @ (((cALL2 @ V0) @ V2) @ V3)) @ (((cALL2 @ V1) @ V2) @ V3))) @ (((cALL2 @ (^[V4]: (^[V5]: ((c/__caret__ @ ((V0 @ V4) @ V5)) @ ((V1 @ V4) @ V5))))) @ V2) @ V3)))))))))))
(TBOUNDED_SUMS_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cbounded @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ V0)) @ (V1 @ V4)))))))) @ (cbounded @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ V0)) @ (V2 @ V4))))))))) @ (cbounded @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cIN @ V4) @ V0)) @ ((cvector_add @ (V1 @ V4)) @ (V2 @ V4))))))))))))))))
(TALL2_MAP2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((cALL2 @ V0) @ ((cMAP @ V1) @ V3)) @ ((cMAP @ V2) @ V4))) @ (((cALL2 @ (^[V5]: (^[V6]: ((V0 @ (V1 @ V5)) @ (V2 @ V6))))) @ V3) @ V4)))))))))))))
(TALL_EL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ ((c< @ V2) @ (cLENGTH @ V1))) @ (V0 @ ((cEL @ V2) @ V1)))))) @ ((cALL @ V0) @ V1)))))))
(TEX_MEM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c/__caret__ @ (V0 @ V2)) @ ((cMEM @ V2) @ V1))))) @ ((cEX @ V0) @ V1)))))))
(TMEM_FILTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMEM @ V1) @ ((cFILTER @ V0) @ V2))) @ ((c/__caret__ @ (V0 @ V1)) @ ((cMEM @ V1) @ V2))))))))))
(TFILTER_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cFILTER @ V0) @ ((cMAP @ V1) @ V2))) @ ((cMAP @ V1) @ ((cFILTER @ ((co @ V0) @ V1)) @ V2))))))))))
(TLIM_TRANSFORM_EVENTUALLY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ceventually @ (^[V4]: ((c= @ (V0 @ V4)) @ (V1 @ V4)))) @ V3)) @ (((c--> @ V0) @ V2) @ V3))) @ (((c--> @ V1) @ V2) @ V3)))))))))))
(TLIM_TRANSFORM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((c--> @ (^[V4]: ((cvector_sub @ (V0 @ V4)) @ (V1 @ V4)))) @ (cvec @ (cNUMERAL @ c_0))) @ V3)) @ (((c--> @ V0) @ V2) @ V3))) @ (((c--> @ V1) @ V2) @ V3)))))))))))
(TFORALL_ALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((cALL @ (V0 @ V2)) @ V1)))) @ ((cALL @ (^[V2]: (c! @ (^[V3]: ((V0 @ V3) @ V2))))) @ V1)))))))
(TEXISTS_EX,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((cEX @ (V0 @ V2)) @ V1)))) @ ((cEX @ (^[V2]: (c? @ (^[V3]: ((V0 @ V3) @ V2))))) @ V1)))))))
(TEX_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cEX @ V0) @ ((cMAP @ V1) @ V2))) @ ((cEX @ ((co @ V0) @ V1)) @ V2)))))))))
(TALL_MEM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ ((cMEM @ V2) @ V1)) @ (V0 @ V2))))) @ ((cALL @ V0) @ V1)))))))
(TEX_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cMEM @ V3) @ V2)) @ (V0 @ V3))) @ (V1 @ V3))))) @ ((cEX @ V0) @ V2))) @ ((cEX @ V1) @ V2)))))))))
(TLIM_TRANSFORM_BOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ceventually @ (^[V3]: ((creal_le @ (cvector_norm @ (V1 @ V3))) @ (cvector_norm @ (V0 @ V3))))) @ V2)) @ (((c--> @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ V2))) @ (((c--> @ V1) @ (cvec @ (cNUMERAL @ c_0))) @ V2)))))))))
(TLIM_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((c--> @ V0) @ V1) @ V3)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV))))) @ (((c--> @ (^[V4]: (clift @ ((c$ @ (V0 @ V4)) @ V2)))) @ (clift @ ((c$ @ V1) @ V2))) @ V3)))))))))))
(TLIM_NULL_COMPARISON,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ceventually @ (^[V3]: ((creal_le @ (cvector_norm @ (V1 @ V3))) @ (V0 @ V3)))) @ V2)) @ (((c--> @ (^[V3]: (clift @ (V0 @ V3)))) @ (cvec @ (cNUMERAL @ c_0))) @ V2))) @ (((c--> @ V1) @ (cvec @ (cNUMERAL @ c_0))) @ V2)))))))))
(TAND_ALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ ((cALL @ V0) @ V2)) @ ((cALL @ V1) @ V2))) @ ((cALL @ (^[V3]: ((c/__caret__ @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)))))))))
(TLIM_NULL_NORM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((c--> @ V0) @ (cvec @ (cNUMERAL @ c_0))) @ V1)) @ (((c--> @ (^[V2]: (clift @ (cvector_norm @ (V0 @ V2))))) @ (cvec @ (cNUMERAL @ c_0))) @ V1)))))))
(TLIM_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c--> @ V0) @ V1) @ V2)) @ (((c--> @ (^[V3]: ((cvector_sub @ (V0 @ V3)) @ V1))) @ (cvec @ (cNUMERAL @ c_0))) @ V2)))))))))
(TALL_MP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cALL @ (^[V3]: ((c==> @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((cALL @ V0) @ V2))) @ ((cALL @ V1) @ V2)))))))))
(TLIM_NEG_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c--> @ (^[V3]: (cvector_neg @ (V0 @ V3)))) @ (cvector_neg @ V1)) @ V2)) @ (((c--> @ V0) @ V1) @ V2)))))))))
(TLIM_NEG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((c--> @ V0) @ V1) @ V2)) @ (((c--> @ (^[V3]: (cvector_neg @ (V0 @ V3)))) @ (cvector_neg @ V1)) @ V2)))))))))
(TLIM_CMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (((c--> @ V0) @ V2) @ V3)) @ (((c--> @ (^[V4]: ((c% @ V1) @ (V0 @ V4)))) @ ((c% @ V1) @ V2)) @ V3)))))))))))
(TALL2_AND_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((cALL2 @ (^[V4]: (^[V5]: ((c/__caret__ @ (V0 @ V4)) @ ((V1 @ V4) @ V5))))) @ V2) @ V3)) @ ((c/__caret__ @ ((cALL @ V0) @ V2)) @ (((cALL2 @ V1) @ V2) @ V3))))))))))))
(TMAP_EQ_DEGEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cALL @ (^[V2]: ((c= @ (V0 @ V2)) @ V2))) @ V1)) @ ((c= @ ((cMAP @ V0) @ V1)) @ V1)))))))
(TALL2_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cALL2 @ V0) @ ((cMAP @ V1) @ V2)) @ V2)) @ ((cALL @ (^[V3]: ((V0 @ (V1 @ V3)) @ V3))) @ V2)))))))))
(TLIM_EVENTUALLY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((ceventually @ (^[V3]: ((c= @ (V0 @ V3)) @ V1))) @ V2)) @ (((c--> @ V0) @ V1) @ V2)))))))))
(Tlim,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((clim @ V1) @ V0)) @ (c__at__ @ (^[V2]: (((c--> @ V0) @ V2) @ V1)))))))))
(Ttendsto,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c--> @ V0) @ V1) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((ceventually @ (^[V4]: ((creal_lt @ (cdistance @ ((c__comma__ @ (V0 @ V4)) @ V1))) @ V3))) @ V2))))))))))))
(TALL_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cALL @ V0) @ ((cMAP @ V1) @ V2))) @ ((cALL @ ((co @ V0) @ V1)) @ V2)))))))))
(TNOT_EVENTUALLY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c~ @ (V0 @ V2))))) @ (c~ @ (ctrivial_limit @ V1)))) @ (c~ @ ((ceventually @ V0) @ V1))))))))
(TALWAYS_EVENTUALLY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (V0 @ V2)))) @ ((ceventually @ V0) @ V1)))))))
(TNOT_ALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((cALL @ V0) @ V1))) @ ((cEX @ (^[V2]: (c~ @ (V0 @ V2)))) @ V1)))))))
(TNOT_EX,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((cEX @ V0) @ V1))) @ ((cALL @ (^[V2]: (c~ @ (V0 @ V2)))) @ V1)))))))
(TALL_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cMEM @ V3) @ V2)) @ (V0 @ V3))) @ (V1 @ V3))))) @ ((cALL @ V0) @ V2))) @ ((cALL @ V1) @ V2)))))))))
(TMAP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cALL @ (^[V3]: ((c= @ (V0 @ V3)) @ (V1 @ V3)))) @ V2)) @ ((c= @ ((cMAP @ V0) @ V2)) @ ((cMAP @ V1) @ V2))))))))))
(TITLIST2_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((((cITLIST2 @ V0) @ cNIL) @ cNIL) @ V1)) @ V1))))))
(TITLIST2_DEF_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((((cITLIST2 @ V0) @ cNIL) @ V1) @ V2)) @ V2))))))))
(TFILTER_conjunct0,(c! @ (^[V0]: ((c= @ ((cFILTER @ V0) @ cNIL)) @ cNIL))))
(TMAP2_conjunct0,(c! @ (^[V0]: ((c= @ (((cMAP2 @ V0) @ cNIL) @ cNIL)) @ cNIL))))
(TMAP2_DEF_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cMAP2 @ V0) @ cNIL) @ V1)) @ cNIL))))))
(TALL2_conjunct0,(c! @ (^[V0]: ((c= @ (((cALL2 @ V0) @ cNIL) @ cNIL)) @ cT))))
(TALL2_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cALL2 @ V0) @ ((cCONS @ V1) @ V2)) @ cNIL)) @ cF))))))))
(TALL2_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cALL2 @ V0) @ cNIL) @ ((cCONS @ V1) @ V2))) @ cF))))))))
(TALL2_DEF_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cALL2 @ V0) @ cNIL) @ V1)) @ ((c= @ V1) @ cNIL)))))))
(TITLIST_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cITLIST @ V0) @ cNIL) @ V1)) @ V1))))))
(TEX_conjunct0,(c! @ (^[V0]: ((c= @ ((cEX @ V0) @ cNIL)) @ cF))))
(TALL_conjunct0,(c! @ (^[V0]: ((c= @ ((cALL @ V0) @ cNIL)) @ cT))))
(TCLOSED_IN_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cclosed_in @ V1) @ V0)) @ ((cSUBSET @ V0) @ (ctopspace @ V1))))))))
(TOPEN_IN_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((copen_in @ V1) @ V0)) @ ((cSUBSET @ V0) @ (ctopspace @ V1))))))))
(TISO_USAGE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cISO @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: (V2 @ V3)))) @ (c? @ (^[V3]: (V2 @ (V1 @ V3)))))))))))))
(TISO_USAGE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cISO @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: (V2 @ V3)))) @ (c! @ (^[V3]: (V2 @ (V1 @ V3)))))))))))))
(TISO_USAGE_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cISO @ V1) @ V0)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ V2) @ (V0 @ V3))) @ ((c= @ (V1 @ V2)) @ V3))))))))))))
(TINTEGER_SIGN,(c! @ (^[V0]: (cinteger @ (csign @ V0)))))
(TINTEGER_PRODUCT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (cinteger @ (V1 @ V2)))))) @ (cinteger @ ((cproduct @ V0) @ V1))))))))
(TDET_LINEAR_ROW_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV))))) @ ((c= @ (cdet @ (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V1)) @ ((cvsum @ V0) @ V2)) @ (V3 @ V4)))))) @ ((csum @ V0) @ (^[V4]: (cdet @ (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V1)) @ (V2 @ V4)) @ (V3 @ V5))))))))))))))))))
(TREAL_MUL_SUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1))) @ ((c= @ ((creal_mul @ ((csum @ V0) @ V2)) @ ((csum @ V1) @ V3))) @ ((csum @ V0) @ (^[V4]: ((csum @ V1) @ (^[V5]: ((creal_mul @ (V2 @ V4)) @ (V3 @ V5)))))))))))))))))
(TPRODUCT_PERMUTE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cpermutes @ V2) @ V0)) @ ((c= @ ((cproduct @ V0) @ V1)) @ ((cproduct @ V0) @ ((co @ V1) @ V2)))))))))))
(TISOMORPHISM_EXPAND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((c= @ ((co @ V1) @ V0)) @ cI)) @ ((c= @ ((co @ V0) @ V1)) @ cI))) @ ((c/__caret__ @ (c! @ (^[V2]: ((c= @ (V1 @ (V0 @ V2))) @ V2)))) @ (c! @ (^[V2]: ((c= @ (V0 @ (V1 @ V2))) @ V2))))))))))
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(TSUBSPACE_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (csubspace @ V2)) @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V0)) @ ((cIN @ (V1 @ V3)) @ V2))))))) @ ((cIN @ ((cvsum @ V0) @ V1)) @ V2)))))))))
(TPASTECART_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cpastecart @ ((cvsum @ V0) @ V1)) @ ((cvsum @ V0) @ V2))) @ ((cvsum @ V0) @ (^[V3]: ((cpastecart @ (V1 @ V3)) @ (V2 @ V3)))))))))))))
(TSNDCART_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (csndcart @ ((cvsum @ V0) @ V1))) @ ((cvsum @ V0) @ (^[V2]: (csndcart @ (V1 @ V2)))))))))))
(TFSTCART_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ (cfstcart @ ((cvsum @ V0) @ V1))) @ ((cvsum @ V0) @ (^[V2]: (cfstcart @ (V1 @ V2)))))))))))
(TDROP_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdrop @ ((cvsum @ V0) @ V1))) @ ((csum @ V0) @ ((co @ cdrop) @ V1))))))))
(TLIFT_SUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (clift @ ((csum @ V0) @ V1))) @ ((cvsum @ V0) @ ((co @ clift) @ V1))))))))
(TVSUM_REAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ V0) @ V1)) @ (clift @ ((csum @ V0) @ ((co @ cdrop) @ V1)))))))))
(TSUM_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((csum @ V0) @ V1)) @ (cdrop @ ((cvsum @ V0) @ ((co @ clift) @ V1)))))))))
(TBILINEAR_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cbilinear @ V2)) @ ((c/__caret__ @ (cFINITE @ V0)) @ (cFINITE @ V1)))) @ ((c= @ ((V2 @ ((cvsum @ V0) @ V3)) @ ((cvsum @ V1) @ V4))) @ ((cvsum @ ((cCROSS @ V0) @ V1)) @ (cGABS @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((cGEQ @ (V5 @ ((c__comma__ @ V6) @ V7))) @ ((V2 @ (V3 @ V6)) @ (V4 @ V7)))))))))))))))))))))))
(TMEASURE,(c! @ (^[V0]: ((c= @ (cMEASURE @ V0)) @ (^[V1]: (^[V2]: ((c< @ (V0 @ V1)) @ (V0 @ V2))))))))
(TLINEAR_VSUM_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (clinear @ V2)) @ (cFINITE @ V0))) @ ((c= @ (V2 @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V1 @ V4)) @ (V3 @ V4)))))) @ ((cvsum @ V0) @ (^[V4]: ((c% @ (V1 @ V4)) @ (V2 @ (V3 @ V4))))))))))))))))
(TLINEAR_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ (cFINITE @ V0))) @ ((c= @ (V1 @ ((cvsum @ V0) @ V2))) @ ((cvsum @ V0) @ ((co @ V1) @ V2)))))))))))
(TLINEAR_COMPOSE_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ (clinear @ (V1 @ V2))))))) @ (clinear @ (^[V2]: ((cvsum @ V0) @ (^[V3]: ((V1 @ V3) @ V2)))))))))))
(TVSUM_CASES_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cIN @ V3) @ V0))) @ ((c= @ ((cvsum @ V0) @ (^[V4]: (((cCOND @ ((c= @ V4) @ V3)) @ V1) @ (V2 @ V4))))) @ ((cvector_add @ ((cvsum @ V0) @ V2)) @ ((cvector_sub @ V1) @ (V2 @ V3))))))))))))))
(TVSUM_ADD_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (c~ @ ((c= @ (V0 @ V4)) @ (cvec @ (cNUMERAL @ c_0)))))) @ V4))))))) @ (cFINITE @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ (c~ @ ((c= @ (V2 @ V4)) @ (cvec @ (cNUMERAL @ c_0)))))) @ V4)))))))) @ ((c= @ ((cvsum @ V1) @ (^[V3]: ((cvector_add @ (V0 @ V3)) @ (V2 @ V3))))) @ ((cvector_add @ ((cvsum @ V1) @ V0)) @ ((cvsum @ V1) @ V2)))))))))))
(TVSUM_SWAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (cFINITE @ V0))) @ ((c= @ ((cvsum @ V1) @ (^[V3]: ((cvsum @ V0) @ (V2 @ V3))))) @ ((cvsum @ V0) @ (^[V3]: ((cvsum @ V1) @ (^[V4]: ((V2 @ V4) @ V3))))))))))))))
(TVSUM_INJECTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((cIN @ (V0 @ V3)) @ V1))))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c= @ (V0 @ V3)) @ (V0 @ V4))))) @ ((c= @ V3) @ V4))))))))) @ ((c= @ ((cvsum @ V1) @ ((co @ V2) @ V0))) @ ((cvsum @ V1) @ V2))))))))))
(TDOT_RSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cdot @ V1) @ ((cvsum @ V0) @ V2))) @ ((csum @ V0) @ (^[V3]: ((cdot @ V1) @ (V2 @ V3)))))))))))))
(TDOT_LSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cdot @ ((cvsum @ V0) @ V1)) @ V2)) @ ((csum @ V0) @ (^[V3]: ((cdot @ (V1 @ V3)) @ V2))))))))))))
(TVSUM_UNION_NONZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cINTER @ V0) @ V1))) @ ((c= @ (V2 @ V3)) @ (cvec @ (cNUMERAL @ c_0))))))))) @ ((c= @ ((cvsum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cvector_add @ ((cvsum @ V0) @ V2)) @ ((cvsum @ V1) @ V2)))))))))))
(TVSUM_VMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c% @ ((csum @ V0) @ V1)) @ V2)) @ ((cvsum @ V0) @ (^[V3]: ((c% @ (V1 @ V3)) @ V2)))))))))))
(TVSUM_NORM_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((creal_le @ ((csum @ V0) @ (^[V3]: (cvector_norm @ (V1 @ V3))))) @ V2))) @ ((creal_le @ (cvector_norm @ ((cvsum @ V0) @ V1))) @ V2)))))))))
(TVSUM_NORM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((creal_le @ (cvector_norm @ ((cvsum @ V0) @ V1))) @ ((csum @ V0) @ (^[V2]: (cvector_norm @ (V1 @ V2)))))))))))
(TVSUM_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ ((cINSERT @ V1) @ cEMPTY)) @ V0)) @ (V0 @ V1)))))))
(TVSUM_RESTRICT_SET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvsum @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ (V1 @ V4))) @ V4)))))) @ V2)) @ ((cvsum @ V0) @ (^[V3]: (((cCOND @ (V1 @ V3)) @ (V2 @ V3)) @ (cvec @ (cNUMERAL @ c_0)))))))))))))
(TVSUM_RESTRICT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ V0) @ (^[V2]: (((cCOND @ ((cIN @ V2) @ V0)) @ (V1 @ V2)) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((cvsum @ V0) @ V1)))))))
(TVSUM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3)))))) @ ((c= @ ((cvsum @ V1) @ V0)) @ ((cvsum @ V1) @ V2))))))))))
(TVSUM_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvsum @ V0) @ (^[V2]: (cvector_neg @ (V1 @ V2))))) @ (cvector_neg @ ((cvsum @ V0) @ V1))))))))
(TVSUM_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cIN @ V2) @ V0))) @ ((c= @ ((cvsum @ ((cDELETE @ V0) @ V2)) @ V1)) @ ((cvector_sub @ ((cvsum @ V0) @ V1)) @ (V1 @ V2)))))))))))
(TVSUM_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((cSUBSET @ V1) @ V0))) @ ((c= @ ((cvsum @ ((cDIFF @ V0) @ V1)) @ V2)) @ ((cvector_sub @ ((cvsum @ V0) @ V2)) @ ((cvsum @ V1) @ V2)))))))))))
(TVSUM_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cDISJOINT @ V0) @ V1)))) @ ((c= @ ((cvsum @ ((cUNION @ V0) @ V1)) @ V2)) @ ((cvector_add @ ((cvsum @ V0) @ V2)) @ ((cvsum @ V1) @ V2)))))))))))
(TVSUM_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((cvsum @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((cvsum @ V0) @ ((co @ V1) @ V2)))))))))))
(TVSUM_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cvsum @ V0) @ (^[V2]: V1))) @ ((c% @ (creal_of_num @ (cCARD @ V0))) @ V1))))))))
(TVSUM_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cvsum @ V1) @ (^[V3]: ((cvector_sub @ (V0 @ V3)) @ (V2 @ V3))))) @ ((cvector_sub @ ((cvsum @ V1) @ V0)) @ ((cvsum @ V1) @ V2)))))))))))
(TVSUM_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cvsum @ V1) @ (^[V3]: ((cvector_add @ (V0 @ V3)) @ (V2 @ V3))))) @ ((cvector_add @ ((cvsum @ V1) @ V0)) @ ((cvsum @ V1) @ V2)))))))))))
(TVSUM_RMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvsum @ V0) @ (^[V3]: ((c% @ (V1 @ V3)) @ V2)))) @ ((c% @ ((csum @ V0) @ V1)) @ V2)))))))))
(TVSUM_0,(c! @ (^[V0]: ((c= @ ((cvsum @ V0) @ (^[V1]: (cvec @ (cNUMERAL @ c_0))))) @ (cvec @ (cNUMERAL @ c_0))))))
(TVSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cvsum @ V0) @ V1)) @ (((citerate @ cvector_add) @ V0) @ V1))))))))
(TVSUM_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((cvsum @ cEMPTY) @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))
(THULLS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ (V1 @ V4))))) @ (V1 @ (cINTERS @ V3)))))) @ ((c/__caret__ @ ((cSUBSET @ V0) @ ((chull @ V1) @ V2))) @ ((cSUBSET @ V2) @ ((chull @ V1) @ V0))))) @ ((c= @ ((chull @ V1) @ V0)) @ ((chull @ V1) @ V2))))))))))
(TIS_HULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ (V1 @ V3))))) @ (V1 @ (cINTERS @ V2)))))) @ ((c= @ (V1 @ V0)) @ (c? @ (^[V2]: ((c= @ V0) @ ((chull @ V1) @ V2)))))))))))
(THULL_IMAGE_GALOIS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (V2 @ ((chull @ V2) @ V4))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ (V2 @ V4)) @ (V2 @ ((cIMAGE @ V1) @ V4)))))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ (V2 @ V4)) @ (V2 @ ((cIMAGE @ V0) @ V4)))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c= @ ((cSUBSET @ V4) @ ((cIMAGE @ V0) @ V5))) @ ((cSUBSET @ ((cIMAGE @ V1) @ V4)) @ V5)))))))))) @ ((c= @ ((chull @ V2) @ ((cIMAGE @ V1) @ V3))) @ ((cIMAGE @ V1) @ ((chull @ V2) @ V3)))))))))))))
(THULL_IMAGE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V1 @ ((chull @ V1) @ V2))) @ (c! @ (^[V3]: ((c==> @ (V1 @ V3)) @ (V1 @ ((cIMAGE @ V0) @ V3))))))) @ ((cSUBSET @ ((chull @ V1) @ ((cIMAGE @ V0) @ V2))) @ ((cIMAGE @ V0) @ ((chull @ V1) @ V2)))))))))))
(THULL_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chull @ V1) @ ((cUNION @ V0) @ V2))) @ ((chull @ V1) @ ((cUNION @ ((chull @ V1) @ V0)) @ ((chull @ V1) @ V2)))))))))))
(THULL_MONO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V0) @ V2)) @ ((cSUBSET @ ((chull @ V1) @ V0)) @ ((chull @ V1) @ V2))))))))))
(TLAMBDA_PAIR,(c! @ (^[V0]: ((c= @ (cGABS @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((cGEQ @ (V1 @ ((c__comma__ @ V2) @ V3))) @ ((V0 @ V2) @ V3))))))))) @ (^[V1]: ((V0 @ (cFST @ V1)) @ (cSND @ V1)))))))
(TAPPROACHABLE_LT_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (V0 @ V3)) @ V2)) @ (V1 @ V3)))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((creal_le @ (V0 @ V3)) @ V2)) @ (V1 @ V3)))))))))))))
(TPRODUCT_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cproduct @ V0) @ (^[V2]: (creal_abs @ (V1 @ V2))))) @ (creal_abs @ ((cproduct @ V0) @ V1)))))))))
(TPRODUCT_LE_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V2))) @ ((creal_le @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))) @ ((creal_le @ ((cproduct @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TPRODUCT_ONE,(c! @ (^[V0]: ((c= @ ((cproduct @ V0) @ (^[V1]: (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TPRODUCT_DIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cproduct @ V1) @ (^[V3]: ((creal_div @ (V0 @ V3)) @ (V2 @ V3))))) @ ((creal_div @ ((cproduct @ V1) @ V0)) @ ((cproduct @ V1) @ V2)))))))))))
(TPRODUCT_INV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((cproduct @ V0) @ (^[V2]: (creal_inv @ (V1 @ V2))))) @ (creal_inv @ ((cproduct @ V0) @ V1)))))))))
(TPRODUCT_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cproduct @ V1) @ (^[V3]: ((creal_mul @ (V0 @ V3)) @ (V2 @ V3))))) @ ((creal_mul @ ((cproduct @ V1) @ V0)) @ ((cproduct @ V1) @ V2)))))))))))
(TPRODUCT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V0 @ V3))) @ ((creal_le @ (V0 @ V3)) @ (V2 @ V3)))))))) @ ((creal_le @ ((cproduct @ V1) @ V0)) @ ((cproduct @ V1) @ V2))))))))))
(TPRODUCT_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((c= @ ((cproduct @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))
(TPRODUCT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V0 @ V3)) @ (V2 @ V3)))))) @ ((c= @ ((cproduct @ V1) @ V0)) @ ((cproduct @ V1) @ V2))))))))))
(TPRODUCT_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cproduct @ ((cINSERT @ V1) @ cEMPTY)) @ V0)) @ (V0 @ V1)))))))
(TPRODUCT_POS_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V2))))))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cproduct @ V0) @ V1))))))))
(TPRODUCT_POS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V2))))))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cproduct @ V0) @ V1))))))))
(TPRODUCT_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ ((c= @ ((cproduct @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((cproduct @ V0) @ ((co @ V1) @ V2)))))))))))
(TPRODUCT_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cDISJOINT @ V0) @ V1)))) @ ((c= @ ((cproduct @ ((cUNION @ V0) @ V1)) @ V2)) @ ((creal_mul @ ((cproduct @ V0) @ V2)) @ ((cproduct @ V1) @ V2)))))))))))
(TPRODUCT_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((cproduct @ cEMPTY) @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TNPRODUCT_ONE,(c! @ (^[V0]: ((c= @ ((cnproduct @ V0) @ (^[V1]: (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TNPRODUCT_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cnproduct @ V1) @ (^[V3]: ((c* @ (V0 @ V3)) @ (V2 @ V3))))) @ ((c* @ ((cnproduct @ V1) @ V0)) @ ((cnproduct @ V1) @ V2)))))))))))
(TNPRODUCT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ c_0)) @ (V0 @ V3))) @ ((c<= @ (V0 @ V3)) @ (V2 @ V3)))))))) @ ((c<= @ ((cnproduct @ V1) @ V0)) @ ((cnproduct @ V1) @ V2))))))))))
(TNPRODUCT_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V0)) @ ((c= @ ((c= @ ((cnproduct @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V0)) @ ((c= @ (V1 @ V2)) @ (cNUMERAL @ c_0))))))))))))
(TNPRODUCT_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cnproduct @ ((cINSERT @ V1) @ cEMPTY)) @ V0)) @ (V0 @ V1)))))))
(TNPRODUCT_POS_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V0)) @ ((c< @ (cNUMERAL @ c_0)) @ (V1 @ V2))))))) @ ((c< @ (cNUMERAL @ c_0)) @ ((cnproduct @ V0) @ V1))))))))
(TNPRODUCT_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V0)) @ ((c/__caret__ @ ((cIN @ V4) @ V0)) @ ((c= @ (V2 @ V3)) @ (V2 @ V4))))) @ ((c= @ V3) @ V4))))))) @ ((c= @ ((cnproduct @ ((cIMAGE @ V2) @ V0)) @ V1)) @ ((cnproduct @ V0) @ ((co @ V1) @ V2)))))))))))
(TNPRODUCT_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V0)) @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cDISJOINT @ V0) @ V1)))) @ ((c= @ ((cnproduct @ ((cUNION @ V0) @ V1)) @ V2)) @ ((c* @ ((cnproduct @ V0) @ V2)) @ ((cnproduct @ V1) @ V2)))))))))))
(TREAL_ABS_SIGN,(c! @ (^[V0]: ((c= @ (creal_abs @ (csign @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TSIGN_IDEMPOTENT,(c! @ (^[V0]: ((c= @ ((creal_mul @ (csign @ V0)) @ (csign @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TSIGN_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpermutation @ V0)) @ (cpermutation @ V1))) @ ((c= @ (csign @ ((co @ V0) @ V1))) @ ((creal_mul @ (csign @ V0)) @ (csign @ V1)))))))))
(TSIGN_INVERSE,(c! @ (^[V0]: ((c==> @ (cpermutation @ V0)) @ ((c= @ (csign @ (cinverse @ V0))) @ (csign @ V0))))))
(TSIGN_NZ,(c! @ (^[V0]: (c~ @ ((c= @ (csign @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(Tsign,(c! @ (^[V0]: ((c= @ (csign @ V0)) @ (((cCOND @ (cevenperm @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TFORALL_UNWIND_THM1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ ((c= @ V1) @ V2)) @ (V0 @ V2))))) @ (V0 @ V1)))))))
(TPERMUTATION_INVERSE_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpermutation @ V1)) @ (cpermutation @ V0))) @ ((c= @ (cinverse @ ((co @ V1) @ V0))) @ ((co @ (cinverse @ V0)) @ (cinverse @ V1)))))))))
(TPERMUTATION_INVERSE_WORKS_conjunct0,(c! @ (^[V0]: ((c==> @ (cpermutation @ V0)) @ ((c= @ ((co @ (cinverse @ V0)) @ V0)) @ cI)))))
(TPERMUTATION_INVERSE_WORKS_conjunct1,(c! @ (^[V0]: ((c==> @ (cpermutation @ V0)) @ ((c= @ ((co @ V0) @ (cinverse @ V0))) @ cI)))))
(TPERMUTATION_BIJECTIVE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cpermutation @ V0)) @ (c?! @ (^[V2]: ((c= @ (V0 @ V2)) @ V1)))))))))
(TEVENPERM_INVERSE,(c! @ (^[V0]: ((c==> @ (cpermutation @ V0)) @ ((c= @ (cevenperm @ (cinverse @ V0))) @ (cevenperm @ V0))))))
(TEVENPERM_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpermutation @ V0)) @ (cpermutation @ V1))) @ ((c= @ (cevenperm @ ((co @ V0) @ V1))) @ ((c= @ (cevenperm @ V0)) @ (cevenperm @ V1)))))))))
(Tevenperm,(c! @ (^[V0]: ((c= @ (cevenperm @ V0)) @ (cEVEN @ (c__at__ @ (^[V1]: ((cswapseq @ V1) @ V0))))))))
(TPERMUTATION_INVERSE,(c! @ (^[V0]: ((c==> @ (cpermutation @ V0)) @ (cpermutation @ (cinverse @ V0))))))
(TPERMUTATION_COMPOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpermutation @ V0)) @ (cpermutation @ V1))) @ (cpermutation @ ((co @ V0) @ V1))))))))
(Tpermutation,(c! @ (^[V0]: ((c= @ (cpermutation @ V0)) @ (c? @ (^[V1]: ((cswapseq @ V1) @ V0)))))))
(TSUM_PERMUTE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cpermutes @ V2) @ V0)) @ ((c= @ ((csum @ V0) @ V1)) @ ((csum @ V0) @ ((co @ V1) @ V2)))))))))))
(TNSUM_PERMUTE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cpermutes @ V2) @ V0)) @ ((c= @ ((cnsum @ V0) @ V1)) @ ((cnsum @ V0) @ ((co @ V1) @ V2)))))))))))
(TITERATE_PERMUTE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V0)) @ ((c==> @ ((cpermutes @ V3) @ V1)) @ ((c= @ (((citerate @ V0) @ V1) @ V2)) @ (((citerate @ V0) @ V1) @ ((co @ V2) @ V3))))))))))))))
(Tfinite_sum_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (cmk_finite_sum @ (cdest_finite_sum @ V0))) @ V0))))
(Tfinite_image_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (cfinite_index @ (cdest_finite_image @ V0))) @ V0))))
(TFINITE_INDEX_WORKS,(c! @ (^[V0]: (c?! @ (^[V1]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c= @ (cfinite_index @ V1)) @ V0))))))))
(TRADICALS_EMPTY_RATIONAL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cwellformed @ V0)) @ ((c= @ (cradicals @ V0)) @ cEMPTY))) @ (crational @ (cvalue @ V0))))))
(TRADICAL_CANONICAL,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (cwellformed @ V0)) @ (c~ @ ((c= @ (cradicals @ V0)) @ cEMPTY)))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ (cradicals @ V0))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (cwellformed @ ((cAddition @ V2) @ ((cMultiplication @ V3) @ (cSqrt @ V1))))) @ ((c/__caret__ @ ((c= @ (cvalue @ V0)) @ (cvalue @ ((cAddition @ V2) @ ((cMultiplication @ V3) @ (cSqrt @ V1)))))) @ ((c/__caret__ @ ((cSUBSET @ (cradicals @ V2)) @ ((cDELETE @ (cradicals @ V0)) @ V1))) @ ((c/__caret__ @ ((cSUBSET @ (cradicals @ V3)) @ ((cDELETE @ (cradicals @ V0)) @ V1))) @ ((cSUBSET @ (cradicals @ V1)) @ ((cDELETE @ (cradicals @ V0)) @ V1)))))))))))))))))
(TRADICAL_TOP,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cradicals @ V0)) @ cEMPTY))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V1) @ (cradicals @ V0))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (cradicals @ V0))) @ (c~ @ ((cIN @ V1) @ (cradicals @ V2)))))))))))))
(Tvalue_conjunct5,(c! @ (^[V0]: ((c= @ (cvalue @ (cSqrt @ V0))) @ (csqrt @ (cvalue @ V0))))))
(Tvalue_conjunct1,(c! @ (^[V0]: ((c= @ (cvalue @ (cNegation @ V0))) @ (creal_neg @ (cvalue @ V0))))))
(Tvalue_conjunct2,(c! @ (^[V0]: ((c= @ (cvalue @ (cInverse @ V0))) @ (creal_inv @ (cvalue @ V0))))))
(Tdepth_conjunct5,(c! @ (^[V0]: ((c= @ (cdepth @ (cSqrt @ V0))) @ ((c+ @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdepth @ V0))))))
(Tdepth_conjunct1,(c! @ (^[V0]: ((c= @ (cdepth @ (cNegation @ V0))) @ (cdepth @ V0)))))
(Tdepth_conjunct2,(c! @ (^[V0]: ((c= @ (cdepth @ (cInverse @ V0))) @ (cdepth @ V0)))))
(Tradicals_conjunct5,(c! @ (^[V0]: ((c= @ (cradicals @ (cSqrt @ V0))) @ ((cINSERT @ V0) @ (cradicals @ V0))))))
(Tradicals_conjunct1,(c! @ (^[V0]: ((c= @ (cradicals @ (cNegation @ V0))) @ (cradicals @ V0)))))
(Tradicals_conjunct2,(c! @ (^[V0]: ((c= @ (cradicals @ (cInverse @ V0))) @ (cradicals @ V0)))))
(Twellformed_conjunct5,(c! @ (^[V0]: ((c= @ (cwellformed @ (cSqrt @ V0))) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cvalue @ V0))) @ (cwellformed @ V0))))))
(Twellformed_conjunct1,(c! @ (^[V0]: ((c= @ (cwellformed @ (cNegation @ V0))) @ (cwellformed @ V0)))))
(Twellformed_conjunct2,(c! @ (^[V0]: ((c= @ (cwellformed @ (cInverse @ V0))) @ ((c/__caret__ @ (c~ @ ((c= @ (cvalue @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ (cwellformed @ V0))))))
(TNOT_IN_OWN_RADICALS,(c! @ (^[V0]: (c~ @ ((cIN @ V0) @ (cradicals @ V0))))))
(TFINITE_RADICALS,(c! @ (^[V0]: (cFINITE @ (cradicals @ V0)))))
(TCUBIC_ROOT_STEP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (crational @ V1)) @ ((c/__caret__ @ (crational @ V2)) @ (crational @ V3)))) @ ((c==> @ ((c/__caret__ @ (cwellformed @ V0)) @ ((c/__caret__ @ (c~ @ ((c= @ (cradicals @ V0)) @ cEMPTY))) @ ((c= @ ((creal_add @ ((creal_pow @ (cvalue @ V0)) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ V1) @ ((creal_pow @ (cvalue @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V2) @ (cvalue @ V0))) @ V3)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ (c? @ (^[V4]: ((c/__caret__ @ (cwellformed @ V4)) @ ((c/__caret__ @ ((cPSUBSET @ (cradicals @ V4)) @ (cradicals @ V0))) @ ((c= @ ((creal_add @ ((creal_pow @ (cvalue @ V4)) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ V1) @ ((creal_pow @ (cvalue @ V4)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ V2) @ (cvalue @ V4))) @ V3)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))))))))
(TRADICALS_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V0) @ (cradicals @ V1))) @ ((cSUBSET @ (cradicals @ V0)) @ (cradicals @ V1))))))))
(TIN_RADICALS_SMALLER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V0) @ (cradicals @ V1))) @ ((c< @ (cdepth @ V0)) @ (cdepth @ V1))))))))
(TRADICAL_CANONICAL_TRIVIAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c==> @ ((cIN @ V1) @ (cradicals @ V0))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (cwellformed @ V2)) @ ((c/__caret__ @ (cwellformed @ V3)) @ ((c/__caret__ @ ((c= @ (cvalue @ V0)) @ ((creal_add @ (cvalue @ V2)) @ ((creal_mul @ (cvalue @ V3)) @ (csqrt @ (cvalue @ V1)))))) @ ((c/__caret__ @ ((cSUBSET @ (cradicals @ V2)) @ ((cDELETE @ (cradicals @ V0)) @ V1))) @ ((c/__caret__ @ ((cSUBSET @ (cradicals @ V3)) @ ((cDELETE @ (cradicals @ V0)) @ V1))) @ ((cSUBSET @ (cradicals @ V1)) @ ((cDELETE @ (cradicals @ V0)) @ V1))))))))))))) @ ((c==> @ (cwellformed @ V0)) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (cwellformed @ V2)) @ ((c/__caret__ @ (cwellformed @ V3)) @ ((c/__caret__ @ ((c= @ (cvalue @ V0)) @ ((creal_add @ (cvalue @ V2)) @ ((creal_mul @ (cvalue @ V3)) @ (csqrt @ (cvalue @ V1)))))) @ ((c/__caret__ @ ((cSUBSET @ (cradicals @ V2)) @ ((cDELETE @ ((cUNION @ (cradicals @ V0)) @ (cradicals @ V1))) @ V1))) @ ((c/__caret__ @ ((cSUBSET @ (cradicals @ V3)) @ ((cDELETE @ ((cUNION @ (cradicals @ V0)) @ (cradicals @ V1))) @ V1))) @ ((cSUBSET @ (cradicals @ V1)) @ ((cDELETE @ ((cUNION @ (cradicals @ V0)) @ (cradicals @ V1))) @ V1))))))))))))))))))
(TWELLFORMED_RADICALS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cwellformed @ V0)) @ ((c==> @ ((cIN @ V1) @ (cradicals @ V0))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cvalue @ V1)))))))))
(TRADICALS_WELLFORMED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cwellformed @ V0)) @ ((c==> @ ((cIN @ V1) @ (cradicals @ V0))) @ (cwellformed @ V1))))))))
(Tvalue_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cvalue @ ((cMultiplication @ V0) @ V1))) @ ((creal_mul @ (cvalue @ V0)) @ (cvalue @ V1))))))))
(Tvalue_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cvalue @ ((cAddition @ V0) @ V1))) @ ((creal_add @ (cvalue @ V0)) @ (cvalue @ V1))))))))
(Tdepth_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdepth @ ((cMultiplication @ V0) @ V1))) @ ((cMAX @ (cdepth @ V0)) @ (cdepth @ V1))))))))
(Tdepth_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdepth @ ((cAddition @ V0) @ V1))) @ ((cMAX @ (cdepth @ V0)) @ (cdepth @ V1))))))))
(Tradicals_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cradicals @ ((cMultiplication @ V0) @ V1))) @ ((cUNION @ (cradicals @ V0)) @ (cradicals @ V1))))))))
(Tradicals_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cradicals @ ((cAddition @ V0) @ V1))) @ ((cUNION @ (cradicals @ V0)) @ (cradicals @ V1))))))))
(Twellformed_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cwellformed @ ((cMultiplication @ V0) @ V1))) @ ((c/__caret__ @ (cwellformed @ V0)) @ (cwellformed @ V1))))))))
(Twellformed_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cwellformed @ ((cAddition @ V0) @ V1))) @ ((c/__caret__ @ (cwellformed @ V0)) @ (cwellformed @ V1))))))))
(TPARDIR_REFL,(c! @ (^[V0]: ((c|| @ V0) @ V0))))
(Tdirection_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (cmk_dir @ (cdest_dir @ V0))) @ V0))))
(TDIRECTION_AXIOM_4_WEAK,(c! @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c|| @ V1) @ V2))) @ ((c/__caret__ @ ((c_|_ @ V1) @ V0)) @ ((c_|_ @ V2) @ V0))))))))))
(TDIRECTION_AXIOM_4,(c! @ (^[V0]: (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (c~ @ ((c|| @ V1) @ V2))) @ ((c/__caret__ @ (c~ @ ((c|| @ V2) @ V3))) @ ((c/__caret__ @ (c~ @ ((c|| @ V1) @ V3))) @ ((c/__caret__ @ ((c_|_ @ V1) @ V0)) @ ((c/__caret__ @ ((c_|_ @ V2) @ V0)) @ ((c_|_ @ V3) @ V0)))))))))))))))
(TDIRECTION_AXIOM_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c|| @ V0) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ ((c_|_ @ V0) @ V2)) @ ((c/__caret__ @ ((c_|_ @ V1) @ V2)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c_|_ @ V0) @ V3)) @ ((c_|_ @ V1) @ V3))) @ ((c|| @ V3) @ V2))))))))))))))
(TPARDIR_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c|| @ V1) @ V0)) @ ((c|| @ V0) @ V1)))))))
(Tpardir,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c|| @ V0) @ V1)) @ ((c= @ ((ccross @ (cdest_dir @ V0)) @ (cdest_dir @ V1))) @ (cvec @ (cNUMERAL @ c_0)))))))))
(Tperpl_th,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c_|_ @ V0) @ V1)) @ ((cperpl @ (cmk_line @ (c|| @ V0))) @ (cmk_line @ (c|| @ V1)))))))))
(Tperpdir,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c_|_ @ V0) @ V1)) @ ((corthogonal @ (cdest_dir @ V0)) @ (cdest_dir @ V1))))))))
(TPARDIR_EQUIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (c|| @ V0)) @ (c|| @ V1))) @ ((c|| @ V0) @ V1)))))))
(TDIRECTION_AXIOM_2,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c_|_ @ V2) @ V0)) @ ((c_|_ @ V2) @ V1)))))))))
(TPARDIR_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c|| @ V1) @ V0)) @ ((c|| @ V0) @ V2))) @ ((c|| @ V1) @ V2)))))))))
(TORTHOGONAL_COMBINE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c_|_ @ V1) @ V0)) @ ((c/__caret__ @ ((c_|_ @ V2) @ V0)) @ (c~ @ ((c|| @ V1) @ V2))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((c_|_ @ V3) @ V0)) @ ((c/__caret__ @ (c~ @ ((c|| @ V1) @ V3))) @ (c~ @ ((c|| @ V2) @ V3))))))))))))))
(TPERPDIR_WELLDEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c|| @ V0) @ V2)) @ ((c|| @ V1) @ V3))) @ ((c= @ ((c_|_ @ V0) @ V1)) @ ((c_|_ @ V2) @ V3))))))))))))
(TDETERMINISM,(c! @ (^[V0]: (cdeterministic @ (csem @ V0)))))
(Tcommand_DISTINCT_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c~ @ ((c= @ ((cSeq @ V0) @ V1)) @ ((cWhile @ V2) @ V3))))))))))))
(Tcommand_DISTINCT_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c~ @ ((c= @ ((cSeq @ V0) @ V1)) @ (((cIte @ V2) @ V3) @ V4))))))))))))))
(Tcommand_INJECTIVE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cSeq @ V0) @ V1)) @ ((cSeq @ V2) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V2)) @ ((c= @ V1) @ V3))))))))))))
(TWP_DO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cwp @ ((cSeq @ V0) @ ((cIF @ V1) @ ((cDO @ V0) @ V1)))) @ V2)) @ ((cwp @ ((cDO @ V0) @ V1)) @ V2)))))))))
(TWP_IF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cwp @ ((cIF @ V1) @ V0)) @ V2)) @ ((cOR @ ((cAND @ V1) @ ((cwp @ V0) @ V2))) @ ((cAND @ (cNOT @ V1)) @ V2))))))))))
(TWP_ITE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cwp @ (((cIte @ V1) @ V0) @ V2)) @ V3)) @ ((cOR @ ((cAND @ V1) @ ((cwp @ V0) @ V3))) @ ((cAND @ (cNOT @ V1)) @ ((cwp @ V2) @ V3)))))))))))))
(TWP_SEQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cwp @ ((cSeq @ V0) @ V1)) @ V2)) @ ((cwp @ V0) @ ((cwp @ V1) @ V2))))))))))
(TWP_DISJUNCTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cOR @ ((cwp @ V0) @ V1)) @ ((cwp @ V0) @ V2))) @ ((cwp @ V0) @ ((cOR @ V1) @ V2))))))))))
(TWP_CONJUNCTIVE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cAND @ ((cwp @ V0) @ V1)) @ ((cwp @ V0) @ V2))) @ ((cwp @ V0) @ ((cAND @ V1) @ V2))))))))))
(TWP_TOTAL,(c! @ (^[V0]: ((c= @ ((cwp @ V0) @ cFALSE)) @ cFALSE))))
(Twp,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cwp @ V0) @ V1) @ V2)) @ ((c/__caret__ @ ((cterminates @ V0) @ V2)) @ (((cwlp @ V0) @ V1) @ V2))))))))))
(Twlp,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cwlp @ V0) @ V2) @ V1)) @ (c! @ (^[V3]: ((c==> @ (((csem @ V0) @ V1) @ V3)) @ (V2 @ V3))))))))))))
(Tterminates,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cterminates @ V0) @ V1)) @ (c? @ (^[V2]: (((csem @ V0) @ V1) @ V2)))))))))
(TSEM_DO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csem @ ((cDO @ V0) @ V1)) @ V2) @ V3)) @ (((csem @ ((cSeq @ V0) @ ((cIF @ V1) @ ((cDO @ V0) @ V1)))) @ V2) @ V3)))))))))))
(TSEM_IF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csem @ ((cIF @ V1) @ V0)) @ V2) @ V3)) @ ((c__caret__/ @ ((c/__caret__ @ (V1 @ V2)) @ (((csem @ V0) @ V2) @ V3))) @ ((c/__caret__ @ (c~ @ (V1 @ V2))) @ ((c= @ V2) @ V3)))))))))))))
(TSEM_ITE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((csem @ (((cIte @ V1) @ V0) @ V2)) @ V3) @ V4)) @ ((c__caret__/ @ ((c/__caret__ @ (V1 @ V3)) @ (((csem @ V0) @ V3) @ V4))) @ ((c/__caret__ @ (c~ @ (V1 @ V3))) @ (((csem @ V2) @ V3) @ V4)))))))))))))))
(TSEM_SEQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((csem @ ((cSeq @ V0) @ V2)) @ V1) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ (((csem @ V0) @ V1) @ V4)) @ (((csem @ V2) @ V4) @ V3))))))))))))))
(Tsem_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((csem @ V0) @ V2) @ V3)) @ (((csem @ V1) @ V3) @ V4))) @ (((csem @ ((cSeq @ V0) @ V1)) @ V2) @ V4)))))))))))))
(Tsem_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((csem @ V0) @ V1) @ V2)) @ ((c__caret__/ @ (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ (cAssign @ V3))) @ ((c= @ V2) @ (V3 @ V1)))))) @ ((c__caret__/ @ (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ ((cSeq @ V3) @ V4))) @ ((c/__caret__ @ (((csem @ V3) @ V1) @ V5)) @ (((csem @ V4) @ V5) @ V2)))))))))) @ ((c__caret__/ @ (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ (((cIte @ V3) @ V4) @ V5))) @ ((c/__caret__ @ (V3 @ V1)) @ (((csem @ V4) @ V1) @ V2)))))))))) @ ((c__caret__/ @ (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ (((cIte @ V3) @ V4) @ V5))) @ ((c/__caret__ @ (c~ @ (V3 @ V1))) @ (((csem @ V5) @ V1) @ V2)))))))))) @ ((c__caret__/ @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((c= @ V0) @ ((cWhile @ V3) @ V4))) @ ((c/__caret__ @ ((c= @ V2) @ V1)) @ (c~ @ (V3 @ V1))))))))) @ (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((c= @ V0) @ ((cWhile @ V3) @ V4))) @ ((c/__caret__ @ (V3 @ V1)) @ ((c/__caret__ @ (((csem @ V4) @ V1) @ V5)) @ (((csem @ ((cWhile @ V3) @ V4)) @ V5) @ V2)))))))))))))))))))))))
(TBSET_MIRROR,(c! @ (^[V0]: ((c= @ (cbset @ (cmirror @ V0))) @ ((cIMAGE @ cint_neg) @ (caset @ V0))))))
(TPLUSINF_MIRROR,(c! @ (^[V0]: ((c= @ (cplusinf @ V0)) @ (cmirror @ (cminusinf @ (cmirror @ V0)))))))
(TMINUSINF_MIRROR,(c! @ (^[V0]: ((c= @ (cminusinf @ (cmirror @ V0))) @ (cmirror @ (cplusinf @ V0))))))
(TMINUSINF_LEMMA,(c! @ (^[V0]: (c? @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cint_lt @ V2) @ V1)) @ ((c= @ ((cinterp @ V2) @ V0)) @ ((cinterp @ V2) @ (cminusinf @ V0)))))))))))
(Tinterp_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cinterp @ V1) @ ((cOr @ V0) @ V2))) @ ((c__caret__/ @ ((cinterp @ V1) @ V0)) @ ((cinterp @ V1) @ V2))))))))))
(Tinterp_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cinterp @ V1) @ ((cAnd @ V0) @ V2))) @ ((c/__caret__ @ ((cinterp @ V1) @ V0)) @ ((cinterp @ V1) @ V2))))))))))
(Talldivide_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((calldivide @ V1) @ ((cOr @ V0) @ V2))) @ ((c/__caret__ @ ((calldivide @ V1) @ V0)) @ ((calldivide @ V1) @ V2))))))))))
(Talldivide_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((calldivide @ V1) @ ((cAnd @ V0) @ V2))) @ ((c/__caret__ @ ((calldivide @ V1) @ V0)) @ ((calldivide @ V1) @ V2))))))))))
(Tbset_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cbset @ ((cOr @ V0) @ V1))) @ ((cUNION @ (cbset @ V0)) @ (cbset @ V1))))))))
(Tbset_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cbset @ ((cAnd @ V0) @ V1))) @ ((cUNION @ (cbset @ V0)) @ (cbset @ V1))))))))
(Taset_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (caset @ ((cOr @ V0) @ V1))) @ ((cUNION @ (caset @ V0)) @ (caset @ V1))))))))
(Taset_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (caset @ ((cAnd @ V0) @ V1))) @ ((cUNION @ (caset @ V0)) @ (caset @ V1))))))))
(Tplusinf_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cplusinf @ ((cOr @ V0) @ V1))) @ ((cOr @ (cplusinf @ V0)) @ (cplusinf @ V1))))))))
(Tplusinf_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cplusinf @ ((cAnd @ V0) @ V1))) @ ((cAnd @ (cplusinf @ V0)) @ (cplusinf @ V1))))))))
(Tmirror_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmirror @ ((cOr @ V0) @ V1))) @ ((cOr @ (cmirror @ V0)) @ (cmirror @ V1))))))))
(Tmirror_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmirror @ ((cAnd @ V0) @ V1))) @ ((cAnd @ (cmirror @ V0)) @ (cmirror @ V1))))))))
(Tminusinf_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cminusinf @ ((cOr @ V0) @ V1))) @ ((cOr @ (cminusinf @ V0)) @ (cminusinf @ V1))))))))
(Tminusinf_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cminusinf @ ((cAnd @ V0) @ V1))) @ ((cAnd @ (cminusinf @ V0)) @ (cminusinf @ V1))))))))
(TMBASIS_EXPANSION,(c! @ (^[V0]: ((c= @ ((cvsum @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ V2)))))) @ (^[V1]: ((c% @ ((c$$ @ V0) @ V1)) @ (cmbasis @ V1))))) @ V0))))
(Treversion,(c! @ (^[V0]: ((c= @ (creversion @ V0)) @ (clambdas @ (^[V1]: ((creal_mul @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cDIV @ ((c* @ (cCARD @ V1)) @ ((c- @ (cCARD @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$$ @ V0) @ V1))))))))
(Tmultivector,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmultivector @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ (c~ @ ((c= @ ((c$$ @ V0) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((cHAS_SIZE @ V2) @ V1))))))))))
(Tsindex,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c$$ @ V0) @ V1)) @ ((c$ @ V0) @ (csetcode @ V1))))))))
(Toutermorphism,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((coutermorphism @ V1) @ V0)) @ ((cvsum @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cSUBSET @ V3) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ V3)))))) @ (^[V2]: ((c% @ ((c$$ @ V0) @ V2)) @ (((cseqiterate @ couter) @ V2) @ ((co @ cmultivec) @ ((co @ V1) @ cbasis))))))))))))
(Touter,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((couter @ V0) @ V1)) @ ((((cProduct @ (^[V2]: (^[V3]: (((cCOND @ (c~ @ ((c= @ ((cINTER @ V2) @ V3)) @ cEMPTY))) @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((cIN @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((cIN @ V6) @ V3)) @ ((c> @ V5) @ V6)))))) @ ((c__comma__ @ V5) @ V6)))))))))))))) @ (^[V2]: (^[V3]: ((cUNION @ ((cDIFF @ V2) @ V3)) @ ((cDIFF @ V3) @ V2))))) @ V0) @ V1)))))))
(TOUTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((couter @ V0) @ V1)) @ ((((cProduct @ (^[V2]: (^[V3]: (((cCOND @ (c~ @ ((c= @ ((cINTER @ V2) @ V3)) @ cEMPTY))) @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((cIN @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((cIN @ V6) @ V3)) @ ((c> @ V5) @ V6)))))) @ ((c__comma__ @ V5) @ V6)))))))))))))) @ cUNION) @ V0) @ V1)))))))
(Tinner,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinner @ V0) @ V1)) @ ((((cProduct @ (^[V2]: (^[V3]: (((cCOND @ ((c__caret__/ @ ((c= @ V2) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ V3) @ cEMPTY)) @ (c~ @ ((c/__caret__ @ ((c= @ ((cDIFF @ V2) @ V3)) @ cEMPTY)) @ (c~ @ ((c= @ ((cDIFF @ V3) @ V2)) @ cEMPTY))))))) @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((cIN @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((cIN @ V6) @ V3)) @ ((c> @ V5) @ V6)))))) @ ((c__comma__ @ V5) @ V6)))))))))))))) @ (^[V2]: (^[V3]: ((cUNION @ ((cDIFF @ V2) @ V3)) @ ((cDIFF @ V3) @ V2))))) @ V0) @ V1)))))))
(Tgeom_mul,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cgeom_mul @ V0) @ V1)) @ ((((cProduct @ (^[V2]: (^[V3]: ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((cIN @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((cIN @ V6) @ V3)) @ ((c> @ V5) @ V6)))))) @ ((c__comma__ @ V5) @ V6))))))))))))) @ (^[V2]: (^[V3]: ((cUNION @ ((cDIFF @ V2) @ V3)) @ ((cDIFF @ V3) @ V2))))) @ V0) @ V1)))))))
(TMULTIVECTOR_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$$ @ V0) @ V2)) @ ((c$$ @ V1) @ V2)))))))))))
(TMULTIVECTOR_ADD_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cSUBSET @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$$ @ ((cvector_add @ V0) @ V1)) @ V2)) @ ((creal_add @ ((c$$ @ V0) @ V2)) @ ((c$$ @ V1) @ V2)))))))))))
(TProduct_DEF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((cProduct @ V2) @ V3) @ V0) @ V1)) @ ((cvsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cSUBSET @ V5) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ V5)))))) @ (^[V4]: ((cvsum @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((cSUBSET @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ V6)))))) @ (^[V5]: ((c% @ ((creal_mul @ ((c$$ @ V0) @ V4)) @ ((creal_mul @ ((c$$ @ V1) @ V5)) @ ((V2 @ V4) @ V5)))) @ (cmbasis @ ((V3 @ V4) @ V5)))))))))))))))))
(TOUTER_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((couter @ V0) @ ((couter @ V1) @ V2))) @ ((couter @ ((couter @ V0) @ V1)) @ V2)))))))))
(TGEOM_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cgeom_mul @ V0) @ ((cgeom_mul @ V1) @ V2))) @ ((cgeom_mul @ ((cgeom_mul @ V0) @ V1)) @ V2)))))))))
(TOUTER_ACI_conjunct6,(c! @ (^[V0]: ((c= @ ((couter @ V0) @ (cmbasis @ cEMPTY))) @ V0))))
(TOUTER_ACI_conjunct5,(c! @ (^[V0]: ((c= @ ((couter @ (cmbasis @ cEMPTY)) @ V0)) @ V0))))
(TOUTER_ACI_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((couter @ ((couter @ V0) @ V1)) @ V2)) @ ((couter @ V0) @ ((couter @ V1) @ V2))))))))))
(TOUTER_MBASIS_RSCALAR,(c! @ (^[V0]: ((c= @ ((couter @ V0) @ (cmbasis @ cEMPTY))) @ V0))))
(TOUTER_MBASIS_LSCALAR,(c! @ (^[V0]: ((c= @ ((couter @ (cmbasis @ cEMPTY)) @ V0)) @ V0))))
(TINNER_LZERO,(c! @ (^[V0]: ((c= @ ((cinner @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))
(TINNER_RZERO,(c! @ (^[V0]: ((c= @ ((cinner @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))))
(TINNER_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinner @ (cvector_neg @ V0)) @ V1)) @ (cvector_neg @ ((cinner @ V0) @ V1))))))))
(TINNER_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cinner @ V0) @ (cvector_neg @ V1))) @ (cvector_neg @ ((cinner @ V0) @ V1))))))))
(TINNER_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cinner @ ((cvector_add @ V0) @ V1)) @ V2)) @ ((cvector_add @ ((cinner @ V0) @ V2)) @ ((cinner @ V1) @ V2))))))))))
(TINNER_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cinner @ V1) @ ((cvector_add @ V0) @ V2))) @ ((cvector_add @ ((cinner @ V1) @ V0)) @ ((cinner @ V1) @ V2))))))))))
(TOUTER_LZERO,(c! @ (^[V0]: ((c= @ ((couter @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))
(TOUTER_RZERO,(c! @ (^[V0]: ((c= @ ((couter @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))))
(TOUTER_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((couter @ (cvector_neg @ V0)) @ V1)) @ (cvector_neg @ ((couter @ V0) @ V1))))))))
(TOUTER_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((couter @ V0) @ (cvector_neg @ V1))) @ (cvector_neg @ ((couter @ V0) @ V1))))))))
(TOUTER_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((couter @ ((cvector_add @ V0) @ V1)) @ V2)) @ ((cvector_add @ ((couter @ V0) @ V2)) @ ((couter @ V1) @ V2))))))))))
(TOUTER_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((couter @ V1) @ ((cvector_add @ V0) @ V2))) @ ((cvector_add @ ((couter @ V1) @ V0)) @ ((couter @ V1) @ V2))))))))))
(TGEOM_LZERO,(c! @ (^[V0]: ((c= @ ((cgeom_mul @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))
(TGEOM_RZERO,(c! @ (^[V0]: ((c= @ ((cgeom_mul @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))))
(TGEOM_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cgeom_mul @ (cvector_neg @ V0)) @ V1)) @ (cvector_neg @ ((cgeom_mul @ V0) @ V1))))))))
(TGEOM_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cgeom_mul @ V0) @ (cvector_neg @ V1))) @ (cvector_neg @ ((cgeom_mul @ V0) @ V1))))))))
(TGEOM_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cgeom_mul @ ((cvector_add @ V0) @ V1)) @ V2)) @ ((cvector_add @ ((cgeom_mul @ V0) @ V2)) @ ((cgeom_mul @ V1) @ V2))))))))))
(TGEOM_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cgeom_mul @ V1) @ ((cvector_add @ V0) @ V2))) @ ((cvector_add @ ((cgeom_mul @ V1) @ V0)) @ ((cgeom_mul @ V1) @ V2))))))))))
(TPRODUCT_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((((cProduct @ V1) @ V2) @ ((cvector_add @ V0) @ V3)) @ V4)) @ ((cvector_add @ ((((cProduct @ V1) @ V2) @ V0) @ V4)) @ ((((cProduct @ V1) @ V2) @ V3) @ V4))))))))))))))
(TPRODUCT_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((((cProduct @ V1) @ V2) @ V3) @ ((cvector_add @ V0) @ V4))) @ ((cvector_add @ ((((cProduct @ V1) @ V2) @ V3) @ V0)) @ ((((cProduct @ V1) @ V2) @ V3) @ V4))))))))))))))
(TGRADE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cgrade @ V1) @ ((cvector_add @ V0) @ V2))) @ ((cvector_add @ ((cgrade @ V1) @ V0)) @ ((cgrade @ V1) @ V2))))))))))
(TMULTIVECTOR_ETA,(c! @ (^[V0]: ((c= @ (clambdas @ (^[V1]: ((c$$ @ V0) @ V1)))) @ V0))))
(TSNDCART_NEG,(c! @ (^[V0]: ((c= @ (cvector_neg @ (csndcart @ V0))) @ (csndcart @ (cvector_neg @ V0))))))
(TFSTCART_NEG,(c! @ (^[V0]: ((c= @ (cvector_neg @ (cfstcart @ V0))) @ (cfstcart @ (cvector_neg @ V0))))))
(TSNDCART_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csndcart @ ((cvector_sub @ V0) @ V1))) @ ((cvector_sub @ (csndcart @ V0)) @ (csndcart @ V1))))))))
(TSNDCART_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csndcart @ ((cvector_add @ V0) @ V1))) @ ((cvector_add @ (csndcart @ V0)) @ (csndcart @ V1))))))))
(TFSTCART_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cfstcart @ ((cvector_sub @ V0) @ V1))) @ ((cvector_sub @ (cfstcart @ V0)) @ (cfstcart @ V1))))))))
(TFSTCART_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cfstcart @ ((cvector_add @ V0) @ V1))) @ ((cvector_add @ (cfstcart @ V0)) @ (cfstcart @ V1))))))))
(TDIST_SNDCART,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cdistance @ ((c__comma__ @ (csndcart @ V0)) @ (csndcart @ V1)))) @ (cdistance @ ((c__comma__ @ V0) @ V1))))))))
(TNORM_SNDCART,(c! @ (^[V0]: ((creal_le @ (cvector_norm @ (csndcart @ V0))) @ (cvector_norm @ V0)))))
(TDIST_FSTCART,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cdistance @ ((c__comma__ @ (cfstcart @ V0)) @ (cfstcart @ V1)))) @ (cdistance @ ((c__comma__ @ V0) @ V1))))))))
(TNORM_FSTCART,(c! @ (^[V0]: ((creal_le @ (cvector_norm @ (cfstcart @ V0))) @ (cvector_norm @ V0)))))
(TVECTOR_EXPAND_4,(c! @ (^[V0]: ((c= @ V0) @ (cvector @ ((cCONS @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cCONS @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((cCONS @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ cNIL)))))))))
(TDOT_4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ V0) @ V1)) @ ((creal_add @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_add @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))
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(TMEASURE_INTERVAL_4_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (copen_interval @ ((c__comma__ @ V0) @ V1)))) @ (((cCOND @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TMEASURE_INTERVAL_4_ALT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (((cCOND @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TMEASURE_INTERVAL_4_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (((cCOND @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TGRASSMANN_PLUCKER_4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c= @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V7) @ ((cCONS @ V1) @ ((cCONS @ V2) @ ((cCONS @ V3) @ cNIL))))))) @ (cdet @ (cvector @ ((cCONS @ V4) @ ((cCONS @ V5) @ ((cCONS @ V6) @ ((cCONS @ V0) @ cNIL)))))))) @ ((creal_add @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V4) @ ((cCONS @ V1) @ ((cCONS @ V2) @ ((cCONS @ V3) @ cNIL))))))) @ (cdet @ (cvector @ ((cCONS @ V7) @ ((cCONS @ V5) @ ((cCONS @ V6) @ ((cCONS @ V0) @ cNIL)))))))) @ ((creal_add @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V5) @ ((cCONS @ V1) @ ((cCONS @ V2) @ ((cCONS @ V3) @ cNIL))))))) @ (cdet @ (cvector @ ((cCONS @ V4) @ ((cCONS @ V7) @ ((cCONS @ V6) @ ((cCONS @ V0) @ cNIL)))))))) @ ((creal_add @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V6) @ ((cCONS @ V1) @ ((cCONS @ V2) @ ((cCONS @ V3) @ cNIL))))))) @ (cdet @ (cvector @ ((cCONS @ V4) @ ((cCONS @ V5) @ ((cCONS @ V7) @ ((cCONS @ V0) @ cNIL)))))))) @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V1) @ ((cCONS @ V2) @ ((cCONS @ V3) @ cNIL))))))) @ (cdet @ (cvector @ ((cCONS @ V4) @ ((cCONS @ V5) @ ((cCONS @ V6) @ ((cCONS @ V7) @ cNIL))))))))))))))))))))))))))))
(TCROSS_BASIS_NONZERO,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c__caret__/ @ (c~ @ ((c= @ ((ccross @ V0) @ (cbasis @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c__caret__/ @ (c~ @ ((c= @ ((ccross @ V0) @ (cbasis @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cvec @ (cNUMERAL @ c_0))))) @ (c~ @ ((c= @ ((ccross @ V0) @ (cbasis @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ (cvec @ (cNUMERAL @ c_0))))))))))
(Tprojp,(c! @ (^[V0]: ((c= @ (cprojp @ V0)) @ (cmk_point @ (cprojl @ V0))))))
(Tprojl,(c! @ (^[V0]: ((c= @ (cprojl @ V0)) @ (cmk_line @ (c|| @ (cmk_dir @ V0)))))))
(TCROSS_LZERO,(c! @ (^[V0]: ((c= @ ((ccross @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))
(TCROSS_RZERO,(c! @ (^[V0]: ((c= @ ((ccross @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))))
(TCROSS_REFL,(c! @ (^[V0]: ((c= @ ((ccross @ V0) @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))
(TVECTOR_EXPAND_3,(c! @ (^[V0]: ((c= @ V0) @ (cvector @ ((cCONS @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cCONS @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ cNIL))))))))
(Tdirection_tybij_conjunct1,(c! @ (^[V0]: ((c= @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ (cdest_dir @ (cmk_dir @ V0))) @ V0)))))
(TCOMPUTE_FACES_2_STEP_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V4) @ ((cINSERT @ V0) @ V1))) @ ((c/__caret__ @ ((cIN @ V5) @ ((cINSERT @ V0) @ V1))) @ ((c/__caret__ @ ((cIN @ V6) @ ((cINSERT @ V0) @ V1))) @ ((cLET @ (^[V7]: (cLET_END @ ((c/__caret__ @ (c~ @ ((c= @ V7) @ (cvec @ (cNUMERAL @ c_0))))) @ ((cLET @ (^[V8]: (cLET_END @ ((c/__caret__ @ ((c__caret__/ @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ V3)) @ ((creal_le @ ((cdot @ V7) @ V9)) @ V8))))) @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ V3)) @ ((creal_ge @ ((cdot @ V7) @ V9)) @ V8)))))) @ ((c= @ V2) @ ((chull @ cconvex) @ ((cINTER @ V3) @ (cGSPEC @ (^[V9]: (c? @ (^[V10]: (((cSETSPEC @ V9) @ ((c= @ ((cdot @ V7) @ V10)) @ V8)) @ V10)))))))))))) @ ((cdot @ V7) @ V4)))))) @ ((ccross @ ((cvector_sub @ V6) @ V4)) @ ((cvector_sub @ V5) @ V4))))))))))))) @ ((c__caret__/ @ (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cLET @ (^[V6]: (cLET_END @ ((c/__caret__ @ (c~ @ ((c= @ V6) @ (cvec @ (cNUMERAL @ c_0))))) @ ((cLET @ (^[V7]: (cLET_END @ ((c/__caret__ @ ((c__caret__/ @ (c! @ (^[V8]: ((c==> @ ((cIN @ V8) @ V3)) @ ((creal_le @ ((cdot @ V6) @ V8)) @ V7))))) @ (c! @ (^[V8]: ((c==> @ ((cIN @ V8) @ V3)) @ ((creal_ge @ ((cdot @ V6) @ V8)) @ V7)))))) @ ((c= @ V2) @ ((chull @ cconvex) @ ((cINTER @ V3) @ (cGSPEC @ (^[V8]: (c? @ (^[V9]: (((cSETSPEC @ V8) @ ((c= @ ((cdot @ V6) @ V9)) @ V7)) @ V9)))))))))))) @ ((cdot @ V6) @ V0)))))) @ ((ccross @ ((cvector_sub @ V5) @ V0)) @ ((cvector_sub @ V4) @ V0)))))))))) @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cLET @ (^[V7]: (cLET_END @ ((c/__caret__ @ (c~ @ ((c= @ V7) @ (cvec @ (cNUMERAL @ c_0))))) @ ((cLET @ (^[V8]: (cLET_END @ ((c/__caret__ @ ((c__caret__/ @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ V3)) @ ((creal_le @ ((cdot @ V7) @ V9)) @ V8))))) @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ V3)) @ ((creal_ge @ ((cdot @ V7) @ V9)) @ V8)))))) @ ((c= @ V2) @ ((chull @ cconvex) @ ((cINTER @ V3) @ (cGSPEC @ (^[V9]: (c? @ (^[V10]: (((cSETSPEC @ V9) @ ((c= @ ((cdot @ V7) @ V10)) @ V8)) @ V10)))))))))))) @ ((cdot @ V7) @ V4)))))) @ ((ccross @ ((cvector_sub @ V6) @ V4)) @ ((cvector_sub @ V5) @ V4)))))))))))))))))))))))
(TCOMPUTE_FACES_2_STEP_2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V5) @ ((cINSERT @ V0) @ V1))) @ ((c/__caret__ @ ((cIN @ V6) @ ((cINSERT @ V0) @ V1))) @ ((cLET @ (^[V7]: (cLET_END @ ((c/__caret__ @ (c~ @ ((c= @ V7) @ (cvec @ (cNUMERAL @ c_0))))) @ ((cLET @ (^[V8]: (cLET_END @ ((c/__caret__ @ ((c__caret__/ @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ V3)) @ ((creal_le @ ((cdot @ V7) @ V9)) @ V8))))) @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ V3)) @ ((creal_ge @ ((cdot @ V7) @ V9)) @ V8)))))) @ ((c= @ V2) @ ((chull @ cconvex) @ ((cINTER @ V3) @ (cGSPEC @ (^[V9]: (c? @ (^[V10]: (((cSETSPEC @ V9) @ ((c= @ ((cdot @ V7) @ V10)) @ V8)) @ V10)))))))))))) @ ((cdot @ V7) @ V4)))))) @ ((ccross @ ((cvector_sub @ V6) @ V4)) @ ((cvector_sub @ V5) @ V4)))))))))) @ ((c__caret__/ @ (c? @ (^[V5]: ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((cLET @ (^[V6]: (cLET_END @ ((c/__caret__ @ (c~ @ ((c= @ V6) @ (cvec @ (cNUMERAL @ c_0))))) @ ((cLET @ (^[V7]: (cLET_END @ ((c/__caret__ @ ((c__caret__/ @ (c! @ (^[V8]: ((c==> @ ((cIN @ V8) @ V3)) @ ((creal_le @ ((cdot @ V6) @ V8)) @ V7))))) @ (c! @ (^[V8]: ((c==> @ ((cIN @ V8) @ V3)) @ ((creal_ge @ ((cdot @ V6) @ V8)) @ V7)))))) @ ((c= @ V2) @ ((chull @ cconvex) @ ((cINTER @ V3) @ (cGSPEC @ (^[V8]: (c? @ (^[V9]: (((cSETSPEC @ V8) @ ((c= @ ((cdot @ V6) @ V9)) @ V7)) @ V9)))))))))))) @ ((cdot @ V6) @ V4)))))) @ ((ccross @ ((cvector_sub @ V5) @ V4)) @ ((cvector_sub @ V0) @ V4))))))) @ (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ ((cIN @ V6) @ V1)) @ ((cLET @ (^[V7]: (cLET_END @ ((c/__caret__ @ (c~ @ ((c= @ V7) @ (cvec @ (cNUMERAL @ c_0))))) @ ((cLET @ (^[V8]: (cLET_END @ ((c/__caret__ @ ((c__caret__/ @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ V3)) @ ((creal_le @ ((cdot @ V7) @ V9)) @ V8))))) @ (c! @ (^[V9]: ((c==> @ ((cIN @ V9) @ V3)) @ ((creal_ge @ ((cdot @ V7) @ V9)) @ V8)))))) @ ((c= @ V2) @ ((chull @ cconvex) @ ((cINTER @ V3) @ (cGSPEC @ (^[V9]: (c? @ (^[V10]: (((cSETSPEC @ V9) @ ((c= @ ((cdot @ V7) @ V10)) @ V8)) @ V10)))))))))))) @ ((cdot @ V7) @ V4)))))) @ ((ccross @ ((cvector_sub @ V6) @ V4)) @ ((cvector_sub @ V5) @ V4))))))))))))))))))))))
(TORTHOGONAL_CROSS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((corthogonal @ ((ccross @ V1) @ V0)) @ V1))))))
(TORTHOGONAL_CROSS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((corthogonal @ ((ccross @ V0) @ V1)) @ V1))))))
(TORTHOGONAL_CROSS_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((corthogonal @ V1) @ ((ccross @ V0) @ V1)))))))
(TORTHOGONAL_CROSS_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((corthogonal @ V0) @ ((ccross @ V0) @ V1)))))))
(TNORM_CROSS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_pow @ (cvector_norm @ ((ccross @ V0) @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((creal_mul @ ((creal_pow @ (cvector_norm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_pow @ ((cdot @ V0) @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TNORM_CROSS_DOT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_add @ ((creal_pow @ (cvector_norm @ ((ccross @ V0) @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ ((cdot @ V0) @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_pow @ ((creal_mul @ (cvector_norm @ V0)) @ (cvector_norm @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))
(TDOT_CROSS_SELF_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ ((ccross @ V1) @ V0)) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TDOT_CROSS_SELF_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ ((ccross @ V0) @ V1)) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TDOT_CROSS_SELF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ V0) @ ((ccross @ V1) @ V0))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TDOT_CROSS_SELF_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ V0) @ ((ccross @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TDOT_3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ V0) @ V1)) @ ((creal_add @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))))))))
(TCROSS_COMPONENTS_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c$ @ ((ccross @ V1) @ V0)) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((creal_mul @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TCROSS_COMPONENTS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c$ @ ((ccross @ V1) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_sub @ ((creal_mul @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))))))))
(TCROSS_COMPONENTS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c$ @ ((ccross @ V1) @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((creal_mul @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TMEASURE_INTERVAL_3_ALT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (copen_interval @ ((c__comma__ @ V0) @ V1)))) @ (((cCOND @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TMEASURE_INTERVAL_3_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (copen_interval @ ((c__comma__ @ V0) @ V1)))) @ (((cCOND @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TMEASURE_INTERVAL_3_ALT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (((cCOND @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TMEASURE_INTERVAL_3_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (((cCOND @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TCROSS_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccross @ (cvector_neg @ V0)) @ V1)) @ (cvector_neg @ ((ccross @ V0) @ V1))))))))
(TCROSS_SKEW,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccross @ V1) @ V0)) @ (cvector_neg @ ((ccross @ V0) @ V1))))))))
(TCROSS_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccross @ V0) @ (cvector_neg @ V1))) @ (cvector_neg @ ((ccross @ V0) @ V1))))))))
(Tcross,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccross @ V0) @ V1)) @ (cvector @ ((cCONS @ ((creal_sub @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((cCONS @ ((creal_sub @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))) @ ((cCONS @ ((creal_sub @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ cNIL))))))))))
(TCROSS_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((ccross @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))) @ (ccollinear @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))))
(TCROSS_EQ_SELF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((ccross @ V0) @ V1)) @ V1)) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TCROSS_EQ_SELF_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((ccross @ V0) @ V1)) @ V0)) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TNORM_AND_CROSS_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((c= @ ((cdot @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ ((ccross @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c__caret__/ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))))))))
(TNORMAL_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((corthogonal @ V0) @ V2)) @ ((corthogonal @ V1) @ V2))))))))))
(TCROSS_DOT_CANCEL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c= @ ((cdot @ V0) @ V1)) @ ((cdot @ V0) @ V2))) @ ((c/__caret__ @ ((c= @ ((ccross @ V0) @ V1)) @ ((ccross @ V0) @ V2))) @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((c= @ V1) @ V2)))))))))
(TCROSS_TRIPLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ ((ccross @ V2) @ V0)) @ V1)) @ ((cdot @ ((ccross @ V0) @ V1)) @ V2)))))))))
(TDOT_CROSS_DET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ V0) @ ((ccross @ V1) @ V2))) @ (cdet @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL)))))))))))))
(TCROSS_JACOBI,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvector_add @ ((ccross @ V1) @ ((ccross @ V2) @ V0))) @ ((cvector_add @ ((ccross @ V2) @ ((ccross @ V0) @ V1))) @ ((ccross @ V0) @ ((ccross @ V1) @ V2))))) @ (cvec @ (cNUMERAL @ c_0))))))))))
(TCROSS_LSUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccross @ ((cvector_sub @ V0) @ V1)) @ V2)) @ ((cvector_sub @ ((ccross @ V0) @ V2)) @ ((ccross @ V1) @ V2))))))))))
(TCROSS_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccross @ ((cvector_add @ V0) @ V1)) @ V2)) @ ((cvector_add @ ((ccross @ V0) @ V2)) @ ((ccross @ V1) @ V2))))))))))
(TCROSS_RSUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccross @ V1) @ ((cvector_sub @ V0) @ V2))) @ ((cvector_sub @ ((ccross @ V1) @ V0)) @ ((ccross @ V1) @ V2))))))))))
(TCROSS_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccross @ V1) @ ((cvector_add @ V0) @ V2))) @ ((cvector_add @ ((ccross @ V1) @ V0)) @ ((ccross @ V1) @ V2))))))))))
(TCROSS_LAGRANGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccross @ V0) @ ((ccross @ V1) @ V2))) @ ((cvector_sub @ ((c% @ ((cdot @ V0) @ V2)) @ V1)) @ ((c% @ ((cdot @ V0) @ V1)) @ V2))))))))))
(TNEGLIGIBLE_CONVEX_HULL_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (cnegligible @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))))
(TNEGLIGIBLE_AFFINE_HULL_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (cnegligible @ ((chull @ caffine) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))))
(THAS_MEASURE_TETRAHEDRON,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((chas_measure @ ((chull @ cconvex) @ ((cINSERT @ V3) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY)))))) @ ((creal_div @ (creal_abs @ ((creal_add @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ ((creal_add @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ (cBIT1 @ c_0))))))))))))))))
(TDOT_CROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cdot @ ((ccross @ V0) @ V2)) @ ((ccross @ V3) @ V1))) @ ((creal_sub @ ((creal_mul @ ((cdot @ V0) @ V3)) @ ((cdot @ V2) @ V1))) @ ((creal_mul @ ((cdot @ V0) @ V1)) @ ((cdot @ V2) @ V3)))))))))))))
(TMEASURE_TETRAHEDRON,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (cmeasure @ ((chull @ cconvex) @ ((cINSERT @ V3) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))) @ ((creal_div @ (creal_abs @ ((creal_add @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ ((creal_add @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ (cBIT1 @ c_0))))))))))))))))
(TCROSS_CROSS_DET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((ccross @ ((ccross @ V0) @ V1)) @ ((ccross @ V2) @ V3))) @ ((cvector_sub @ ((c% @ (cdet @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V1) @ ((cCONS @ V3) @ cNIL)))))) @ V2)) @ ((c% @ (cdet @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL)))))) @ V3))))))))))))
(TGRASSMANN_PLUCKER_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c= @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V5) @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL)))))) @ (cdet @ (cvector @ ((cCONS @ V3) @ ((cCONS @ V4) @ ((cCONS @ V0) @ cNIL))))))) @ ((creal_add @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V3) @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL)))))) @ (cdet @ (cvector @ ((cCONS @ V5) @ ((cCONS @ V4) @ ((cCONS @ V0) @ cNIL))))))) @ ((creal_add @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V4) @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL)))))) @ (cdet @ (cvector @ ((cCONS @ V3) @ ((cCONS @ V5) @ ((cCONS @ V0) @ cNIL))))))) @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL)))))) @ (cdet @ (cvector @ ((cCONS @ V3) @ ((cCONS @ V4) @ ((cCONS @ V5) @ cNIL))))))))))))))))))))))
(TINFNORM_EQ_1_IMP_conjunct0,(c! @ (^[V0]: ((c==> @ ((c= @ (cinfnorm @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_le @ (creal_abs @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TINFNORM_EQ_1_IMP_conjunct1,(c! @ (^[V0]: ((c==> @ ((c= @ (cinfnorm @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_le @ (creal_abs @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(Tconstructible_RULES_conjunct0,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ (crational @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (crational @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (cconstructible @ V0)))))
(TCONSTRUCTIBLE_RADICAL_conjunct0,(c! @ (^[V0]: ((c==> @ (cconstructible @ V0)) @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TCONSTRUCTIBLE_RADICAL_conjunct1,(c! @ (^[V0]: ((c==> @ (cconstructible @ V0)) @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))
(TMEASURE_CONVEX_HULL_2_TRIVIAL_conjunct0,(c! @ (^[V0]: ((c= @ (cmeasure @ ((chull @ cconvex) @ ((cINSERT @ V0) @ cEMPTY)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TINFNORM_2,(c! @ (^[V0]: ((c= @ (cinfnorm @ V0)) @ ((creal_max @ (creal_abs @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_abs @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))
(TRE_DEF,(c! @ (^[V0]: ((c= @ (cRe @ V0)) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TIM_DEF,(c! @ (^[V0]: ((c= @ (cIm @ V0)) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))
(Tcomplex_pow_conjunct0,(c! @ (^[V0]: ((c= @ ((ccomplex_pow @ V0) @ (cNUMERAL @ c_0))) @ (cCx @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TVECTOR_SUB_ELIM_THM_conjunct0,(c! @ (^[V0]: ((c= @ (cvector_neg @ V0)) @ ((c% @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)))))
(Tcomplex_neg,(c! @ (^[V0]: ((c= @ (cvector_neg @ V0)) @ (ccomplex @ ((c__comma__ @ (creal_neg @ (cRe @ V0))) @ (creal_neg @ (cIm @ V0))))))))
(Tcomplex_inv,(c! @ (^[V0]: ((c= @ (ccomplex_inv @ V0)) @ (ccomplex @ ((c__comma__ @ ((creal_div @ (cRe @ V0)) @ ((creal_add @ ((creal_pow @ (cRe @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cIm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_div @ (creal_neg @ (cIm @ V0))) @ ((creal_add @ ((creal_pow @ (cRe @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cIm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TCOMPLEX,(c! @ (^[V0]: ((c= @ (ccomplex @ ((c__comma__ @ (cRe @ V0)) @ (cIm @ V0)))) @ V0))))
(Tcexp,(c! @ (^[V0]: ((c= @ (ccexp @ V0)) @ ((cinfsum @ (cfrom @ (cNUMERAL @ c_0))) @ (^[V1]: ((ccomplex_div @ ((ccomplex_pow @ V0) @ V1)) @ (cCx @ (creal_of_num @ (cFACT @ V1))))))))))
(TVECTOR_EXPAND_2,(c! @ (^[V0]: ((c= @ V0) @ (cvector @ ((cCONS @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cCONS @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ cNIL)))))))
(TINFNORM_EQ_1_2,(c! @ (^[V0]: ((c= @ ((c= @ (cinfnorm @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_le @ (creal_abs @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_le @ (creal_abs @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c__caret__/ @ ((c= @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c__caret__/ @ ((c= @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c__caret__/ @ ((c= @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c= @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TCOMPLEX_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ V0) @ (cCx @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((creal_add @ ((creal_pow @ (cRe @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cIm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(Tconstructible_CASES,(c! @ (^[V0]: ((c= @ (cconstructible @ V0)) @ ((c__caret__/ @ ((c/__caret__ @ (crational @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (crational @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((c__caret__/ @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (cconstructible @ V1)) @ ((c/__caret__ @ (cconstructible @ V2)) @ ((c/__caret__ @ (cconstructible @ V3)) @ ((c/__caret__ @ (cconstructible @ V4)) @ ((c/__caret__ @ (c~ @ ((cparallel @ ((c__comma__ @ V1) @ V2)) @ ((c__comma__ @ V3) @ V4)))) @ (((cis_intersection @ V0) @ ((c__comma__ @ V1) @ V2)) @ ((c__comma__ @ V3) @ V4)))))))))))))))) @ ((c__caret__/ @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: ((c/__caret__ @ (cconstructible @ V1)) @ ((c/__caret__ @ (cconstructible @ V2)) @ ((c/__caret__ @ (cconstructible @ V3)) @ ((c/__caret__ @ (cconstructible @ V4)) @ ((c/__caret__ @ (cconstructible @ V5)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ ((c/__caret__ @ (((ccollinear3 @ V1) @ V0) @ V2)) @ ((c= @ (clength @ ((c__comma__ @ V3) @ V0))) @ (clength @ ((c__comma__ @ V4) @ V5))))))))))))))))))))) @ (c? @ (^[V1]: (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ (cconstructible @ V1)) @ ((c/__caret__ @ (cconstructible @ V2)) @ ((c/__caret__ @ (cconstructible @ V3)) @ ((c/__caret__ @ (cconstructible @ V4)) @ ((c/__caret__ @ (cconstructible @ V5)) @ ((c/__caret__ @ (cconstructible @ V6)) @ ((c/__caret__ @ (c~ @ ((c/__caret__ @ ((c= @ V1) @ V4)) @ ((c= @ (clength @ ((c__comma__ @ V2) @ V3))) @ (clength @ ((c__comma__ @ V5) @ V6)))))) @ ((c/__caret__ @ ((c= @ (clength @ ((c__comma__ @ V1) @ V0))) @ (clength @ ((c__comma__ @ V2) @ V3)))) @ ((c= @ (clength @ ((c__comma__ @ V4) @ V0))) @ (clength @ ((c__comma__ @ V5) @ V6))))))))))))))))))))))))))))))
(TCIRCLES_TANGENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c__caret__/ @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V2))) @ ((creal_add @ V1) @ V3))) @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V2))) @ (creal_abs @ ((creal_sub @ V1) @ V3))))))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V0) @ V2)) @ ((c= @ V1) @ V3))) @ (c?! @ (^[V4]: ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V4))) @ V1)) @ ((c= @ (cdistance @ ((c__comma__ @ V2) @ V4))) @ V3)))))))))))))))
(Tcomplex_pow_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccomplex_pow @ V0) @ (cSUC @ V1))) @ ((ccomplex_mul @ V0) @ ((ccomplex_pow @ V0) @ V1))))))))
(TORTHOGONAL_SUM_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cALL @ (corthogonal @ V0)) @ V2)) @ ((c/__caret__ @ ((corthogonal @ V0) @ V3)) @ ((c= @ (cLENGTH @ V1)) @ (cLENGTH @ V2))))) @ ((corthogonal @ V0) @ ((((cITLIST2 @ (^[V4]: (^[V5]: (^[V6]: ((cvector_add @ ((c% @ V4) @ V5)) @ V6))))) @ V1) @ V2) @ V3))))))))))))
(THAS_PATH_INTEGRAL_INTEGRABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_path_integral @ V1) @ V0) @ V2)) @ ((cpath_integrable_on @ V1) @ V2)))))))))
(TINTERIOR_CONVEX_HULL_3_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (ccollinear @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))) @ ((c= @ (cinterior @ ((chull @ cconvex) @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((creal_lt @ ((creal_add @ V3) @ V4)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((cvector_add @ ((c% @ V3) @ V0)) @ ((c% @ V4) @ V1))))))))))))))))
(TDOT_2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ V0) @ V1)) @ ((creal_add @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TMEASURE_CONVEX_HULL_2_TRIVIAL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TMEASURE_INTERVAL_2_ALT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (copen_interval @ ((c__comma__ @ V0) @ V1)))) @ (((cCOND @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TMEASURE_INTERVAL_2_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (copen_interval @ ((c__comma__ @ V0) @ V1)))) @ (((cCOND @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TMEASURE_INTERVAL_2_ALT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (((cCOND @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_lt @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TMEASURE_INTERVAL_2_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (((cCOND @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(Tlength_def,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (clength @ ((c__comma__ @ V1) @ V0))) @ (cvector_norm @ ((cvector_sub @ V0) @ V1))))))))
(TTARSKI_AXIOM_1_EUCLIDEAN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdistance @ ((c__comma__ @ V1) @ V0))) @ (cdistance @ ((c__comma__ @ V0) @ V1))))))))
(TVECTOR_SUB_ELIM_THM_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_sub @ V0) @ V1)) @ ((cvector_add @ V0) @ ((c% @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V1))))))))
(Tcomplex_sub,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_sub @ V0) @ V1)) @ ((cvector_add @ V0) @ (cvector_neg @ V1))))))))
(Tcomplex_add,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_add @ V0) @ V1)) @ (ccomplex @ ((c__comma__ @ ((creal_add @ (cRe @ V0)) @ (cRe @ V1))) @ ((creal_add @ (cIm @ V0)) @ (cIm @ V1))))))))))
(Tcomplex_mul,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccomplex_mul @ V0) @ V1)) @ (ccomplex @ ((c__comma__ @ ((creal_sub @ ((creal_mul @ (cRe @ V0)) @ (cRe @ V1))) @ ((creal_mul @ (cIm @ V0)) @ (cIm @ V1)))) @ ((creal_add @ ((creal_mul @ (cRe @ V0)) @ (cIm @ V1))) @ ((creal_mul @ (cIm @ V0)) @ (cRe @ V1)))))))))))
(Tcomplex_div,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccomplex_div @ V0) @ V1)) @ ((ccomplex_mul @ V0) @ (ccomplex_inv @ V1))))))))
(TCOMPLEX_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ ((c/__caret__ @ ((c= @ (cRe @ V0)) @ (cRe @ V1))) @ ((c= @ (cIm @ V0)) @ (cIm @ V1)))))))))
(TCOLLINEAR_3_2Dzero,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccollinear @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))) @ ((c= @ ((creal_mul @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TNEGLIGIBLE_CONVEX_HULL_2,(c! @ (^[V0]: (c! @ (^[V1]: (cnegligible @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))))
(TNEGLIGIBLE_AFFINE_HULL_2,(c! @ (^[V0]: (c! @ (^[V1]: (cnegligible @ ((chull @ caffine) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))))
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(TSEGMENT_HORIZONTAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c= @ ((cIN @ V1) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ ((c/__caret__ @ ((c= @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((c= @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c__caret__/ @ ((c/__caret__ @ ((creal_le @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_le @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_le @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))))))
(TMIDPOINT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cbetween @ V0) @ ((c__comma__ @ V1) @ V2))) @ ((c= @ (clength @ ((c__comma__ @ V1) @ V0))) @ (clength @ ((c__comma__ @ V2) @ V0))))) @ ((cis_midpoint @ V0) @ ((c__comma__ @ V1) @ V2))))))))))
(TORTHOGONAL_TO_ORTHOGONAL_2D,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((corthogonal @ V0) @ V1)) @ ((corthogonal @ V0) @ V2)))) @ (ccollinear @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))))
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(TINTERIOR_CONVEX_HULL_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY)))))) @ ((c= @ (cinterior @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY)))))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ (c? @ (^[V5]: (c? @ (^[V6]: (c? @ (^[V7]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((c/__caret__ @ ((creal_lt @ V5) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V6)) @ ((c/__caret__ @ ((creal_lt @ V6) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V7)) @ ((c/__caret__ @ ((creal_lt @ V7) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((c= @ ((creal_add @ V5) @ ((creal_add @ V6) @ V7))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cvector_add @ ((c% @ V5) @ V0)) @ ((cvector_add @ ((c% @ V6) @ V1)) @ ((c% @ V7) @ V2)))) @ V4))))))))))))))) @ V4))))))))))))))
(TMEASURE_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cmeasure @ ((chull @ cconvex) @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))) @ ((creal_div @ (creal_abs @ ((creal_sub @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))
(TINTERIOR_OF_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cinterior @ ((chull @ cconvex) @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))) @ ((cDIFF @ ((chull @ cconvex) @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))) @ ((cUNION @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL))) @ ((cUNION @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))))
(TINSIDE_OF_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cinside @ ((cUNION @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ ((cUNION @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))))) @ (cinterior @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY)))))))))))))
(TFRONTIER_OF_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cfrontier @ ((chull @ cconvex) @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))) @ ((cUNION @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL))) @ ((cUNION @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))))
(Tcollinear3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((ccollinear3 @ V1) @ V0) @ V2)) @ ((cparallel @ ((c__comma__ @ V1) @ V0)) @ ((c__comma__ @ V1) @ V2))))))))))
(Ton_circle,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((con_circle @ V0) @ ((c__comma__ @ V1) @ V2))) @ ((c= @ (clength @ ((c__comma__ @ V1) @ V0))) @ (clength @ ((c__comma__ @ V1) @ V2)))))))))))
(Tis_midpoint,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cis_midpoint @ V0) @ ((c__comma__ @ V1) @ V2))) @ ((c= @ V0) @ ((c% @ ((creal_div @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((cvector_add @ V1) @ V2)))))))))))
(TBETWEEN_THM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cbetween @ V0) @ ((c__comma__ @ V1) @ V2))) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c/__caret__ @ ((creal_le @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ V0) @ ((cvector_add @ ((c% @ V3) @ V1)) @ ((c% @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3)) @ V2)))))))))))))))
(TCOLLINEAR_3_2D,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (ccollinear @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))) @ ((c= @ ((creal_mul @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))
(TCOLLINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))) @ ((c= @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))
(TTRIANGLE_ADDITIVE_DECOMPOSITION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (ccompact @ V5)) @ (ccompact @ V6))) @ ((c= @ (V3 @ ((cUNION @ V5) @ V6))) @ ((creal_add @ (V3 @ V5)) @ ((creal_sub @ (V3 @ V6)) @ (V3 @ ((cINTER @ V5) @ V6))))))))))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V2))) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ ((c/__caret__ @ (c~ @ (caffine_dependent @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY)))))) @ ((cIN @ V4) @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))) @ ((c= @ (V3 @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY)))))) @ ((creal_add @ ((creal_sub @ ((creal_add @ (V3 @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V4) @ cEMPTY)))))) @ ((creal_add @ (V3 @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V2) @ ((cINSERT @ V4) @ cEMPTY)))))) @ (V3 @ ((chull @ cconvex) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ ((cINSERT @ V4) @ cEMPTY)))))))) @ ((creal_add @ (V3 @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V4) @ cEMPTY))))) @ ((creal_add @ (V3 @ ((chull @ cconvex) @ ((cINSERT @ V1) @ ((cINSERT @ V4) @ cEMPTY))))) @ (V3 @ ((chull @ cconvex) @ ((cINSERT @ V2) @ ((cINSERT @ V4) @ cEMPTY)))))))) @ (V3 @ ((chull @ cconvex) @ ((cINSERT @ V4) @ cEMPTY)))))))))))))))))
(TTRIANGLE_DECOMPOSITION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cIN @ V1) @ ((chull @ cconvex) @ ((cINSERT @ V2) @ ((cINSERT @ V3) @ ((cINSERT @ V0) @ cEMPTY)))))) @ ((c= @ ((chull @ cconvex) @ ((cINSERT @ V2) @ ((cINSERT @ V3) @ ((cINSERT @ V0) @ cEMPTY))))) @ ((cUNION @ ((chull @ cconvex) @ ((cINSERT @ V1) @ ((cINSERT @ V3) @ ((cINSERT @ V0) @ cEMPTY))))) @ ((cUNION @ ((chull @ cconvex) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ cEMPTY))))) @ ((chull @ cconvex) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ ((cINSERT @ V3) @ cEMPTY)))))))))))))))))
(TSYLVESTER_GALLAI_LEMMA_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cbetween @ V1) @ ((c__comma__ @ V3) @ V0))) @ ((c/__caret__ @ (c~ @ ((cIN @ V2) @ ((chull @ caffine) @ ((cINSERT @ V3) @ ((cINSERT @ V0) @ cEMPTY)))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V2) @ V3)) @ ((cvector_sub @ V0) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ (c~ @ ((c= @ V0) @ V3))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ ((chull @ caffine) @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ cEMPTY))))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V1) @ V4))) @ (cdistance @ ((c__comma__ @ V2) @ V3))))))))))))))))
(TSYLVESTER_GALLAI_LEMMA_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cbetween @ V1) @ ((c__comma__ @ V0) @ V3))) @ ((c/__caret__ @ (c~ @ ((cIN @ V2) @ ((chull @ caffine) @ ((cINSERT @ V0) @ ((cINSERT @ V3) @ cEMPTY)))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V2) @ V0)) @ ((cvector_sub @ V3) @ V0))) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V1))) @ (c~ @ ((c= @ V3) @ V0))))))) @ (c~ @ ((cIN @ V1) @ ((chull @ caffine) @ ((cINSERT @ V2) @ ((cINSERT @ V3) @ cEMPTY)))))))))))))))
(TGRASSMANN_PLUCKER_2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V3) @ ((cCONS @ V1) @ cNIL))))) @ (cdet @ (cvector @ ((cCONS @ V2) @ ((cCONS @ V0) @ cNIL)))))) @ ((creal_add @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V2) @ ((cCONS @ V1) @ cNIL))))) @ (cdet @ (cvector @ ((cCONS @ V3) @ ((cCONS @ V0) @ cNIL)))))) @ ((creal_mul @ (cdet @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V1) @ cNIL))))) @ (cdet @ (cvector @ ((cCONS @ V2) @ ((cCONS @ V3) @ cNIL))))))))))))))))
(Tparallel,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cparallel @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))) @ ((c= @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_mul @ ((creal_sub @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))))
(TTARSKI_AXIOM_4_EUCLIDEAN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((cbetween @ V1) @ ((c__comma__ @ V0) @ V4))) @ ((c= @ (cdistance @ ((c__comma__ @ V1) @ V4))) @ (cdistance @ ((c__comma__ @ V2) @ V3)))))))))))))))
(TTARSKI_AXIOM_7_EUCLIDEAN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cbetween @ V1) @ ((c__comma__ @ V4) @ V0))) @ ((cbetween @ V3) @ ((c__comma__ @ V2) @ V0)))) @ (c? @ (^[V5]: ((c/__caret__ @ ((cbetween @ V5) @ ((c__comma__ @ V1) @ V2))) @ ((cbetween @ V5) @ ((c__comma__ @ V3) @ V4)))))))))))))))))
(TTARSKI_AXIOM_9_EUCLIDEAN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V2) @ V0))) @ (cdistance @ ((c__comma__ @ V2) @ V1)))) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V4) @ V0))) @ (cdistance @ ((c__comma__ @ V4) @ V1)))) @ ((c= @ (cdistance @ ((c__comma__ @ V3) @ V0))) @ (cdistance @ ((c__comma__ @ V3) @ V1))))))) @ ((c__caret__/ @ ((cbetween @ V4) @ ((c__comma__ @ V2) @ V3))) @ ((c__caret__/ @ ((cbetween @ V3) @ ((c__comma__ @ V4) @ V2))) @ ((cbetween @ V2) @ ((c__comma__ @ V3) @ V4))))))))))))))))
(TRADICAL_LINE_LINE_INTERSECTION_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (c~ @ ((cparallel @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3)))) @ (((cis_intersection @ V4) @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3)))))))))))) @ (cradical @ ((c$ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))))
(TRADICAL_LINE_LINE_INTERSECTION_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (c~ @ ((cparallel @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3)))) @ (((cis_intersection @ V4) @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3)))))))))))) @ (cradical @ ((c$ @ V4) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))))
(Tconstructible_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cconstructible @ V0)) @ ((c/__caret__ @ (cconstructible @ V1)) @ ((c/__caret__ @ (cconstructible @ V2)) @ ((c/__caret__ @ (cconstructible @ V3)) @ ((c/__caret__ @ (c~ @ ((cparallel @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3)))) @ (((cis_intersection @ V4) @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3)))))))) @ (cconstructible @ V4)))))))))))))
(Tis_intersection,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((cis_intersection @ V3) @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V4))) @ ((c/__caret__ @ (((ccollinear3 @ V0) @ V3) @ V1)) @ (((ccollinear3 @ V2) @ V3) @ V4))))))))))))))
(TRADICAL_LINE_CIRCLE_INTERSECTION_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V4) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c/__caret__ @ (((ccollinear3 @ V0) @ V5) @ V1)) @ ((c= @ (clength @ ((c__comma__ @ V2) @ V5))) @ (clength @ ((c__comma__ @ V3) @ V4)))))))))))))))) @ (cradical @ ((c$ @ V5) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))))))
(TRADICAL_LINE_CIRCLE_INTERSECTION_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V4) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c/__caret__ @ (((ccollinear3 @ V0) @ V5) @ V1)) @ ((c= @ (clength @ ((c__comma__ @ V2) @ V5))) @ (clength @ ((c__comma__ @ V3) @ V4)))))))))))))))) @ (cradical @ ((c$ @ V5) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))))))
(Tconstructible_RULES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cconstructible @ V0)) @ ((c/__caret__ @ (cconstructible @ V1)) @ ((c/__caret__ @ (cconstructible @ V2)) @ ((c/__caret__ @ (cconstructible @ V3)) @ ((c/__caret__ @ (cconstructible @ V4)) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c/__caret__ @ (((ccollinear3 @ V0) @ V5) @ V1)) @ ((c= @ (clength @ ((c__comma__ @ V2) @ V5))) @ (clength @ ((c__comma__ @ V3) @ V4))))))))))) @ (cconstructible @ V5)))))))))))))))
(TRADICAL_CIRCLE_CIRCLE_INTERSECTION_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V4) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V5) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V5) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((c= @ (clength @ ((c__comma__ @ V0) @ V6))) @ (clength @ ((c__comma__ @ V2) @ V3)))) @ ((c/__caret__ @ ((c= @ (clength @ ((c__comma__ @ V1) @ V6))) @ (clength @ ((c__comma__ @ V4) @ V5)))) @ (c~ @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ (clength @ ((c__comma__ @ V2) @ V3))) @ (clength @ ((c__comma__ @ V4) @ V5)))))))))))))))))))) @ (cradical @ ((c$ @ V6) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))))))))
(TRADICAL_CIRCLE_CIRCLE_INTERSECTION_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V1) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V4) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V4) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V5) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (cradical @ ((c$ @ V5) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c/__caret__ @ ((c= @ (clength @ ((c__comma__ @ V0) @ V6))) @ (clength @ ((c__comma__ @ V2) @ V3)))) @ ((c/__caret__ @ ((c= @ (clength @ ((c__comma__ @ V1) @ V6))) @ (clength @ ((c__comma__ @ V4) @ V5)))) @ (c~ @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ (clength @ ((c__comma__ @ V2) @ V3))) @ (clength @ ((c__comma__ @ V4) @ V5)))))))))))))))))))) @ (cradical @ ((c$ @ V6) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))))))))
(Tconstructible_RULES_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (cconstructible @ V0)) @ ((c/__caret__ @ (cconstructible @ V1)) @ ((c/__caret__ @ (cconstructible @ V2)) @ ((c/__caret__ @ (cconstructible @ V3)) @ ((c/__caret__ @ (cconstructible @ V4)) @ ((c/__caret__ @ (cconstructible @ V5)) @ ((c/__caret__ @ (c~ @ ((c/__caret__ @ ((c= @ V0) @ V3)) @ ((c= @ (clength @ ((c__comma__ @ V1) @ V2))) @ (clength @ ((c__comma__ @ V4) @ V5)))))) @ ((c/__caret__ @ ((c= @ (clength @ ((c__comma__ @ V0) @ V6))) @ (clength @ ((c__comma__ @ V1) @ V2)))) @ ((c= @ (clength @ ((c__comma__ @ V3) @ V6))) @ (clength @ ((c__comma__ @ V4) @ V5)))))))))))) @ (cconstructible @ V6)))))))))))))))))
(TTARSKI_AXIOM_5_EUCLIDEAN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V2))) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V2))) @ (cdistance @ ((c__comma__ @ V1) @ V3)))) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V4))) @ (cdistance @ ((c__comma__ @ V1) @ V6)))) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V2) @ V4))) @ (cdistance @ ((c__comma__ @ V3) @ V6)))) @ ((c/__caret__ @ ((cbetween @ V2) @ ((c__comma__ @ V0) @ V5))) @ ((c/__caret__ @ ((cbetween @ V3) @ ((c__comma__ @ V1) @ V7))) @ ((c= @ (cdistance @ ((c__comma__ @ V2) @ V5))) @ (cdistance @ ((c__comma__ @ V3) @ V7)))))))))) @ ((c= @ (cdistance @ ((c__comma__ @ V4) @ V5))) @ (cdistance @ ((c__comma__ @ V6) @ V7)))))))))))))))))))))
(TNINE_POINT_CIRCLE_1_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: ((c==> @ ((c/__caret__ @ (c~ @ (ccollinear @ ((cINSERT @ V6) @ ((cINSERT @ V7) @ ((cINSERT @ V5) @ cEMPTY)))))) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V6) @ V7))) @ V2)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V7) @ V5))) @ V0)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V5) @ V6))) @ V1)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V0))) @ V10)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V1))) @ V10)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V2))) @ V10)) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V6) @ ((cINSERT @ V7) @ ((cINSERT @ V3) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V6) @ V7)) @ ((cvector_sub @ V5) @ V3))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V7) @ ((cINSERT @ V5) @ ((cINSERT @ V4) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V7) @ V5)) @ ((cvector_sub @ V6) @ V4))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V5) @ ((cINSERT @ V6) @ ((cINSERT @ V9) @ cEMPTY))))) @ ((corthogonal @ ((cvector_sub @ V5) @ V6)) @ ((cvector_sub @ V7) @ V9))))))))))))))) @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V9))) @ V10)))))))))))))))))))))))))
(TNINE_POINT_CIRCLE_1_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: ((c==> @ ((c/__caret__ @ (c~ @ (ccollinear @ ((cINSERT @ V5) @ ((cINSERT @ V6) @ ((cINSERT @ V4) @ cEMPTY)))))) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V5) @ V6))) @ V2)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V6) @ V4))) @ V0)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V4) @ V5))) @ V1)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V0))) @ V10)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V1))) @ V10)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V2))) @ V10)) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V5) @ ((cINSERT @ V6) @ ((cINSERT @ V9) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V5) @ V6)) @ ((cvector_sub @ V4) @ V9))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V6) @ ((cINSERT @ V4) @ ((cINSERT @ V3) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V6) @ V4)) @ ((cvector_sub @ V5) @ V3))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V4) @ ((cINSERT @ V5) @ ((cINSERT @ V7) @ cEMPTY))))) @ ((corthogonal @ ((cvector_sub @ V4) @ V5)) @ ((cvector_sub @ V6) @ V7))))))))))))))) @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V9))) @ V10)))))))))))))))))))))))))
(TNINE_POINT_CIRCLE_1_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: ((c==> @ ((c/__caret__ @ (c~ @ (ccollinear @ ((cINSERT @ V5) @ ((cINSERT @ V6) @ ((cINSERT @ V4) @ cEMPTY)))))) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V5) @ V6))) @ V2)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V6) @ V4))) @ V0)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V4) @ V5))) @ V1)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V0))) @ V10)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V1))) @ V10)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V2))) @ V10)) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V5) @ ((cINSERT @ V6) @ ((cINSERT @ V3) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V5) @ V6)) @ ((cvector_sub @ V4) @ V3))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V6) @ ((cINSERT @ V4) @ ((cINSERT @ V9) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V6) @ V4)) @ ((cvector_sub @ V5) @ V9))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V4) @ ((cINSERT @ V5) @ ((cINSERT @ V7) @ cEMPTY))))) @ ((corthogonal @ ((cvector_sub @ V4) @ V5)) @ ((cvector_sub @ V6) @ V7))))))))))))))) @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V9))) @ V10)))))))))))))))))))))))))
(TFEUERBACH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: (c! @ (^[V11]: (c! @ (^[V12]: ((c==> @ ((c/__caret__ @ (c~ @ (ccollinear @ ((cINSERT @ V6) @ ((cINSERT @ V4) @ ((cINSERT @ V7) @ cEMPTY)))))) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V6) @ V4))) @ V2)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V4) @ V7))) @ V0)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V7) @ V6))) @ V1)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V9) @ V0))) @ V10)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V9) @ V1))) @ V10)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V9) @ V2))) @ V10)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V11) @ V5))) @ V12)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V11) @ V8))) @ V12)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V11) @ V3))) @ V12)) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V6) @ ((cINSERT @ V4) @ ((cINSERT @ V3) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V6) @ V4)) @ ((cvector_sub @ V11) @ V3))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V4) @ ((cINSERT @ V7) @ ((cINSERT @ V5) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V4) @ V7)) @ ((cvector_sub @ V11) @ V5))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V6) @ ((cINSERT @ V7) @ ((cINSERT @ V8) @ cEMPTY))))) @ ((corthogonal @ ((cvector_sub @ V6) @ V7)) @ ((cvector_sub @ V11) @ V8)))))))))))))))))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ V9) @ V11)) @ ((c= @ V10) @ V12))) @ (c?! @ (^[V13]: ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V9) @ V13))) @ V10)) @ ((c= @ (cdistance @ ((c__comma__ @ V11) @ V13))) @ V12)))))))))))))))))))))))))))))))))
(TNINE_POINT_CIRCLE_2_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: (c! @ (^[V11]: ((c==> @ ((c/__caret__ @ (c~ @ (ccollinear @ ((cINSERT @ V3) @ ((cINSERT @ V5) @ ((cINSERT @ V10) @ cEMPTY)))))) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V3) @ V5))) @ V2)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V5) @ V10))) @ V0)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V10) @ V3))) @ V1)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V0))) @ V11)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V1))) @ V11)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V2))) @ V11)) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V3) @ ((cINSERT @ V5) @ ((cINSERT @ V7) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V3) @ V5)) @ ((cvector_sub @ V10) @ V7))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V5) @ ((cINSERT @ V10) @ ((cINSERT @ V4) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V5) @ V10)) @ ((cvector_sub @ V3) @ V4))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V10) @ ((cINSERT @ V3) @ ((cINSERT @ V6) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V10) @ V3)) @ ((cvector_sub @ V5) @ V6))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V9) @ ((cINSERT @ V3) @ ((cINSERT @ V4) @ cEMPTY))))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V9) @ ((cINSERT @ V5) @ ((cINSERT @ V6) @ cEMPTY))))) @ (ccollinear @ ((cINSERT @ V9) @ ((cINSERT @ V10) @ ((cINSERT @ V7) @ cEMPTY)))))))))))))))))))) @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ (cmidpoint @ ((c__comma__ @ V9) @ V10))))) @ V11)))))))))))))))))))))))))))
(TNINE_POINT_CIRCLE_2_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: (c! @ (^[V11]: ((c==> @ ((c/__caret__ @ (c~ @ (ccollinear @ ((cINSERT @ V3) @ ((cINSERT @ V10) @ ((cINSERT @ V6) @ cEMPTY)))))) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V3) @ V10))) @ V2)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V10) @ V6))) @ V0)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V6) @ V3))) @ V1)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V0))) @ V11)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V1))) @ V11)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V2))) @ V11)) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V3) @ ((cINSERT @ V10) @ ((cINSERT @ V7) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V3) @ V10)) @ ((cvector_sub @ V6) @ V7))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V10) @ ((cINSERT @ V6) @ ((cINSERT @ V4) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V10) @ V6)) @ ((cvector_sub @ V3) @ V4))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V6) @ ((cINSERT @ V3) @ ((cINSERT @ V5) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V6) @ V3)) @ ((cvector_sub @ V10) @ V5))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V9) @ ((cINSERT @ V3) @ ((cINSERT @ V4) @ cEMPTY))))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V9) @ ((cINSERT @ V10) @ ((cINSERT @ V5) @ cEMPTY))))) @ (ccollinear @ ((cINSERT @ V9) @ ((cINSERT @ V6) @ ((cINSERT @ V7) @ cEMPTY)))))))))))))))))))) @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ (cmidpoint @ ((c__comma__ @ V9) @ V10))))) @ V11)))))))))))))))))))))))))))
(TNINE_POINT_CIRCLE_2_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: (c! @ (^[V10]: (c! @ (^[V11]: ((c==> @ ((c/__caret__ @ (c~ @ (ccollinear @ ((cINSERT @ V10) @ ((cINSERT @ V4) @ ((cINSERT @ V6) @ cEMPTY)))))) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V10) @ V4))) @ V2)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V4) @ V6))) @ V0)) @ ((c/__caret__ @ ((c= @ (cmidpoint @ ((c__comma__ @ V6) @ V10))) @ V1)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V0))) @ V11)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V1))) @ V11)) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ V2))) @ V11)) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V10) @ ((cINSERT @ V4) @ ((cINSERT @ V7) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V10) @ V4)) @ ((cvector_sub @ V6) @ V7))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V4) @ ((cINSERT @ V6) @ ((cINSERT @ V3) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V4) @ V6)) @ ((cvector_sub @ V10) @ V3))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V6) @ ((cINSERT @ V10) @ ((cINSERT @ V5) @ cEMPTY))))) @ ((c/__caret__ @ ((corthogonal @ ((cvector_sub @ V6) @ V10)) @ ((cvector_sub @ V4) @ V5))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V9) @ ((cINSERT @ V10) @ ((cINSERT @ V3) @ cEMPTY))))) @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V9) @ ((cINSERT @ V4) @ ((cINSERT @ V5) @ cEMPTY))))) @ (ccollinear @ ((cINSERT @ V9) @ ((cINSERT @ V6) @ ((cINSERT @ V7) @ cEMPTY)))))))))))))))))))) @ ((c= @ (cdistance @ ((c__comma__ @ V8) @ (cmidpoint @ ((c__comma__ @ V9) @ V10))))) @ V11)))))))))))))))))))))))))))
(TCONTINUOUS_AT_SQRT,(c! @ (^[V0]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ V0))) @ ((ccontinuous @ ((co @ clift) @ ((co @ csqrt) @ cdrop))) @ (cat @ V0))))))
(TNORM_1_POS,(c! @ (^[V0]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ V0))) @ ((c= @ (cvector_norm @ V0)) @ (cdrop @ V0))))))
(TNORM_REAL,(c! @ (^[V0]: ((c= @ (cvector_norm @ V0)) @ (creal_abs @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TABS_DROP,(c! @ (^[V0]: ((c= @ (cvector_norm @ V0)) @ (creal_abs @ (cdrop @ V0))))))
(TDROP_NEG,(c! @ (^[V0]: ((c= @ (cdrop @ (cvector_neg @ V0))) @ (creal_neg @ (cdrop @ V0))))))
(Tdrop,(c! @ (^[V0]: ((c= @ (cdrop @ V0)) @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TLIFT_DROP_conjunct0,(c! @ (^[V0]: ((c= @ (clift @ (cdrop @ V0))) @ V0))))
(TVECTOR_EXPAND_1,(c! @ (^[V0]: ((c= @ V0) @ (cvector @ ((cCONS @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ cNIL))))))
(TVECTOR_ONE,(c! @ (^[V0]: ((c= @ V0) @ (clambda @ (^[V1]: ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TDROP_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cdrop @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))
(TNEGLIGIBLE_CONVEX_HULL_1,(c! @ (^[V0]: (cnegligible @ ((chull @ cconvex) @ ((cINSERT @ V0) @ cEMPTY))))))
(TNEGLIGIBLE_AFFINE_HULL_1,(c! @ (^[V0]: (cnegligible @ ((chull @ caffine) @ ((cINSERT @ V0) @ cEMPTY))))))
(TSPHERE_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csphere @ ((c__comma__ @ V0) @ V1))) @ (((cCOND @ ((creal_lt @ V1) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ cEMPTY) @ ((cINSERT @ ((cvector_sub @ V0) @ (clift @ V1))) @ ((cINSERT @ ((cvector_add @ V0) @ (clift @ V1))) @ cEMPTY)))))))))
(TCBALL_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccball @ ((c__comma__ @ V0) @ V1))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cvector_sub @ V0) @ (clift @ V1))) @ ((cvector_add @ V0) @ (clift @ V1)))) @ cNIL))))))))
(TBALL_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cball @ ((c__comma__ @ V0) @ V1))) @ (copen_interval @ ((c__comma__ @ ((cvector_sub @ V0) @ (clift @ V1))) @ ((cvector_add @ V0) @ (clift @ V1))))))))))
(TFINITE_SPHERE_1,(c! @ (^[V0]: (c! @ (^[V1]: (cFINITE @ (csphere @ ((c__comma__ @ V0) @ V1))))))))
(THAS_BOUNDED_VARIATION_AFFINITY2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((chas_bounded_variation_on @ (^[V4]: (V2 @ ((cvector_add @ ((c% @ V1) @ V4)) @ V0)))) @ ((cIMAGE @ (^[V4]: ((cvector_add @ ((c% @ (creal_inv @ V1)) @ V4)) @ (cvector_neg @ ((c% @ (creal_inv @ V1)) @ V0))))) @ V3))) @ ((c__caret__/ @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((chas_bounded_variation_on @ V2) @ V3))))))))))))
(TVECTOR_VARIATION_AFFINITY2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cvector_variation @ ((cIMAGE @ (^[V4]: ((cvector_add @ ((c% @ (creal_inv @ V1)) @ V4)) @ (cvector_neg @ ((c% @ (creal_inv @ V1)) @ V0))))) @ V2)) @ (^[V4]: (V3 @ ((cvector_add @ ((c% @ V1) @ V4)) @ V0))))) @ (((cCOND @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cvector_variation @ V2) @ V3))))))))))))
(TIN_IMAGE_LIFT_DROP_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ ((cIMAGE @ clift) @ V1))) @ ((cIN @ (cdrop @ V0)) @ V1)))))))
(TSECOND_MEAN_VALUE_THEOREM_BONNET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL))) @ cEMPTY))) @ ((c/__caret__ @ ((cintegrable_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (V1 @ V4)))))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((creal_le @ (cdrop @ V4)) @ (cdrop @ V5))))) @ ((creal_le @ (V1 @ V4)) @ (V1 @ V5))))))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL))) @ (^[V5]: ((c% @ (V1 @ V5)) @ (V3 @ V5))))) @ ((c% @ (V1 @ V2)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V2)) @ cNIL))) @ V3))))))))))))))))
(TSECOND_MEAN_VALUE_THEOREM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL))) @ cEMPTY))) @ ((c/__caret__ @ ((cintegrable_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((creal_le @ (cdrop @ V4)) @ (cdrop @ V5))))) @ ((creal_le @ (V1 @ V4)) @ (V1 @ V5)))))))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL))) @ (^[V5]: ((c% @ (V1 @ V5)) @ (V3 @ V5))))) @ ((cvector_add @ ((c% @ (V1 @ V0)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V4)) @ cNIL))) @ V3))) @ ((c% @ (V1 @ V2)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V2)) @ cNIL))) @ V3)))))))))))))))))
(TINCREASING_VECTOR_VARIATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL))) @ cEMPTY))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))))) @ ((creal_le @ (cdrop @ (V1 @ V3))) @ (cdrop @ (V1 @ V4)))))))))) @ ((c= @ ((cvector_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL))) @ V1)) @ ((creal_sub @ (cdrop @ (V1 @ V0))) @ (cdrop @ (V1 @ V2))))))))))))
(TDECREASING_VECTOR_VARIATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL))) @ cEMPTY))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V4))))) @ ((creal_le @ (cdrop @ (V1 @ V4))) @ (cdrop @ (V1 @ V3)))))))))) @ ((c= @ ((cvector_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL))) @ V1)) @ ((creal_sub @ (cdrop @ (V1 @ V0))) @ (cdrop @ (V1 @ V2))))))))))))
(TVECTOR_VARIATION_CONTINUOUS_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL))))) @ ((c= @ ((ccontinuous @ (^[V4]: (clift @ ((cvector_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V4)) @ cNIL))) @ V1)))) @ ((cwithin @ (cat @ V3)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ ((ccontinuous @ V1) @ ((cwithin @ (cat @ V3)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))))
(TVECTOR_VARIATION_CONTINUOUS_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL)))) @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL))))) @ ((c= @ ((ccontinuous @ (^[V4]: (clift @ ((cvector_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V4)) @ cNIL))) @ V1)))) @ ((cwithin @ (cat @ V2)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ ((ccontinuous @ V1) @ ((cwithin @ (cat @ V2)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))))
(TDECREASING_LEFT_LIMIT_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ ((creal_le @ (cdrop @ V4)) @ (cdrop @ V5))))) @ ((creal_le @ (cdrop @ (V1 @ V5))) @ (cdrop @ (V1 @ V4))))))))) @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL))))) @ (c? @ (^[V4]: (((c--> @ V1) @ V4) @ ((cwithin @ (cat @ V3)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))))
(TINCREASING_LEFT_LIMIT_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ ((creal_le @ (cdrop @ V4)) @ (cdrop @ V5))))) @ ((creal_le @ (cdrop @ (V1 @ V4))) @ (cdrop @ (V1 @ V5))))))))) @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL))))) @ (c? @ (^[V4]: (((c--> @ V1) @ V4) @ ((cwithin @ (cat @ V3)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))))
(TDECREASING_RIGHT_LIMIT_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL)))) @ ((creal_le @ (cdrop @ V4)) @ (cdrop @ V5))))) @ ((creal_le @ (cdrop @ (V1 @ V5))) @ (cdrop @ (V1 @ V4))))))))) @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL))))) @ (c? @ (^[V4]: (((c--> @ V1) @ V4) @ ((cwithin @ (cat @ V2)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))))
(TINCREASING_RIGHT_LIMIT_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL)))) @ ((creal_le @ (cdrop @ V4)) @ (cdrop @ V5))))) @ ((creal_le @ (cdrop @ (V1 @ V4))) @ (cdrop @ (V1 @ V5))))))))) @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL))))) @ (c? @ (^[V4]: (((c--> @ V1) @ V4) @ ((cwithin @ (cat @ V2)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))))
(TPATH_IMAGE_SHIFTPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1)))) @ ((c= @ (cpath_image @ ((cshiftpath @ V0) @ V1))) @ (cpath_image @ V1))))))))
(TPATH_SHIFTPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))) @ ((cIN @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))))) @ (cpath @ ((cshiftpath @ V0) @ V1))))))))
(TPIECEWISE_DIFFERENTIABLE_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_le @ (cdrop @ V3)) @ (cdrop @ V0))) @ ((c/__caret__ @ ((creal_le @ (cdrop @ V0)) @ (cdrop @ V4))) @ ((c/__caret__ @ ((c= @ (V1 @ V0)) @ (V2 @ V0))) @ ((c/__caret__ @ ((cpiecewise_differentiable_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V0)) @ cNIL)))) @ ((cpiecewise_differentiable_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V4)) @ cNIL)))))))) @ ((cpiecewise_differentiable_on @ (^[V5]: (((cCOND @ ((creal_le @ (cdrop @ V5)) @ (cdrop @ V0))) @ (V1 @ V5)) @ (V2 @ V5)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))
(THAS_BOUNDED_VARIATION_TRANSLATION2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chas_bounded_variation_on @ (^[V3]: (V1 @ ((cvector_add @ V0) @ V3)))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ (cvector_neg @ V0)) @ V3))) @ V2))) @ ((chas_bounded_variation_on @ V1) @ V2)))))))))
(TPATHSTART_SUBPATH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cpathstart @ (((csubpath @ V2) @ V0) @ V1))) @ (V1 @ V2)))))))))
(TPATHFINISH_SUBPATH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cpathfinish @ (((csubpath @ V0) @ V2) @ V1))) @ (V1 @ V2)))))))))
(THAS_BOUNDED_VARIATION_ON_COMBINE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_le @ (cdrop @ V0)) @ (cdrop @ V2))) @ ((creal_le @ (cdrop @ V2)) @ (cdrop @ V3)))) @ ((c= @ ((chas_bounded_variation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL)))) @ ((c/__caret__ @ ((chas_bounded_variation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((chas_bounded_variation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))))
(THAS_BOUNDED_VECTOR_VARIATION_LEFT_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL))))) @ (c? @ (^[V4]: (((c--> @ V1) @ V4) @ ((cwithin @ (cat @ V3)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))))
(THAS_BOUNDED_VECTOR_VARIATION_RIGHT_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL)))) @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL))))) @ (c? @ (^[V4]: (((c--> @ V1) @ V4) @ ((cwithin @ (cat @ V2)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))))
(THAS_INTEGRAL_COMBINE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((creal_le @ (cdrop @ V4)) @ (cdrop @ V0))) @ ((c/__caret__ @ ((creal_le @ (cdrop @ V0)) @ (cdrop @ V5))) @ ((c/__caret__ @ (((chas_integral @ V1) @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V0)) @ cNIL)))) @ (((chas_integral @ V1) @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V5)) @ cNIL))))))) @ (((chas_integral @ V1) @ ((cvector_add @ V2) @ V3)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))))))))))))))))
(TINTEGRABLE_COMBINE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_le @ (cdrop @ V2)) @ (cdrop @ V0))) @ ((c/__caret__ @ ((creal_le @ (cdrop @ V0)) @ (cdrop @ V3))) @ ((c/__caret__ @ ((cintegrable_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ ((cintegrable_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL))))))) @ ((cintegrable_on @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))))))))))))
(TSIMPLE_PATH_SHIFTPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csimple_path @ V1)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))) @ ((cIN @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))))) @ (csimple_path @ ((cshiftpath @ V0) @ V1))))))))
(TSHIFTPATH_SHIFTPATH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))) @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))))) @ ((c= @ (((cshiftpath @ ((cvector_sub @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ ((cshiftpath @ V0) @ V1)) @ V2)) @ (V1 @ V2))))))))))
(TCLOSED_SHIFTPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))) @ ((cIN @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL))))) @ ((c= @ (cpathfinish @ ((cshiftpath @ V0) @ V1))) @ (cpathstart @ ((cshiftpath @ V0) @ V1)))))))))
(TCONTINUOUS_WITHIN_LIFT_SQRT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdrop @ V2)))))) @ ((ccontinuous @ ((co @ clift) @ ((co @ csqrt) @ cdrop))) @ ((cwithin @ (cat @ V0)) @ V1))))))))
(TDROP_IN_IMAGE_DROP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ (cdrop @ V0)) @ ((cIMAGE @ cdrop) @ V1))) @ ((cIN @ V0) @ V1)))))))
(TVECTOR_VARIATION_TRANSLATION2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvector_variation @ ((cIMAGE @ (^[V3]: ((cvector_add @ (cvector_neg @ V0)) @ V3))) @ V1)) @ (^[V3]: (V2 @ ((cvector_add @ V0) @ V3))))) @ ((cvector_variation @ V1) @ V2)))))))))
(TVECTOR_VARIATION_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvector_variation @ V1) @ (^[V3]: (V2 @ ((cvector_add @ V0) @ V3))))) @ ((cvector_variation @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ V2)))))))))
(THAS_BOUNDED_VARIATION_ON_ID,(c! @ (^[V0]: (c! @ (^[V1]: ((chas_bounded_variation_on @ (^[V2]: V2)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
(TCONTENT_POS_LT_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_lt @ (cdrop @ V0)) @ (cdrop @ V1))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))))
(THOMEOMORPHIC_OPEN_INTERVAL_UNIV_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_lt @ (cdrop @ V0)) @ (cdrop @ V1))) @ ((chomeomorphic @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ cUNIV)))))))
(TCONTENT_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_le @ (cdrop @ V1)) @ (cdrop @ V0))) @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL)))) @ ((creal_sub @ (cdrop @ V0)) @ (cdrop @ V1)))))))))
(TINTERVAL_LOWERBOUND_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_le @ (cdrop @ V1)) @ (cdrop @ V0))) @ ((c= @ (cinterval_lowerbound @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL)))) @ V1)))))))
(TCLOSED_OPEN_INTERVAL_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((creal_le @ (cdrop @ V0)) @ (cdrop @ V1))) @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ ((cUNION @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))))
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(TCLOSED_DIFF_OPEN_INTERVAL_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDIFF @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (copen_interval @ ((c__comma__ @ V0) @ V1)))) @ (((cCOND @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ cEMPTY)) @ cEMPTY) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))))
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(TARC_SIMPLE_PATH_SUBPATH_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (csimple_path @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ (cvec @ (cNUMERAL @ (cBIT1 @ c_0))))) @ cNIL)))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((creal_lt @ (creal_abs @ ((creal_sub @ (cdrop @ V0)) @ (cdrop @ V1)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))) @ (carc @ (((csubpath @ V0) @ V1) @ V2))))))))))
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(TIN_INTERVAL_1_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ V1) @ (copen_interval @ ((c__comma__ @ V0) @ V2)))) @ ((c/__caret__ @ ((creal_lt @ (cdrop @ V0)) @ (cdrop @ V1))) @ ((creal_lt @ (cdrop @ V1)) @ (cdrop @ V2)))))))))))
(TIN_INTERVAL_1_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((creal_le @ (cdrop @ V0)) @ (cdrop @ V1))) @ ((creal_le @ (cdrop @ V1)) @ (cdrop @ V2)))))))))))
(TVECTOR_VARIATION_MINUS_FUNCTION_MONOTONE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((chas_bounded_variation_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V2)) @ cNIL)))) @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL))) @ cEMPTY))))) @ ((creal_le @ ((creal_sub @ ((cvector_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL))) @ V3)) @ (cdrop @ ((cvector_sub @ (V3 @ V0)) @ (V3 @ V1))))) @ ((creal_sub @ ((cvector_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V2)) @ cNIL))) @ V3)) @ (cdrop @ ((cvector_sub @ (V3 @ V2)) @ (V3 @ V4)))))))))))))))))
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(TDISJOINT_INTERVAL_1_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V0)) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ cEMPTY)) @ ((c__caret__/ @ ((creal_lt @ (cdrop @ V0)) @ (cdrop @ V3))) @ ((c__caret__/ @ ((creal_lt @ (cdrop @ V2)) @ (cdrop @ V1))) @ ((c__caret__/ @ ((creal_lt @ (cdrop @ V0)) @ (cdrop @ V1))) @ ((creal_lt @ (cdrop @ V2)) @ (cdrop @ V3)))))))))))))))
(TEQ_INTERVAL_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V3)) @ cNIL)))) @ ((c__caret__/ @ ((c/__caret__ @ ((creal_lt @ (cdrop @ V2)) @ (cdrop @ V0))) @ ((creal_lt @ (cdrop @ V3)) @ (cdrop @ V1)))) @ ((c/__caret__ @ ((c= @ (cdrop @ V0)) @ (cdrop @ V1))) @ ((c= @ (cdrop @ V2)) @ (cdrop @ V3))))))))))))))
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(TSUMMABLE_BILINEAR_PARTIAL_PRE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cbilinear @ V2)) @ ((c/__caret__ @ (((c--> @ (^[V5]: ((V2 @ (V3 @ ((c+ @ V5) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V4 @ V5)))) @ V0) @ csequentially)) @ ((csummable @ (cfrom @ V1)) @ (^[V5]: ((V2 @ ((cvector_sub @ (V3 @ ((c+ @ V5) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (V3 @ V5))) @ (V4 @ V5))))))) @ ((csummable @ (cfrom @ V1)) @ (^[V5]: ((V2 @ (V3 @ V5)) @ ((cvector_sub @ (V4 @ V5)) @ (V4 @ ((c- @ V5) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))))))))))
(THAS_DERIVATIVE_SQNORM_AT,(c! @ (^[V0]: (((chas_derivative @ (^[V1]: (clift @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (^[V1]: ((c% @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (clift @ ((cdot @ V0) @ V1))))) @ (cat @ V0)))))
(TL1_LE_NORM,(c! @ (^[V0]: ((creal_le @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V1]: (creal_abs @ ((c$ @ V0) @ V1))))) @ ((creal_mul @ (csqrt @ (creal_of_num @ (cdimindex @ cUNIV)))) @ (cvector_norm @ V0))))))
(TNORM_LE_L1,(c! @ (^[V0]: ((creal_le @ (cvector_norm @ V0)) @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V1]: (creal_abs @ ((c$ @ V0) @ V1))))))))
(TNORM_LE_INFNORM,(c! @ (^[V0]: ((creal_le @ (cvector_norm @ V0)) @ ((creal_mul @ (csqrt @ (creal_of_num @ (cdimindex @ cUNIV)))) @ (cinfnorm @ V0))))))
(TMEASURABLE_ON_CONST,(c! @ (^[V0]: ((cmeasurable_on @ (^[V1]: V0)) @ cUNIV))))
(TLIMPT_OF_UNIV,(c! @ (^[V0]: ((climit_point_of @ V0) @ cUNIV))))
(TDIFFERENTIABLE_SQNORM_AT,(c! @ (^[V0]: ((cdifferentiable @ (^[V1]: (clift @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (cat @ V0)))))
(TCONTINUOUS_AT_LIFT_INFNORM,(c! @ (^[V0]: ((ccontinuous @ ((co @ clift) @ cinfnorm)) @ (cat @ V0)))))
(TVECTOR_IN_ORTHONORMAL_BASIS,(c! @ (^[V0]: ((c==> @ ((c= @ (cvector_norm @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V0) @ V1)) @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ V1)) @ ((c/__caret__ @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((c= @ (cvector_norm @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((c/__caret__ @ (cindependent @ V1)) @ ((c/__caret__ @ ((cHAS_SIZE @ V1) @ (cdimindex @ cUNIV))) @ ((c= @ (cspan @ V1)) @ cUNIV))))))))))))
(TORTHOGONAL_MATRIX_EXISTS_BASIS,(c! @ (^[V0]: ((c==> @ ((c= @ (cvector_norm @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c? @ (^[V1]: ((c/__caret__ @ (corthogonal_matrix @ V1)) @ ((c= @ ((cmatrix_vector_mul @ V1) @ (cbasis @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0))))))))
(TPATH_CONNECTED_PUNCTURED_UNIVERSE,(c! @ (^[V0]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (cpath_connected @ ((cDIFF @ cUNIV) @ ((cINSERT @ V0) @ cEMPTY)))))))
(TCONNECTED_PUNCTURED_UNIVERSE,(c! @ (^[V0]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (cconnected @ ((cDIFF @ cUNIV) @ ((cINSERT @ V0) @ cEMPTY)))))))
(TORTHOGONAL_TO_VECTOR_EXISTS,(c! @ (^[V0]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((corthogonal @ V0) @ V1))))))))
(TROTATION_MATRIX_EXISTS_BASIS,(c! @ (^[V0]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c= @ (cvector_norm @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ (c? @ (^[V1]: ((c/__caret__ @ (crotation_matrix @ V1)) @ ((c= @ ((cmatrix_vector_mul @ V1) @ (cbasis @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0))))))))
(TDIM_HYPERPLANE,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ (cdim @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c= @ ((cdot @ V0) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V2))))))) @ ((c- @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TROTOINVERSION_MATRIX_REFLECT_ALONG,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ (crotoinversion_matrix @ (cmatrix @ (creflect_along @ V0)))))))
(TVECTOR_IN_ORTHOGONAL_BASIS,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ (c? @ (^[V1]: ((c/__caret__ @ ((cIN @ V0) @ V1)) @ ((c/__caret__ @ (c~ @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V1))) @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ V1)) @ ((c/__caret__ @ (cindependent @ V1)) @ ((c/__caret__ @ ((cHAS_SIZE @ V1) @ (cdimindex @ cUNIV))) @ ((c= @ (cspan @ V1)) @ cUNIV))))))))))))
(TONORM_CONST,(c! @ (^[V0]: ((c= @ (conorm @ (^[V1]: V0))) @ (cvector_norm @ V0)))))
(Tinfnorm,(c! @ (^[V0]: ((c= @ (cinfnorm @ V0)) @ (csup @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (creal_abs @ ((c$ @ V0) @ V2))))))))))))
(TDET_MATRIX_REFLECT_ALONG,(c! @ (^[V0]: ((c= @ (cdet @ (cmatrix @ (creflect_along @ V0)))) @ (((cCOND @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TWITHIN_UNIV,(c! @ (^[V0]: ((c= @ ((cwithin @ (cat @ V0)) @ cUNIV)) @ (cat @ V0)))))
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(THOMEOMORPHIC_HYPERPLANE_STANDARD_HYPERPLANE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV))))) @ ((chomeomorphic @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V0) @ V5)) @ V1)) @ V5)))))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((c$ @ V5) @ V2)) @ V3)) @ V5))))))))))))))))
(TDIVISION_OF_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cdivision_of @ ((cIMAGE @ (cIMAGE @ (^[V4]: ((cvector_add @ ((c% @ V1) @ V4)) @ V0)))) @ V2)) @ ((cIMAGE @ (^[V4]: ((cvector_add @ ((c% @ V1) @ V4)) @ V0))) @ V3))) @ (((cCOND @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (((cCOND @ ((c= @ V3) @ cEMPTY)) @ ((c= @ V2) @ cEMPTY)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ (c~ @ ((c= @ V4) @ cEMPTY)))))))) @ ((cdivision_of @ V2) @ V3))))))))))))
(TBROUWER_BALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ (ccball @ ((c__comma__ @ V0) @ V1)))) @ ((cSUBSET @ ((cIMAGE @ V2) @ (ccball @ ((c__comma__ @ V0) @ V1)))) @ (ccball @ ((c__comma__ @ V0) @ V1)))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ (ccball @ ((c__comma__ @ V0) @ V1)))) @ ((c= @ (V2 @ V3)) @ V3))))))))))))
(TCONVEX_INTERMEDIATE_BALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ (cball @ ((c__comma__ @ V0) @ V1))) @ V2)) @ ((cSUBSET @ V2) @ (ccball @ ((c__comma__ @ V0) @ V1))))) @ (cconvex @ V2)))))))))
(TOPEN_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (copen @ V2)) @ (c~ @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ (copen @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ ((c% @ V1) @ V3)))) @ V2))))))))))
(TFACE_OF_INTER_SUPPORTING_HYPERPLANE_LE_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4)))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ ((cdot @ V0) @ V3)) @ V1)))))) @ ((cface_of @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4))))))) @ V2)))))))))
(TFACE_OF_INTER_SUPPORTING_HYPERPLANE_GE_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4)))))))) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_ge @ ((cdot @ V0) @ V3)) @ V1)))))) @ ((cface_of @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4))))))) @ V2)))))))))
(TFACE_OF_INTER_SUPPORTING_HYPERPLANE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ ((cdot @ V0) @ V3)) @ V1)))))) @ ((cface_of @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4))))))) @ V2)))))))))
(TEXPOSED_FACE_OF_INTER_SUPPORTING_HYPERPLANE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_le @ ((cdot @ V0) @ V3)) @ V1)))))) @ ((cexposed_face_of @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4))))))) @ V2)))))))))
(TFACE_OF_INTER_SUPPORTING_HYPERPLANE_GE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_ge @ ((cdot @ V0) @ V3)) @ V1)))))) @ ((cface_of @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4))))))) @ V2)))))))))
(TEXPOSED_FACE_OF_INTER_SUPPORTING_HYPERPLANE_GE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V2)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((creal_ge @ ((cdot @ V0) @ V3)) @ V1)))))) @ ((cexposed_face_of @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4))))))) @ V2)))))))))
(THOMEOMORPHIC_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((chomeomorphic @ V2) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ ((c% @ V1) @ V3)))) @ V2))))))))))
(TCONVEX_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cconvex @ V2)) @ (cconvex @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ ((c% @ V1) @ V3)))) @ V2))))))))))
(TCOMPACT_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (ccompact @ V2)) @ (ccompact @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ ((c% @ V1) @ V3)))) @ V2))))))))))
(TAFFINE_PARALLEL_SLICE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (caffine @ V2)) @ ((c__caret__/ @ ((c= @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((creal_le @ ((cdot @ V0) @ V4)) @ V1)) @ V4))))))) @ cEMPTY)) @ ((c__caret__/ @ ((cSUBSET @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((creal_le @ ((cdot @ V0) @ V4)) @ V1)) @ V4))))))) @ (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ (c~ @ ((c= @ V3) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((c= @ ((cINTER @ V2) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((cdot @ V3) @ V6)) @ V4)) @ V6))))))) @ ((cINTER @ V2) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ ((cdot @ V0) @ V6)) @ V1)) @ V6)))))))) @ ((c/__caret__ @ ((c= @ ((cINTER @ V2) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c= @ ((cdot @ V3) @ V6)) @ V4)) @ V6))))))) @ ((cINTER @ V2) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c= @ ((cdot @ V0) @ V6)) @ V1)) @ V6)))))))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((cIN @ ((cvector_add @ V5) @ V3)) @ V2)))))))))))))))))))))
(TAFF_DIM_AFFINE_INTER_HYPERPLANE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (caffine @ V2)) @ ((c= @ (caff_dim @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4)))))))) @ (((cCOND @ ((c= @ ((cINTER @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4))))))) @ cEMPTY)) @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (((cCOND @ ((cSUBSET @ V2) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c= @ ((cdot @ V0) @ V4)) @ V1)) @ V4))))))) @ (caff_dim @ V2)) @ ((cint_sub @ (caff_dim @ V2)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))))
(TAFFINE_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (caffine @ V2)) @ (caffine @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ ((c% @ V1) @ V3)))) @ V2))))))))))
(TCONVEX_HULL_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chull @ cconvex) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ ((c% @ V1) @ V3)))) @ V2))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ ((c% @ V1) @ V3)))) @ ((chull @ cconvex) @ V2))))))))))
(THOMEOMORPHIC_PUNCTURED_AFFINE_SPHERE_AFFINE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((cIN @ V3) @ (csphere @ ((c__comma__ @ V0) @ V1)))) @ ((c/__caret__ @ (caffine @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((c/__caret__ @ ((cIN @ V3) @ V2)) @ ((c/__caret__ @ (caffine @ V4)) @ ((c= @ (caff_dim @ V2)) @ ((cint_add @ (caff_dim @ V4)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))) @ ((chomeomorphic @ ((cDELETE @ ((cINTER @ (csphere @ ((c__comma__ @ V0) @ V1))) @ V2)) @ V3)) @ V4)))))))))))))
(TNULLHOMOTOPIC_INTO_SPHERE_EXTENSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cclosed @ V2)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ cEMPTY))) @ ((cSUBSET @ ((cIMAGE @ V3) @ V2)) @ (csphere @ ((c__comma__ @ V0) @ V1))))))) @ ((c= @ (c? @ (^[V4]: ((((chomotopic_with @ (^[V5]: cT)) @ ((c__comma__ @ V2) @ (csphere @ ((c__comma__ @ V0) @ V1)))) @ V3) @ (^[V5]: V4))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ cUNIV)) @ ((c/__caret__ @ ((cSUBSET @ ((cIMAGE @ V4) @ cUNIV)) @ (csphere @ ((c__comma__ @ V0) @ V1)))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((c= @ (V4 @ V5)) @ (V3 @ V5))))))))))))))))))))
(TSPHERE_RETRACT_OF_PUNCTURED_UNIVERSE_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ (cball @ ((c__comma__ @ V0) @ V1)))) @ ((cretract_of @ (csphere @ ((c__comma__ @ V0) @ V1))) @ ((cDELETE @ cUNIV) @ V2))))))))))
(TCONTRACTIBLE_PUNCTURED_SPHERE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((cIN @ V2) @ (csphere @ ((c__comma__ @ V0) @ V1))))) @ (ccontractible @ ((cDELETE @ (csphere @ ((c__comma__ @ V0) @ V1))) @ V2))))))))))
(THOMEOMORPHIC_PUNCTURED_SPHERE_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ (csphere @ ((c__comma__ @ V0) @ V1)))) @ ((c= @ (cdimindex @ cUNIV)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((chomeomorphic @ ((cDELETE @ (csphere @ ((c__comma__ @ V0) @ V1))) @ V2)) @ cUNIV)))))))))
(THOMEOMORPHIC_SPHERES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ ((chomeomorphic @ (csphere @ ((c__comma__ @ V0) @ V1))) @ (csphere @ ((c__comma__ @ V2) @ V3)))))))))))))
(THOMEOMORPHIC_CBALLS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ ((chomeomorphic @ (ccball @ ((c__comma__ @ V0) @ V1))) @ (ccball @ ((c__comma__ @ V2) @ V3)))))))))))))
(THOMEOMORPHIC_BALLS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ ((chomeomorphic @ (cball @ ((c__comma__ @ V0) @ V1))) @ (cball @ ((c__comma__ @ V2) @ V3)))))))))))))
(THOMEOMORPHIC_HYPERPLANES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0)))))) @ ((chomeomorphic @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V0) @ V5)) @ V1)) @ V5)))))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V2) @ V5)) @ V3)) @ V5))))))))))))))))
(TSUBSET_HYPERPLANES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cSUBSET @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V0) @ V5)) @ V1)) @ V5)))))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V2) @ V5)) @ V3)) @ V5))))))) @ ((c__caret__/ @ ((c= @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V0) @ V5)) @ V1)) @ V5)))))) @ cEMPTY)) @ ((c__caret__/ @ ((c= @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V2) @ V5)) @ V3)) @ V5)))))) @ cUNIV)) @ ((c= @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V0) @ V5)) @ V1)) @ V5)))))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V2) @ V5)) @ V3)) @ V5))))))))))))))))))
(TIN_AFFINE_ADD_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (caffine @ V3)) @ ((c/__caret__ @ ((cIN @ V0) @ V3)) @ ((cIN @ ((cvector_add @ V0) @ V2)) @ V3)))) @ ((cIN @ ((cvector_add @ V0) @ ((c% @ V1) @ V2))) @ V3)))))))))))
(TEXPOSED_POINT_OF_INTER_SUPPORTING_HYPERPLANE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((creal_le @ ((cdot @ V0) @ V4)) @ V1))))) @ ((c= @ ((cINTER @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V0) @ V5)) @ V1)) @ V5))))))) @ ((cINSERT @ V2) @ cEMPTY)))) @ ((cexposed_face_of @ ((cINSERT @ V2) @ cEMPTY)) @ V3)))))))))))
(TEXPOSED_POINT_OF_INTER_SUPPORTING_HYPERPLANE_GE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((creal_ge @ ((cdot @ V0) @ V4)) @ V1))))) @ ((c= @ ((cINTER @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V0) @ V5)) @ V1)) @ V5))))))) @ ((cINSERT @ V2) @ cEMPTY)))) @ ((cexposed_face_of @ ((cINSERT @ V2) @ cEMPTY)) @ V3)))))))))))
(THOMEOMORPHIC_PUNCTURED_SPHERE_AFFINE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ (csphere @ ((c__comma__ @ V0) @ V1)))) @ ((c/__caret__ @ (caffine @ V3)) @ ((c= @ ((cint_add @ (caff_dim @ V3)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cint_of_num @ (cdimindex @ cUNIV))))))) @ ((chomeomorphic @ ((cDELETE @ (csphere @ ((c__comma__ @ V0) @ V1))) @ V2)) @ V3)))))))))))
(TCONTENT_IMAGE_AFFINITY_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (ccontent @ ((cIMAGE @ (^[V4]: ((cvector_add @ ((c% @ V1) @ V4)) @ V0))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))) @ ((creal_mul @ ((creal_pow @ (creal_abs @ V1)) @ (cdimindex @ cUNIV))) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))
(TIMAGE_AFFINITY_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cIMAGE @ (^[V4]: ((cvector_add @ ((c% @ V1) @ V4)) @ V3))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL)))) @ (((cCOND @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V0)) @ cNIL))) @ cEMPTY)) @ cEMPTY) @ (((cCOND @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cvector_add @ ((c% @ V1) @ V2)) @ V3)) @ ((cvector_add @ ((c% @ V1) @ V0)) @ V3))) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cvector_add @ ((c% @ V1) @ V0)) @ V3)) @ ((cvector_add @ ((c% @ V1) @ V2)) @ V3))) @ cNIL))))))))))))))
(THOMEOMORPHIC_PUNCTURED_SPHERE_HYPERPLANE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ (csphere @ ((c__comma__ @ V0) @ V1)))) @ (c~ @ ((c= @ V3) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((chomeomorphic @ ((cDELETE @ (csphere @ ((c__comma__ @ V0) @ V1))) @ V2)) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c= @ ((cdot @ V3) @ V6)) @ V4)) @ V6))))))))))))))))))
(TIN_AFFINE_SUB_MUL_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (caffine @ V4)) @ ((c/__caret__ @ ((cIN @ V0) @ V4)) @ ((c/__caret__ @ ((cIN @ V2) @ V4)) @ ((cIN @ V3) @ V4))))) @ ((cIN @ ((cvector_sub @ V0) @ ((c% @ V1) @ ((cvector_sub @ V2) @ V3)))) @ V4)))))))))))))
(TIN_AFFINE_ADD_MUL_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (caffine @ V4)) @ ((c/__caret__ @ ((cIN @ V0) @ V4)) @ ((c/__caret__ @ ((cIN @ V2) @ V4)) @ ((cIN @ V3) @ V4))))) @ ((cIN @ ((cvector_add @ V0) @ ((c% @ V1) @ ((cvector_sub @ V2) @ V3)))) @ V4)))))))))))))
(TOPEN_CLOSED_INTERVAL_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ (copen_interval @ ((c__comma__ @ V3) @ V4)))) @ ((c/__caret__ @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ ((creal_le @ V1) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cIN @ ((cvector_add @ ((c% @ V1) @ V0)) @ ((c% @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V1)) @ V2))) @ (copen_interval @ ((c__comma__ @ V3) @ V4)))))))))))))))
(TDOT_BASIS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ ((cdot @ (cbasis @ V1)) @ V0)) @ ((c$ @ V0) @ V1))))))))
(TDOT_BASIS_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ ((cdot @ V0) @ (cbasis @ V1))) @ ((c$ @ V0) @ V1))))))))
(TREFLECT_ALONG_BASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ ((creflect_along @ (cbasis @ V1)) @ V0)) @ ((cvector_sub @ V0) @ ((c% @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ V0) @ V1))) @ (cbasis @ V1))))))))))
(TORTHOGONAL_BASIS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ ((corthogonal @ (cbasis @ V1)) @ V0)) @ ((c= @ ((c$ @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))
(TVECTOR_NEG_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c$ @ (cvector_neg @ V0)) @ V1)) @ (creal_neg @ ((c$ @ V0) @ V1))))))))
(TNORM_BOUND_COMPONENT_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((creal_lt @ (cvector_norm @ V0)) @ V2)) @ ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((creal_lt @ (creal_abs @ ((c$ @ V0) @ V1))) @ V2))))))))))
(TNORM_BOUND_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((creal_le @ (cvector_norm @ V0)) @ V2)) @ ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_abs @ ((c$ @ V0) @ V1))) @ V2))))))))))
(TINTERVAL_DOUBLESPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V4)) @ cNIL))) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((creal_le @ (creal_abs @ ((creal_sub @ ((c$ @ V6) @ V1)) @ V2))) @ V3)) @ V6))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V1)) @ ((creal_max @ ((c$ @ V0) @ V1)) @ ((creal_sub @ V2) @ V3))) @ ((c$ @ V0) @ V5))))) @ (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V1)) @ ((creal_min @ ((c$ @ V4) @ V1)) @ ((creal_add @ V2) @ V3))) @ ((c$ @ V4) @ V5)))))) @ cNIL)))))))))))))))
(TINTERVAL_SPLIT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((creal_le @ ((c$ @ V5) @ V1)) @ V2)) @ V5))))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V1)) @ ((creal_min @ ((c$ @ V3) @ V1)) @ V2)) @ ((c$ @ V3) @ V4)))))) @ cNIL)))))))))))))
(TLAMBDA_SWAP_GALOIS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))))) @ ((c= @ ((c= @ V0) @ (clambda @ (^[V4]: ((c$ @ V3) @ ((cswap @ ((c__comma__ @ V1) @ V2)) @ V4)))))) @ ((c= @ (clambda @ (^[V4]: ((c$ @ V0) @ ((cswap @ ((c__comma__ @ V1) @ V2)) @ V4))))) @ V3))))))))))))
(TSUMS_OFFSET_REV,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((csums @ V2) @ V0) @ (cfrom @ V1))) @ ((c< @ V3) @ V1))) @ (((csums @ V2) @ ((cvector_add @ V0) @ ((cvsum @ ((c.. @ V3) @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V2))) @ (cfrom @ V3))))))))))))
(TSUMS_OFFSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((csums @ V2) @ V0) @ (cfrom @ V1))) @ ((c< @ V1) @ V3))) @ (((csums @ V2) @ ((cvector_sub @ V0) @ ((cvsum @ ((c.. @ V1) @ ((c- @ V3) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V2))) @ (cfrom @ V3))))))))))))
(TDET_ROW_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdet @ (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V1)) @ ((cvector_add @ V0) @ V2)) @ (V3 @ V4)))))) @ ((creal_add @ (cdet @ (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V1)) @ V0) @ (V3 @ V4)))))) @ (cdet @ (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V1)) @ V2) @ (V3 @ V4)))))))))))))))))
(TCRAMER_LEMMA_TRANSP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdet @ (clambda @ (^[V3]: (((cCOND @ ((c= @ V3) @ V1)) @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V4]: ((c% @ ((c$ @ V0) @ V4)) @ ((crow @ V4) @ V2))))) @ ((crow @ V3) @ V2)))))) @ ((creal_mul @ ((c$ @ V0) @ V1)) @ (cdet @ V2)))))))))))
(TCRAMER_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdet @ (clambda @ (^[V3]: (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V1)) @ ((c$ @ ((cmatrix_vector_mul @ V2) @ V0)) @ V3)) @ ((c$ @ ((c$ @ V2) @ V3)) @ V4)))))))) @ ((creal_mul @ ((c$ @ V0) @ V1)) @ (cdet @ V2)))))))))))
(TLIM_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (((c--> @ (^[V2]: V0)) @ V0) @ V1))))))
(THAS_MEASURE_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (cLENGTH @ V1)) @ (cdimindex @ cUNIV))) @ ((chas_measure @ ((chull @ cconvex) @ (cset_of_list @ ((cCONS @ V0) @ V1)))) @ ((creal_div @ (creal_abs @ (cdet @ (cvector @ ((cMAP @ (^[V2]: ((cvector_sub @ V2) @ V0))) @ V1))))) @ (creal_of_num @ (cFACT @ (cdimindex @ cUNIV)))))))))))
(TMEASURE_SIMPLEX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (cLENGTH @ V1)) @ (cdimindex @ cUNIV))) @ ((c= @ (cmeasure @ ((chull @ cconvex) @ (cset_of_list @ ((cCONS @ V0) @ V1))))) @ ((creal_div @ (creal_abs @ (cdet @ (cvector @ ((cMAP @ (^[V2]: ((cvector_sub @ V2) @ V0))) @ V1))))) @ (creal_of_num @ (cFACT @ (cdimindex @ cUNIV)))))))))))
(TNORM_ELIM_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (V1 @ (cvector_norm @ V0))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c= @ ((creal_pow @ V2) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cdot @ V0) @ V0)))) @ (V1 @ V2))))))))))
(TIMAGE_STRETCH_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIMAGE @ (^[V3]: (clambda @ (^[V4]: ((creal_mul @ (V1 @ V4)) @ ((c$ @ V3) @ V4)))))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ (((cCOND @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL))) @ cEMPTY)) @ cEMPTY) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (clambda @ (^[V3]: ((creal_min @ ((creal_mul @ (V1 @ V3)) @ ((c$ @ V0) @ V3))) @ ((creal_mul @ (V1 @ V3)) @ ((c$ @ V2) @ V3)))))) @ (clambda @ (^[V3]: ((creal_max @ ((creal_mul @ (V1 @ V3)) @ ((c$ @ V0) @ V3))) @ ((creal_mul @ (V1 @ V3)) @ ((c$ @ V2) @ V3))))))) @ cNIL)))))))))))
(TCOMPACT_SEQUENCE_WITH_LIMIT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (((c--> @ V1) @ V0) @ csequentially)) @ (ccompact @ ((cINSERT @ V0) @ ((cIMAGE @ V1) @ cUNIV)))))))))
(TSEQUENCE_INFINITE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c! @ (^[V2]: (c~ @ ((c= @ (V1 @ V2)) @ V0))))) @ (((c--> @ V1) @ V0) @ csequentially))) @ (cINFINITE @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c? @ (^[V4]: ((c= @ V3) @ (V1 @ V4))))) @ V3))))))))))))
(TSUMS_FINITE_DIFF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V3) @ V2)) @ ((c/__caret__ @ (cFINITE @ V3)) @ (((csums @ V1) @ V0) @ V2)))) @ (((csums @ V1) @ ((cvector_sub @ V0) @ ((cvsum @ V3) @ V1))) @ ((cDIFF @ V2) @ V3))))))))))))
(TSUMS_FINITE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V3)) @ (((csums @ V1) @ V0) @ V2))) @ (((csums @ V1) @ ((cvector_add @ V0) @ ((cvsum @ ((cDIFF @ V3) @ V2)) @ V1))) @ ((cUNION @ V2) @ V3))))))))))))
(TLOCALLY_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (V1 @ ((cIMAGE @ (^[V5]: ((cvector_add @ V3) @ V5))) @ V4))) @ (V1 @ V4))))))) @ ((c= @ ((clocally @ V1) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((clocally @ V1) @ V2))))))))))
(TDIVISION_OF_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdivision_of @ ((cIMAGE @ (cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3)))) @ V1)) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((cdivision_of @ V1) @ V2)))))))))
(TINSIDE_SIMPLE_CURVE_IMP_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csimple_path @ V1)) @ ((cIN @ V0) @ (cinside @ (cpath_image @ V1))))) @ ((c= @ (cpathfinish @ V1)) @ (cpathstart @ V1))))))))
(TNOT_ON_PATH_CBALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ (c~ @ ((cIN @ V0) @ (cpath_image @ V1))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c= @ ((cINTER @ (ccball @ ((c__comma__ @ V0) @ V2))) @ (cpath_image @ V1))) @ cEMPTY))))))))))
(TNOT_ON_PATH_BALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cpath @ V1)) @ (c~ @ ((cIN @ V0) @ (cpath_image @ V1))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c= @ ((cINTER @ (cball @ ((c__comma__ @ V0) @ V2))) @ (cpath_image @ V1))) @ cEMPTY))))))))))
(TSIMPLE_PATH_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csimple_path @ ((co @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (csimple_path @ V1)))))))
(TPATH_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpath @ ((co @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cpath @ V1)))))))
(TARC_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (carc @ ((co @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (carc @ V1)))))))
(TJOINPATHS_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c++ @ ((co @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ ((co @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((co @ (^[V3]: ((cvector_add @ V0) @ V3))) @ ((c++ @ V1) @ V2))))))))))
(THAS_BOUNDED_VARIATION_ON_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((chas_bounded_variation_on @ (^[V2]: V0)) @ V1))))))
(TCONTINUOUS_INJECTIVE_IMAGE_OPEN_SEGMENT_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c= @ (V1 @ V3)) @ (V1 @ V4))))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((cIMAGE @ V1) @ (copen_segment @ ((c__comma__ @ V0) @ V2)))) @ (copen_segment @ ((c__comma__ @ (V1 @ V0)) @ (V1 @ V2))))))))))))
(TCONTINUOUS_INJECTIVE_IMAGE_SEGMENT_1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V1) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((c= @ (V1 @ V3)) @ (V1 @ V4))))) @ ((c= @ V3) @ V4)))))))) @ ((c= @ ((cIMAGE @ V1) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ (V1 @ V0)) @ (V1 @ V2))) @ cNIL)))))))))))
(TLIM_COMPOSE_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (((c--> @ V2) @ V0) @ V4)) @ ((c/__caret__ @ ((ceventually @ (^[V5]: ((c==> @ ((c= @ (V2 @ V5)) @ V0)) @ ((c= @ (V1 @ V0)) @ V3)))) @ V4)) @ (((c--> @ V1) @ V3) @ (cat @ V0))))) @ (((c--> @ ((co @ V1) @ V2)) @ V3) @ V4)))))))))))))
(THOMOTOPY_EQUIVALENT_TRANSLATION_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((chomotopy_equivalent @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1)) @ V1))))))
(THOMEOMORPHIC_TRANSLATION_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((chomeomorphic @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1)) @ V1))))))
(THOMEOMORPHIC_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((chomeomorphic @ V1) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1)))))))
(TFRONTIER_OF_CONNECTED_COMPONENT_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ (cfrontier @ ((cconnected_component @ V1) @ V0))) @ (cfrontier @ V1)))))))
(TLIMPT_OF_LIMPTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((climit_point_of @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((climit_point_of @ V3) @ V1)) @ V3))))))) @ ((climit_point_of @ V0) @ V1)))))))
(TEXTREME_POINT_OF_CONVEX_HULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cextreme_point_of @ V0) @ ((chull @ cconvex) @ V1))) @ ((cIN @ V0) @ V1)))))))
(TEXTREME_POINT_NOT_IN_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cextreme_point_of @ V0) @ V1)) @ (c~ @ ((cIN @ V0) @ (cinterior @ V1)))))))))
(TCONVEX_HULL_EXCHANGE_UNION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V0) @ ((chull @ cconvex) @ V1))) @ ((c= @ ((chull @ cconvex) @ V1)) @ (cUNIONS @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cDELETE @ V1) @ V3))))))))))))))))
(TINTERIOR_LIMIT_POINT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V0) @ (cinterior @ V1))) @ ((climit_point_of @ V0) @ V1)))))))
(TEXTREME_POINT_NOT_IN_RELATIVE_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((cextreme_point_of @ V0) @ V1)) @ (c~ @ ((c= @ V1) @ ((cINSERT @ V0) @ cEMPTY))))) @ (c~ @ ((cIN @ V0) @ (crelative_interior @ V1)))))))))
(TAFFINE_INDEPENDENT_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ (caffine_dependent @ V1))) @ (c~ @ ((cIN @ V0) @ ((chull @ caffine) @ V1))))) @ (c~ @ (caffine_dependent @ ((cINSERT @ V0) @ V1)))))))))
(TLIMPT_OF_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (copen @ V1)) @ ((cIN @ V0) @ V1))) @ ((climit_point_of @ V0) @ V1)))))))
(TINTERVAL_CONTAINS_COMPACT_NEIGHBOURHOOD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cis_interval @ V1)) @ ((cIN @ V0) @ V1))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((c/__caret__ @ ((cIN @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL)))) @ ((c/__caret__ @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V1)) @ ((cSUBSET @ ((cINTER @ (cball @ ((c__comma__ @ V0) @ V4))) @ V1)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))))))
(TIS_INTERVAL_POINTWISE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cis_interval @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ ((c= @ ((c$ @ V3) @ V2)) @ ((c$ @ V0) @ V2)))))))))) @ ((cIN @ V0) @ V1)))))))
(TDEPENDENT_IMP_AFFINE_DEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cdependent @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ V1)) @ ((cvector_sub @ V3) @ V0)))))))) @ (c~ @ ((cIN @ V0) @ V1)))) @ (caffine_dependent @ ((cINSERT @ V0) @ V1))))))))
(TSEPARATING_HYPERPLANE_SET_POINT_INAFF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c~ @ ((cIN @ V0) @ V1))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ ((cvector_add @ V0) @ V2)) @ ((chull @ caffine) @ ((cINSERT @ V0) @ V1)))) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c/__caret__ @ ((creal_le @ ((cdot @ V2) @ V0)) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((creal_ge @ ((cdot @ V2) @ V4)) @ V3)))))))))))))))))
(TRELATIVE_INTERIOR_UNBOUNDED_CONVEX_CONTAINS_RAY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (c~ @ (cbounded @ V1))) @ ((cIN @ V0) @ (crelative_interior @ V1))))) @ (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ (c! @ (^[V3]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((cIN @ ((cvector_add @ V0) @ ((c% @ V3) @ V2))) @ (crelative_interior @ V1))))))))))))))
(TUNBOUNDED_CONVEX_CLOSED_CONTAINS_RAY,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (c~ @ (cbounded @ V1))) @ ((c/__caret__ @ (cclosed @ V1)) @ ((cIN @ V0) @ V1))))) @ (c? @ (^[V2]: ((c/__caret__ @ (c~ @ ((c= @ V2) @ (cvec @ (cNUMERAL @ c_0))))) @ (c! @ (^[V3]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((cIN @ ((cvector_add @ V0) @ ((c% @ V3) @ V2))) @ V1)))))))))))))
(TSUPPORTING_HYPERPLANE_CLOSED_POINT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c~ @ ((cIN @ V0) @ V1)))))) @ (c? @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ ((cdot @ V2) @ V0)) @ V3)) @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ ((c= @ ((cdot @ V2) @ V4)) @ V3)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ ((creal_ge @ ((cdot @ V2) @ V5)) @ V3)))))))))))))))))))
(TSEPARATING_HYPERPLANE_CLOSED_POINT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (cclosed @ V1)) @ (c~ @ ((cIN @ V0) @ V1))))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ ((cdot @ V2) @ V0)) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V1)) @ ((creal_gt @ ((cdot @ V2) @ V4)) @ V3)))))))))))))))
(TCONNECTED_IMP_PERFECT_AFF_DIM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconnected @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ (caff_dim @ V1)) @ (cint_of_num @ (cNUMERAL @ c_0))))) @ ((cIN @ V0) @ V1)))) @ ((climit_point_of @ V0) @ V1)))))))
(TCONNECTED_IMP_PERFECT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cconnected @ V1)) @ ((c/__caret__ @ (c~ @ (c? @ (^[V2]: ((c= @ V1) @ ((cINSERT @ V2) @ cEMPTY)))))) @ ((cIN @ V0) @ V1)))) @ ((climit_point_of @ V0) @ V1)))))))
(TCOMPACT_FRONTIER_LINE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V1)) @ ((c/__caret__ @ ((cIN @ (cvec @ (cNUMERAL @ c_0))) @ V1)) @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c/__caret__ @ ((cIN @ ((c% @ V2) @ V0)) @ (cfrontier @ V1))) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ V2) @ V3)) @ (c~ @ ((cIN @ ((c% @ V3) @ V0)) @ V1)))))))))))))))
(TSTARLIKE_COMPACT_PROJECTIVE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V1)) @ ((c/__caret__ @ ((cIN @ V0) @ (crelative_interior @ V1))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cSUBSET @ (copen_segment @ ((c__comma__ @ V0) @ V2))) @ (crelative_interior @ V1)))))))) @ ((chomeomorphic @ ((cDIFF @ V1) @ (crelative_interior @ V1))) @ ((cINTER @ (csphere @ ((c__comma__ @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((chull @ caffine) @ V1)))))))))
(TSTARLIKE_COMPACT_PROJECTIVE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V1)) @ ((c/__caret__ @ ((cIN @ V0) @ (crelative_interior @ V1))) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cSUBSET @ (copen_segment @ ((c__comma__ @ V0) @ V2))) @ (crelative_interior @ V1)))))))) @ ((chomeomorphic @ V1) @ ((cINTER @ (ccball @ ((c__comma__ @ V0) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((chull @ caffine) @ V1)))))))))
(TEXTREME_POINT_OF_CONVEX_HULL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cPSUBSET @ V2) @ V1)) @ (c~ @ ((c= @ ((chull @ cconvex) @ V2)) @ ((chull @ cconvex) @ V1)))))))) @ ((c= @ ((cextreme_point_of @ V0) @ ((chull @ cconvex) @ V1))) @ ((cIN @ V0) @ V1))))))))
(TEXTREME_POINT_OF_CONVEX_HULL_CONVEX_INDEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (ccompact @ V1)) @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ (c~ @ ((cIN @ V2) @ ((chull @ cconvex) @ ((cDELETE @ V1) @ V2))))))))) @ ((c= @ ((cextreme_point_of @ V0) @ ((chull @ cconvex) @ V1))) @ ((cIN @ V0) @ V1))))))))
(TCLOSEST_POINT_IN_RELATIVE_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((cIN @ V0) @ ((chull @ caffine) @ V1))))) @ ((c= @ ((cIN @ ((cclosest_point @ V1) @ V0)) @ (crelative_interior @ V1))) @ ((cIN @ V0) @ (crelative_interior @ V1)))))))))
(TCLOSEST_POINT_IN_RELATIVE_FRONTIER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((cIN @ V0) @ ((cDIFF @ ((chull @ caffine) @ V1)) @ (crelative_interior @ V1)))))) @ ((cIN @ ((cclosest_point @ V1) @ V0)) @ (crelative_frontier @ V1))))))))
(TCLOSEST_POINT_IN_FRONTIER,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ (c~ @ ((cIN @ V0) @ (cinterior @ V1)))))) @ ((cIN @ ((cclosest_point @ V1) @ V0)) @ (cfrontier @ V1))))))))
(TSEGMENT_TO_CLOSEST_POINT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY)))) @ ((c= @ ((cINTER @ (copen_segment @ ((c__comma__ @ V0) @ ((cclosest_point @ V1) @ V0)))) @ V1)) @ cEMPTY)))))))
(TCLOSEST_POINT_IN_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY)))) @ ((c= @ ((cIN @ ((cclosest_point @ V1) @ V0)) @ (cinterior @ V1))) @ ((cIN @ V0) @ (cinterior @ V1)))))))))
(TCLOSEST_POINT_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY)))) @ ((c= @ ((c= @ ((cclosest_point @ V1) @ V0)) @ V0)) @ ((cIN @ V0) @ V1))))))))
(TSEGMENT_TO_POINT_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c= @ ((cINTER @ (copen_segment @ ((c__comma__ @ V0) @ V2))) @ V1)) @ cEMPTY))))))))))
(TENR_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ (cENR @ V1))) @ (cENR @ ((cINSERT @ V0) @ V1))))))))
(TANR_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ (cANR @ V1))) @ (cANR @ ((cINSERT @ V0) @ V1))))))))
(TSTARLIKE_NEGLIGIBLE_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c/__caret__ @ ((creal_lt @ V2) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cIN @ ((cvector_add @ V0) @ V3)) @ V1)))) @ (c~ @ ((cIN @ ((cvector_add @ V0) @ ((c% @ V2) @ V3))) @ V1))))))))) @ (cnegligible @ V1)))))))
(TSTARLIKE_NEGLIGIBLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((c/__caret__ @ ((cIN @ ((cvector_add @ V0) @ V3)) @ V1)) @ ((cIN @ ((cvector_add @ V0) @ ((c% @ V2) @ V3))) @ V1)))) @ ((c= @ V2) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))) @ (cnegligible @ V1)))))))
(TIN_FRONTIER_CONVEX_HULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((c<= @ (cCARD @ V1)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cIN @ V0) @ V1)))) @ ((cIN @ V0) @ (cfrontier @ ((chull @ cconvex) @ V1)))))))))
(TNOT_IN_INTERIOR_CONVEX_HULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((c<= @ (cCARD @ V1)) @ ((c+ @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cIN @ V0) @ V1)))) @ (c~ @ ((cIN @ V0) @ (cinterior @ ((chull @ cconvex) @ V1))))))))))
(TEXTREME_POINT_OF_CONVEX_HULL_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c~ @ ((cIN @ V0) @ ((chull @ cconvex) @ V1))))) @ ((cextreme_point_of @ V0) @ ((chull @ cconvex) @ ((cINSERT @ V0) @ V1)))))))))
(TAFFINE_DEPENDENT_CHOOSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (caffine_dependent @ V1))) @ ((c= @ (caffine_dependent @ ((cINSERT @ V0) @ V1))) @ ((c/__caret__ @ (c~ @ ((cIN @ V0) @ V1))) @ ((cIN @ V0) @ ((chull @ caffine) @ V1))))))))))
(TSUBSPACE_TRANSLATION_SELF_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (csubspace @ V1)) @ ((c= @ ((c= @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1)) @ V1)) @ ((cIN @ V0) @ V1))))))))
(TPATH_CONNECTED_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cpath_connected @ V1)) @ (cpath_connected @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TOPEN_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (copen @ V1)) @ (copen @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TNEGLIGIBLE_TRANSLATION_REV,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnegligible @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cnegligible @ V1)))))))
(TNEGLIGIBLE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cnegligible @ V1)) @ (cnegligible @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TMEASURABLE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cmeasurable @ V1)) @ (cmeasurable @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TIS_INTERVAL_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cis_interval @ V1)) @ (cis_interval @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TCOPLANAR_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (ccoplanar @ V1)) @ (ccoplanar @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TCONVEX_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cconvex @ V1)) @ (cconvex @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TCONNECTED_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cconnected @ V1)) @ (cconnected @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TCOMPACT_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (ccompact @ V1)) @ (ccompact @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TCLOSED_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cclosed @ V1)) @ (cclosed @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TBOUNDED_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cbounded @ V1)) @ (cbounded @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TAFFINE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (caffine @ V1)) @ (caffine @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TSYMMETRIC_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cIN @ (cvector_neg @ V2)) @ V1))))) @ ((c==> @ ((cIN @ V0) @ (cinterior @ V1))) @ ((cIN @ (cvector_neg @ V0)) @ (cinterior @ V1)))))))))
(TSYMMETRIC_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ V1)) @ ((cIN @ (cvector_neg @ V2)) @ V1))))) @ ((c==> @ ((cIN @ V0) @ (cclosure @ V1))) @ ((cIN @ (cvector_neg @ V0)) @ (cclosure @ V1)))))))))
(TMEASURE_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ ((cINSERT @ V0) @ V1))) @ (cmeasure @ V1)))))))
(TMEASURE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasure @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cmeasure @ V1)))))))
(TDIM_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdim @ ((cINSERT @ V0) @ V1))) @ (((cCOND @ ((cIN @ V0) @ (cspan @ V1))) @ (cdim @ V1)) @ ((c+ @ (cdim @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TAFF_DIM_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (caff_dim @ ((cINSERT @ V0) @ V1))) @ (((cCOND @ ((cIN @ V0) @ ((chull @ caffine) @ V1))) @ (caff_dim @ V1)) @ ((cint_add @ (caff_dim @ V1)) @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TAFF_DIM_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (caff_dim @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (caff_dim @ V1)))))))
(TFACES_OF_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cface_of @ V3) @ ((cIMAGE @ (^[V4]: ((cvector_add @ V0) @ V4))) @ V1))) @ V3)))))) @ ((cIMAGE @ (cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2)))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cface_of @ V3) @ V1)) @ V3))))))))))))
(TCONVEX_HULL_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ cconvex) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ ((chull @ cconvex) @ V1))))))))
(TRELATIVE_INTERIOR_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (crelative_interior @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ (crelative_interior @ V1))))))))
(TRELATIVE_FRONTIER_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (crelative_frontier @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ (crelative_frontier @ V1))))))))
(TINTERIOR_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinterior @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ (cinterior @ V1))))))))
(TFRONTIER_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cfrontier @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ (cfrontier @ V1))))))))
(TCLOSURE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cclosure @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ (cclosure @ V1))))))))
(TEXTREME_POINTS_OF_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cextreme_point_of @ V3) @ ((cIMAGE @ (^[V4]: ((cvector_add @ V0) @ V4))) @ V1))) @ V3)))))) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cextreme_point_of @ V3) @ V1)) @ V3))))))))))))
(TPATH_COMPONENT_REFL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cpath_component @ V1) @ V0) @ V0)) @ ((cIN @ V0) @ V1)))))))
(TCONNECTED_COMPONENT_REFL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cconnected_component @ V1) @ V0) @ V0)) @ ((cIN @ V0) @ V1)))))))
(TRETRACT_OF_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cretract_of @ ((cINSERT @ V0) @ cEMPTY)) @ V1)) @ ((cIN @ V0) @ V1)))))))
(TLOCALLY_PATH_CONNECTED_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((clocally @ cpath_connected) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((clocally @ cpath_connected) @ V1)))))))
(TLOCALLY_CONNECTED_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((clocally @ cconnected) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((clocally @ cconnected) @ V1)))))))
(TLOCALLY_COMPACT_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((clocally @ ccompact) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((clocally @ ccompact) @ V1)))))))
(TLIMPT_OF_CLOSURE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((climit_point_of @ V0) @ (cclosure @ V1))) @ ((climit_point_of @ V0) @ V1)))))))
(TLIMPT_OF_CONDENSATION_POINTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((climit_point_of @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((ccondensation_point_of @ V3) @ V1)) @ V3))))))) @ ((ccondensation_point_of @ V0) @ V1)))))))
(TLIMPT_INFINITE_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((climit_point_of @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ (copen @ V2))) @ (cINFINITE @ ((cINTER @ V1) @ V2)))))))))))
(TCONDENSATION_POINT_OF_CONDENSATION_POINTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccondensation_point_of @ V0) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((ccondensation_point_of @ V3) @ V1)) @ V3))))))) @ ((ccondensation_point_of @ V0) @ V1)))))))
(TCLOSED_IN_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V1)) @ ((cINSERT @ V0) @ cEMPTY))) @ ((cIN @ V0) @ V1)))))))
(TIN_RELATIVE_INTERIOR_CBALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ (crelative_interior @ V1))) @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((cSUBSET @ ((cINTER @ (ccball @ ((c__comma__ @ V0) @ V2))) @ ((chull @ caffine) @ V1))) @ V1)))))))))))
(TIN_RELATIVE_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ (crelative_interior @ V1))) @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((cSUBSET @ ((cINTER @ (cball @ ((c__comma__ @ V0) @ V2))) @ ((chull @ caffine) @ V1))) @ V1)))))))))))
(TIN_CLOSURE_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ (cclosure @ ((cDELETE @ V1) @ V0)))) @ ((climit_point_of @ V0) @ V1)))))))
(TCONNECTED_COMPONENT_EQ_UNIV,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cconnected_component @ V1) @ V0)) @ cUNIV)) @ ((c= @ V1) @ cUNIV)))))))
(TCONNECTED_COMPONENT_EQ_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cconnected_component @ V1) @ V0)) @ cEMPTY)) @ (c~ @ ((cIN @ V0) @ V1))))))))
(TTRIVIAL_LIMIT_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctrivial_limit @ ((cwithin @ (cat @ V0)) @ V1))) @ (c~ @ ((climit_point_of @ V0) @ V1))))))))
(TSIMPLY_CONNECTED_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csimply_connected @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (csimply_connected @ V1)))))))
(TPOLYTOPE_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpolytope @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cpolytope @ V1)))))))
(TPOLYHEDRON_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpolyhedron @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cpolyhedron @ V1)))))))
(TPATH_CONNECTED_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpath_connected @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cpath_connected @ V1)))))))
(TOPEN_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (copen @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (copen @ V1)))))))
(TNEGLIGIBLE_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnegligible @ ((cINSERT @ V0) @ V1))) @ (cnegligible @ V1)))))))
(TNEGLIGIBLE_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnegligible @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cnegligible @ V1)))))))
(TNEGLIGIBLE_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnegligible @ ((cDELETE @ V1) @ V0))) @ (cnegligible @ V1)))))))
(TMEASURABLE_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasurable @ ((cINSERT @ V0) @ V1))) @ (cmeasurable @ V1)))))))
(TMEASURABLE_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmeasurable @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cmeasurable @ V1)))))))
(TLEBESGUE_MEASURABLE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (clebesgue_measurable @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (clebesgue_measurable @ V1)))))))
(TIS_INTERVAL_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cis_interval @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cis_interval @ V1)))))))
(TINDEPENDENT_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cindependent @ ((cINSERT @ V0) @ V1))) @ (((cCOND @ ((cIN @ V0) @ V1)) @ (cindependent @ V1)) @ ((c/__caret__ @ (cindependent @ V1)) @ (c~ @ ((cIN @ V0) @ (cspan @ V1)))))))))))
(TCOPLANAR_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccoplanar @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (ccoplanar @ V1)))))))
(TCONVEX_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cconvex @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cconvex @ V1)))))))
(TCONTRACTIBLE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccontractible @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (ccontractible @ V1)))))))
(TCONNECTED_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cconnected @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cconnected @ V1)))))))
(TCOMPLETE_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccomplete @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (ccomplete @ V1)))))))
(TCOMPACT_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccompact @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (ccompact @ V1)))))))
(TCLOSED_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cclosed @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cclosed @ V1)))))))
(TBOUNDED_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cbounded @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cbounded @ V1)))))))
(TAFFINE_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (caffine @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (caffine @ V1)))))))
(TENR_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cENR @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cENR @ V1)))))))
(TAR_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cAR @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cAR @ V1)))))))
(TANR_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cANR @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (cANR @ V1)))))))
(THAS_MEASURE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chas_measure @ V1) @ V2)) @ ((chas_measure @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ V2)))))))))
(THAS_MEASURE_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chas_measure @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ V2)) @ ((chas_measure @ V1) @ V2)))))))))
(THAS_MEASURE_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((chas_measure @ V1) @ V3)) @ ((chas_measure @ ((cIMAGE @ (^[V4]: ((cvector_add @ ((c% @ V2) @ V4)) @ V0))) @ V1)) @ ((creal_mul @ ((creal_pow @ (creal_abs @ V2)) @ (cdimindex @ cUNIV))) @ V3))))))))))))
(THOMOTOPIC_LOOPS_IMP_HOMOTOPIC_PATHS_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chomotopic_loops @ V1) @ V2) @ (clinepath @ ((c__comma__ @ V0) @ V0)))) @ (((chomotopic_paths @ V1) @ V2) @ (clinepath @ ((c__comma__ @ (cpathstart @ V2)) @ (cpathstart @ V2))))))))))))
(THOMOTOPIC_PATHS_LOOP_PARTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chomotopic_loops @ V1) @ ((c++ @ V2) @ (creversepath @ V3))) @ (clinepath @ ((c__comma__ @ V0) @ V0)))) @ (cpath @ V3))) @ (((chomotopic_paths @ V1) @ V2) @ V3)))))))))))
(TLIM_COMPOSE_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((c--> @ V3) @ V0) @ V5)) @ ((c/__caret__ @ ((ceventually @ (^[V6]: ((c/__caret__ @ ((cIN @ (V3 @ V6)) @ V1)) @ ((c==> @ ((c= @ (V3 @ V6)) @ V0)) @ ((c= @ (V2 @ V0)) @ V4))))) @ V5)) @ (((c--> @ V2) @ V4) @ ((cwithin @ (cat @ V0)) @ V1))))) @ (((c--> @ ((co @ V2) @ V3)) @ V4) @ V5)))))))))))))))
(THAUSDIST_COMPACT_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cbounded @ V1)) @ ((c/__caret__ @ (ccompact @ V2)) @ (c~ @ ((c= @ V2) @ cEMPTY))))) @ ((c==> @ ((cIN @ V0) @ V1)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V2)) @ ((creal_le @ (cdistance @ ((c__comma__ @ V0) @ V3))) @ (chausdist @ ((c__comma__ @ V1) @ V2)))))))))))))))
(TSETDIST_SING_LE_HAUSDIST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cbounded @ V1)) @ ((c/__caret__ @ (cbounded @ V2)) @ ((cIN @ V0) @ V1)))) @ ((creal_le @ (csetdist @ ((c__comma__ @ ((cINSERT @ V0) @ cEMPTY)) @ V2))) @ (chausdist @ ((c__comma__ @ V1) @ V2)))))))))))
(TSETDIST_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (csetdist @ ((c__comma__ @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2)))) @ (csetdist @ ((c__comma__ @ V1) @ V2))))))))))
(THAUSDIST_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (chausdist @ ((c__comma__ @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2)))) @ (chausdist @ ((c__comma__ @ V1) @ V2))))))))))
(TRETRACT_OF_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cretract_of @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((cretract_of @ V1) @ V2)))))))))
(TFACET_OF_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cfacet_of @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((cfacet_of @ V1) @ V2)))))))))
(TFACE_OF_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cface_of @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((cface_of @ V1) @ V2)))))))))
(TEXPOSED_FACE_OF_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cexposed_face_of @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((cexposed_face_of @ V1) @ V2)))))))))
(TEDGE_OF_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cedge_of @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((cedge_of @ V1) @ V2)))))))))
(THOMOTOPY_EQUIVALENT_TRANSLATION_LEFT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chomotopy_equivalent @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ V2)) @ ((chomotopy_equivalent @ V1) @ V2)))))))))
(THOMEOMORPHIC_TRANSLATION_LEFT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chomeomorphic @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ V2)) @ ((chomeomorphic @ V1) @ V2)))))))))
(TGRAM_SCHMIDT_STEP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cpairwise @ corthogonal) @ V1)) @ ((cIN @ V0) @ (cspan @ V1)))) @ ((corthogonal @ V0) @ ((cvector_sub @ V2) @ ((cvsum @ V1) @ (^[V3]: ((c% @ ((creal_div @ ((cdot @ V3) @ V2)) @ ((cdot @ V3) @ V3))) @ V3)))))))))))))
(TSPAN_BREAKDOWN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((cIN @ V0) @ (cspan @ V1)))) @ (c? @ (^[V3]: ((cIN @ ((cvector_sub @ V0) @ ((c% @ V3) @ V2))) @ (cspan @ ((cDELETE @ V1) @ V2)))))))))))))
(TIN_CLOSURE_CONNECTED_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ (copen @ V1))) @ ((c= @ ((cIN @ V0) @ (cclosure @ ((cconnected_component @ V1) @ V2)))) @ ((cIN @ V0) @ ((cconnected_component @ V1) @ V2)))))))))))
(TCOBOUNDED_UNIQUE_UNBOUNDED_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (cbounded @ ((cDIFF @ cUNIV) @ V1))) @ ((c/__caret__ @ (c~ @ (cbounded @ ((cconnected_component @ V1) @ V0)))) @ (c~ @ (cbounded @ ((cconnected_component @ V1) @ V2))))))) @ ((c= @ ((cconnected_component @ V1) @ V0)) @ ((cconnected_component @ V1) @ V2))))))))))
(TCLOSEST_POINT_DOT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((cIN @ V0) @ V1)))) @ ((creal_le @ ((cdot @ ((cvector_sub @ V2) @ ((cclosest_point @ V1) @ V2))) @ ((cvector_sub @ V0) @ ((cclosest_point @ V1) @ V2)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))
(TCLOSEST_POINT_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((creal_le @ (cdistance @ ((c__comma__ @ V2) @ V0))) @ (cdistance @ ((c__comma__ @ V2) @ V3)))))))))) @ ((c= @ V0) @ ((cclosest_point @ V1) @ V2))))))))))
(TCLOSEST_POINT_AFFINE_ORTHOGONAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (caffine @ V1)) @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ cEMPTY))) @ ((cIN @ V0) @ V1)))) @ ((corthogonal @ ((cvector_sub @ V0) @ ((cclosest_point @ V1) @ V2))) @ ((cvector_sub @ V2) @ ((cclosest_point @ V1) @ V2)))))))))))
(TCONNECTED_COMPONENT_NONOVERLAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cINTER @ ((cconnected_component @ V1) @ V0)) @ ((cconnected_component @ V1) @ V2))) @ cEMPTY)) @ ((c__caret__/ @ (c~ @ ((cIN @ V0) @ V1))) @ ((c__caret__/ @ (c~ @ ((cIN @ V2) @ V1))) @ (c~ @ ((c= @ ((cconnected_component @ V1) @ V0)) @ ((cconnected_component @ V1) @ V2)))))))))))))
(TCONNECTED_COMPONENT_OVERLAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c~ @ ((c= @ ((cINTER @ ((cconnected_component @ V1) @ V0)) @ ((cconnected_component @ V1) @ V2))) @ cEMPTY))) @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ ((c/__caret__ @ ((cIN @ V2) @ V1)) @ ((c= @ ((cconnected_component @ V1) @ V0)) @ ((cconnected_component @ V1) @ V2))))))))))))
(TPATH_COMPONENT_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cpath_component @ V1) @ V2) @ V0)) @ (((cpath_component @ V1) @ V0) @ V3))) @ (((cpath_component @ V1) @ V2) @ V3)))))))))))
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(TINTEGRABLE_ON_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cintegrable_on @ (^[V2]: V0)) @ V1)) @ ((c__caret__/ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (cmeasurable @ V1))))))))
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(TORTHOGONAL_RVSUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ ((corthogonal @ V0) @ (V2 @ V3))))))) @ ((corthogonal @ V0) @ ((cvsum @ V1) @ V2))))))))))
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(TNORM_TRIANGLE_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cvector_norm @ V0)) @ ((creal_add @ (cvector_norm @ V1)) @ (cvector_norm @ ((cvector_sub @ V0) @ V1)))))))))
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(TNORM_CAUCHY_SCHWARZ_ABS,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (creal_abs @ ((cdot @ V0) @ V1))) @ ((creal_mul @ (cvector_norm @ V0)) @ (cvector_norm @ V1))))))))
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(THAS_MEASURE_INTERVAL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((chas_measure @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))))))))
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(TCONTINUOUS_AT_LIFT_DIST,(c! @ (^[V0]: (c! @ (^[V1]: ((ccontinuous @ ((co @ clift) @ (^[V2]: (cdistance @ ((c__comma__ @ V0) @ V2))))) @ (cat @ V1)))))))
(TMIDPOINT_IN_SEGMENT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cIN @ (cmidpoint @ ((c__comma__ @ V0) @ V1))) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
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(TNORM_ADD_PYTHAGOREAN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((corthogonal @ V0) @ V1)) @ ((c= @ ((creal_pow @ (cvector_norm @ ((cvector_add @ V0) @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ (cvector_norm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TORTHOGONAL_TRANSFORMATION_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (cvector_norm @ V0)) @ (cvector_norm @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ (corthogonal_transformation @ V2)) @ ((c= @ (V2 @ V0)) @ V1))))))))))
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(TROTATION_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c= @ (cvector_norm @ V0)) @ (cvector_norm @ V1)))) @ (c? @ (^[V2]: ((c/__caret__ @ (corthogonal_transformation @ V2)) @ ((c/__caret__ @ ((c= @ (cdet @ (cmatrix @ V2))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (V2 @ V0)) @ V1)))))))))))
(TROTATION_EXISTS_1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c= @ (cvector_norm @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cvector_norm @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c? @ (^[V2]: ((c/__caret__ @ (corthogonal_transformation @ V2)) @ ((c/__caret__ @ ((c= @ (cdet @ (cmatrix @ V2))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (V2 @ V0)) @ V1)))))))))))
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(TINTEGRAL_VECTOR_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cintegral_vector @ V0)) @ (cintegral_vector @ V1))) @ (cintegral_vector @ ((cvector_add @ V0) @ V1))))))))
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(TAFF_DIM_INTERVAL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (caff_dim @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (((cCOND @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ cEMPTY)) @ (cint_neg @ (cint_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cint_of_num @ (cCARD @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c/__caret__ @ ((c<= @ V3) @ (cdimindex @ cUNIV))) @ ((creal_lt @ ((c$ @ V0) @ V3)) @ ((c$ @ V1) @ V3))))) @ V3))))))))))))))
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(TAFFINE_HULL_SEGMENT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ caffine) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((chull @ caffine) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))))
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(TREFLECT_INTERVAL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIMAGE @ cvector_neg) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvector_neg @ V1)) @ (cvector_neg @ V0))) @ cNIL))))))))
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(TRELATIVE_INTERIOR_SEGMENT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (crelative_interior @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (((cCOND @ ((c= @ V0) @ V1)) @ ((cINSERT @ V0) @ cEMPTY)) @ (copen_segment @ ((c__comma__ @ V0) @ V1)))))))))
(TSEGMENT_AS_BALL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (copen_segment @ ((c__comma__ @ V0) @ V1))) @ ((cINTER @ ((chull @ caffine) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))) @ (cball @ ((c__comma__ @ ((c% @ (creal_inv @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((cvector_add @ V0) @ V1))) @ ((creal_div @ (cvector_norm @ ((cvector_sub @ V1) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))))
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(Topen_interval,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V4)) @ ((c<= @ V4) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V0) @ V4)) @ ((c$ @ V3) @ V4))) @ ((creal_lt @ ((c$ @ V3) @ V4)) @ ((c$ @ V1) @ V4))))))) @ V3)))))))))))
(TINTERIOR_SEGMENT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinterior @ (copen_segment @ ((c__comma__ @ V0) @ V1)))) @ (((cCOND @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ cEMPTY) @ (copen_segment @ ((c__comma__ @ V0) @ V1)))))))))
(TINTERIOR_SEGMENT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinterior @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (((cCOND @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ cEMPTY) @ (copen_segment @ ((c__comma__ @ V0) @ V1)))))))))
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(TCLOSURE_SEGMENT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cclosure @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
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(TVECTOR_ADD_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_sub @ ((cvector_add @ V0) @ V1)) @ V0)) @ V1))))))
(TVECTOR_SUB_RADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_sub @ V0) @ ((cvector_add @ V0) @ V1))) @ (cvector_neg @ V1)))))))
(TVECTOR_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_sub @ V0) @ V1)) @ ((cvector_add @ V0) @ (cvector_neg @ V1))))))))
(Tvector_sub,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_sub @ V0) @ V1)) @ (clambda @ (^[V2]: ((creal_sub @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2))))))))))
(TVECTOR_SUB_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_add @ ((cvector_sub @ V1) @ V0)) @ V0)) @ V1))))))
(TVECTOR_ADD_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_add @ V1) @ V0)) @ ((cvector_add @ V0) @ V1)))))))
(TVECTOR_SUB_ADD2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_add @ V0) @ ((cvector_sub @ V1) @ V0))) @ V1))))))
(Tvector_add,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_add @ V0) @ V1)) @ (clambda @ (^[V2]: ((creal_add @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2))))))))))
(Treflect_along,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creflect_along @ V1) @ V0)) @ ((cvector_sub @ V0) @ ((c% @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_div @ ((cdot @ V0) @ V1)) @ ((cdot @ V1) @ V1)))) @ V1))))))))
(TREFLECT_ALONG_INVOLUTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creflect_along @ V0) @ ((creflect_along @ V0) @ V1))) @ V1))))))
(TVECTOR_NEG_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cvector_neg @ ((cvector_sub @ V1) @ V0))) @ ((cvector_sub @ V0) @ V1)))))))
(TCONTENT_POS_LT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((creal_lt @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2)))))))))))
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(TDOT_CAUCHY_SCHWARZ_EQUAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((creal_pow @ ((cdot @ V0) @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((cdot @ V0) @ V0)) @ ((cdot @ V1) @ V1)))) @ (ccollinear @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))))
(TNORM_CAUCHY_SCHWARZ_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cdot @ V1) @ V0)) @ ((creal_mul @ (cvector_norm @ V1)) @ (cvector_norm @ V0)))) @ ((c= @ ((c% @ (cvector_norm @ V1)) @ V0)) @ ((c% @ (cvector_norm @ V0)) @ V1))))))))
(TNORM_TRIANGLE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cvector_norm @ ((cvector_add @ V1) @ V0))) @ ((creal_add @ (cvector_norm @ V1)) @ (cvector_norm @ V0)))) @ ((c= @ ((c% @ (cvector_norm @ V1)) @ V0)) @ ((c% @ (cvector_norm @ V0)) @ V1))))))))
(TNORM_CAUCHY_SCHWARZ_ABS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (creal_abs @ ((cdot @ V1) @ V0))) @ ((creal_mul @ (cvector_norm @ V1)) @ (cvector_norm @ V0)))) @ ((c__caret__/ @ ((c= @ ((c% @ (cvector_norm @ V1)) @ V0)) @ ((c% @ (cvector_norm @ V0)) @ V1))) @ ((c= @ ((c% @ (cvector_norm @ V1)) @ V0)) @ ((c% @ (creal_neg @ (cvector_norm @ V0))) @ V1)))))))))
(TNORM_CAUCHY_SCHWARZ_EQUAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (creal_abs @ ((cdot @ V0) @ V1))) @ ((creal_mul @ (cvector_norm @ V0)) @ (cvector_norm @ V1)))) @ (ccollinear @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))))
(TCONTENT_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((creal_le @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2))))))))))))
(TCONTENT_EQ_0_INTERIOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ (cinterior @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ cEMPTY)))))))
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(TINTERVAL_EQ_EMPTY_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (copen_interval @ ((c__comma__ @ V1) @ V0))) @ cEMPTY)) @ (c? @ (^[V2]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((creal_le @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2))))))))))))
(TINTERVAL_EQ_EMPTY_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL))) @ cEMPTY)) @ (c? @ (^[V2]: ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((creal_lt @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2))))))))))))
(TREFLECT_ALONG_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((creflect_along @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TREFLECT_ALONG_EQ_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((creflect_along @ V0) @ V1)) @ V1)) @ ((corthogonal @ V0) @ V1)))))))
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(TINTERVAL_NE_EMPTY_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c= @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ cEMPTY))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((creal_lt @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2)))))))))))
(TINTERVAL_NE_EMPTY_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ cEMPTY))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((creal_le @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2)))))))))))
(TSEPARATION_T0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c= @ V0) @ V1))) @ (c? @ (^[V2]: ((c/__caret__ @ (copen @ V2)) @ (c~ @ ((c= @ ((cIN @ V0) @ V2)) @ ((cIN @ V1) @ V2))))))))))))
(TSEPARATION_T2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c= @ V0) @ V1))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ (copen @ V3)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((c/__caret__ @ ((cIN @ V1) @ V3)) @ ((c= @ ((cINTER @ V2) @ V3)) @ cEMPTY)))))))))))))))
(TSEPARATION_T1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c= @ V0) @ V1))) @ (c? @ (^[V2]: (c? @ (^[V3]: ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ (copen @ V3)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((c/__caret__ @ (c~ @ ((cIN @ V1) @ V2))) @ ((c/__caret__ @ (c~ @ ((cIN @ V0) @ V3))) @ ((cIN @ V1) @ V3))))))))))))))))
(TSIMPLE_PATH_LINEPATH_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csimple_path @ (clinepath @ ((c__comma__ @ V0) @ V1)))) @ (c~ @ ((c= @ V0) @ V1))))))))
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(TCOLLINEAR_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccollinear @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ ((cINSERT @ V1) @ ((cINSERT @ V0) @ cEMPTY))))) @ ((c__caret__/ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: ((c= @ V0) @ ((c% @ V2) @ V1))))))))))))
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(TFINITE_SEGMENT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cFINITE @ (copen_segment @ ((c__comma__ @ V0) @ V1)))) @ ((c= @ V0) @ V1)))))))
(TFINITE_SEGMENT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cFINITE @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c= @ V0) @ V1)))))))
(TAR_INTERVAL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cAR @ (copen_interval @ ((c__comma__ @ V0) @ V1)))) @ (c~ @ ((c= @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ cEMPTY))))))))
(TAR_INTERVAL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cAR @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ cEMPTY))))))))
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(TNORM_SEGMENT_LOWERBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c/__caret__ @ ((c= @ (cvector_norm @ V0)) @ V3)) @ ((c/__caret__ @ ((c= @ (cvector_norm @ V1)) @ V3)) @ ((c/__caret__ @ ((cIN @ V4) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c= @ ((cdot @ V0) @ V1)) @ ((creal_mul @ V2) @ ((creal_pow @ V3) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))) @ ((creal_le @ ((creal_mul @ (csqrt @ ((creal_div @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_abs @ V2))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ V3)) @ (cvector_norm @ V4))))))))))))))
(TFIXED_POINT_INESSENTIAL_SPHERE_MAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((((chomotopic_with @ (^[V4]: cT)) @ ((c__comma__ @ (csphere @ ((c__comma__ @ V1) @ V2))) @ (csphere @ ((c__comma__ @ V1) @ V2)))) @ V3) @ (^[V4]: V0)))) @ (c? @ (^[V4]: ((c/__caret__ @ ((cIN @ V4) @ (csphere @ ((c__comma__ @ V1) @ V2)))) @ ((c= @ (V3 @ V4)) @ V4))))))))))))))
(TNORM_SEGMENT_ORTHOGONAL_LOWERBOUND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_le @ V2) @ (cvector_norm @ V0))) @ ((c/__caret__ @ ((creal_le @ V2) @ (cvector_norm @ V1))) @ ((c/__caret__ @ ((corthogonal @ V0) @ V1)) @ ((cIN @ V3) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))) @ ((creal_le @ ((creal_div @ V2) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cvector_norm @ V3))))))))))))
(TRELATIVE_INTERIOR_CONVEX_CONTAINS_SAME_RAY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cconvex @ V4)) @ ((c/__caret__ @ ((cIN @ V1) @ (crelative_interior @ V4))) @ (c! @ (^[V5]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((cIN @ ((cvector_add @ V0) @ ((c% @ V5) @ V3))) @ (crelative_interior @ V4)))))))) @ ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((cIN @ ((cvector_add @ V1) @ ((c% @ V2) @ V3))) @ (crelative_interior @ V4)))))))))))))))
(TCONVEX_CLOSED_CONTAINS_SAME_RAY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cconvex @ V4)) @ ((c/__caret__ @ (cclosed @ V4)) @ ((c/__caret__ @ ((cIN @ V1) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((cIN @ ((cvector_add @ V0) @ ((c% @ V5) @ V3))) @ V4)))))))) @ ((c==> @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((cIN @ ((cvector_add @ V1) @ ((c% @ V2) @ V3))) @ V4))))))))))))))
(TVECTOR_SUB_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c$ @ ((cvector_sub @ V0) @ V1)) @ V2)) @ ((creal_sub @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2))))))))))
(TVECTOR_ADD_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c$ @ ((cvector_add @ V0) @ V1)) @ V2)) @ ((creal_add @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2))))))))))
(TCONTENT_SPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((creal_add @ (ccontent @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((creal_le @ ((c$ @ V5) @ V2)) @ V3)) @ V5)))))))) @ (ccontent @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((creal_ge @ ((c$ @ V5) @ V2)) @ V3)) @ V5)))))))))))))))))))
(TCONTENT_DOUBLESPLIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((creal_lt @ (ccontent @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((creal_le @ (creal_abs @ ((creal_sub @ ((c$ @ V7) @ V2)) @ V3))) @ V5)) @ V7)))))))) @ V4))))))))))))))))
(TMEM_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMEM @ ((cvector_add @ V0) @ V1)) @ ((cMAP @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((cMEM @ V1) @ V2)))))))))
(TTAGGED_DIVISION_FINER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (cgauge @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ctagged_division_of @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((cfine @ V3) @ V4)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ ((c__comma__ @ V5) @ V6)) @ V2)) @ ((cSUBSET @ V6) @ (V3 @ V5)))) @ ((cIN @ ((c__comma__ @ V5) @ V6)) @ V4))))))))))))))))))))
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(TEXISTS_SUBPATH_OF_PATH,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ (cpath_image @ V2))) @ ((cIN @ V1) @ (cpath_image @ V2))))) @ (c? @ (^[V3]: ((c/__caret__ @ (cpath @ V3)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V3)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V3)) @ V1)) @ ((cSUBSET @ (cpath_image @ V3)) @ (cpath_image @ V2)))))))))))))))
(TEXISTS_SUBPATH_OF_ARC_NOENDS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (carc @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ (cpath_image @ V2))) @ ((c/__caret__ @ ((cIN @ V1) @ (cpath_image @ V2))) @ ((c= @ ((cINTER @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))) @ ((cINSERT @ (cpathstart @ V2)) @ ((cINSERT @ (cpathfinish @ V2)) @ cEMPTY)))) @ cEMPTY))))) @ (c? @ (^[V3]: ((c/__caret__ @ (cpath @ V3)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V3)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V3)) @ V1)) @ ((cSUBSET @ (cpath_image @ V3)) @ ((cDIFF @ (cpath_image @ V2)) @ ((cINSERT @ (cpathstart @ V2)) @ ((cINSERT @ (cpathfinish @ V2)) @ cEMPTY)))))))))))))))))
(TEXISTS_SUBARC_OF_ARC_NOENDS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (carc @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ (cpath_image @ V2))) @ ((c/__caret__ @ ((cIN @ V1) @ (cpath_image @ V2))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c= @ ((cINTER @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))) @ ((cINSERT @ (cpathstart @ V2)) @ ((cINSERT @ (cpathfinish @ V2)) @ cEMPTY)))) @ cEMPTY)))))) @ (c? @ (^[V3]: ((c/__caret__ @ (carc @ V3)) @ ((c/__caret__ @ ((c= @ (cpathstart @ V3)) @ V0)) @ ((c/__caret__ @ ((c= @ (cpathfinish @ V3)) @ V1)) @ ((cSUBSET @ (cpath_image @ V3)) @ ((cDIFF @ (cpath_image @ V2)) @ ((cINSERT @ (cpathstart @ V2)) @ ((cINSERT @ (cpathfinish @ V2)) @ cEMPTY)))))))))))))))))
(TCONTINUOUS_IVT_LOCAL_EXTREMUM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ V1))) @ ((c= @ (V2 @ V0)) @ (V2 @ V1))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ (copen_segment @ ((c__comma__ @ V0) @ V1)))) @ ((c__caret__/ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((creal_le @ (cdrop @ (V2 @ V4))) @ (cdrop @ (V2 @ V3))))))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((creal_le @ (cdrop @ (V2 @ V3))) @ (cdrop @ (V2 @ V4))))))))))))))))))
(TMEASURABLE_ON_COMPOSE_CONTINUOUS_OPEN_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cmeasurable_on @ V3) @ cUNIV)) @ ((c/__caret__ @ (c! @ (^[V4]: ((cIN @ (V3 @ V4)) @ (copen_interval @ ((c__comma__ @ V0) @ V1)))))) @ ((ccontinuous_on @ V2) @ (copen_interval @ ((c__comma__ @ V0) @ V1)))))) @ ((cmeasurable_on @ ((co @ V2) @ V3)) @ cUNIV)))))))))))
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(TSEGMENT_FACE_OF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cface_of @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)) @ ((cextreme_point_of @ V1) @ V2)))))))))
(TSEGMENT_EDGE_OF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cedge_of @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL))) @ V2)) @ ((cextreme_point_of @ V1) @ V2)))))))))
(TSEGMENT_EDGE_OF_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cedge_of @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)) @ ((cextreme_point_of @ V1) @ V2)))))))))
(TEQ_SPAN_INSERT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ ((cvector_sub @ V0) @ V1)) @ (cspan @ V2))) @ ((c= @ (cspan @ ((cINSERT @ V0) @ V2))) @ (cspan @ ((cINSERT @ V1) @ V2)))))))))))
(TCONNECTED_COMPONENT_1_GEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ (((cconnected_component @ V2) @ V0) @ V1)) @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2))))))))))
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(TINSIDE_SAME_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((cconnected_component @ ((cDIFF @ cUNIV) @ V2)) @ V0) @ V1)) @ ((cIN @ V0) @ (cinside @ V2)))) @ ((cIN @ V1) @ (cinside @ V2))))))))))
(TCONTENT_0_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cSUBSET @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (ccontent @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))
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(TIN_SPAN_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ (cspan @ ((cINSERT @ V0) @ V2)))) @ (c~ @ ((cIN @ V1) @ (cspan @ V2))))) @ ((cIN @ V0) @ (cspan @ ((cINSERT @ V1) @ V2)))))))))))
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(TSPAN_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ (cspan @ V2))) @ ((cIN @ V1) @ (cspan @ ((cINSERT @ V0) @ V2))))) @ ((cIN @ V1) @ (cspan @ V2))))))))))
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(TCARD_EQ_PATH_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cpath_connected @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((c/__caret__ @ ((cIN @ V1) @ V2)) @ (c~ @ ((c= @ V0) @ V1)))))) @ ((c=_c @ V2) @ cUNIV)))))))))
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(TCONTINUOUS_INTERVAL_BIJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((ccontinuous @ ((cinterval_bij @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))) @ (cat @ V4)))))))))))))
(TTARSKI_AXIOM_10_EUCLIDEAN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cbetween @ V0) @ ((c__comma__ @ V3) @ V4))) @ ((c/__caret__ @ ((cbetween @ V0) @ ((c__comma__ @ V1) @ V2))) @ (c~ @ ((c= @ V3) @ V0))))) @ (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((cbetween @ V1) @ ((c__comma__ @ V3) @ V5))) @ ((c/__caret__ @ ((cbetween @ V2) @ ((c__comma__ @ V3) @ V6))) @ ((cbetween @ V4) @ ((c__comma__ @ V5) @ V6))))))))))))))))))))
(TIN_INTERVAL_INTERVAL_BIJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ cEMPTY)))) @ ((cIN @ (((cinterval_bij @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V3) @ V4)) @ V2)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))
(TINTERVAL_BIJ_BIJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c<= @ V5) @ (cdimindex @ cUNIV)))) @ ((c/__caret__ @ ((creal_lt @ ((c$ @ V2) @ V5)) @ ((c$ @ V3) @ V5))) @ ((creal_lt @ ((c$ @ V0) @ V5)) @ ((c$ @ V1) @ V5))))))) @ ((c= @ (((cinterval_bij @ ((c__comma__ @ V2) @ V3)) @ ((c__comma__ @ V0) @ V1)) @ (((cinterval_bij @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3)) @ V4))) @ V4)))))))))))))
(Tinterval_bij,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((cinterval_bij @ ((c__comma__ @ V2) @ V1)) @ ((c__comma__ @ V4) @ V3)) @ V0)) @ (clambda @ (^[V5]: ((creal_add @ ((c$ @ V4) @ V5)) @ ((creal_mul @ ((creal_div @ ((creal_sub @ ((c$ @ V0) @ V5)) @ ((c$ @ V2) @ V5))) @ ((creal_sub @ ((c$ @ V1) @ V5)) @ ((c$ @ V2) @ V5)))) @ ((creal_sub @ ((c$ @ V3) @ V5)) @ ((c$ @ V4) @ V5))))))))))))))))))
(TRIGID_TRANSFORMATION_BETWEEN_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V1) @ V3))) @ (cdistance @ ((c__comma__ @ V0) @ V2)))) @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V3) @ V5))) @ (cdistance @ ((c__comma__ @ V2) @ V4)))) @ ((c= @ (cdistance @ ((c__comma__ @ V5) @ V1))) @ (cdistance @ ((c__comma__ @ V4) @ V0)))))) @ (c? @ (^[V6]: (c? @ (^[V7]: ((c/__caret__ @ (corthogonal_transformation @ V7)) @ ((c/__caret__ @ ((c= @ V0) @ ((cvector_add @ V6) @ (V7 @ V1)))) @ ((c/__caret__ @ ((c= @ V2) @ ((cvector_add @ V6) @ (V7 @ V3)))) @ ((c= @ V4) @ ((cvector_add @ V6) @ (V7 @ V5))))))))))))))))))))))))
(TINTEGRAL_SWAP_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((ccontinuous_on @ (^[V5]: ((V4 @ (cfstcart @ V5)) @ (csndcart @ V5)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cpastecart @ V2) @ V0)) @ ((cpastecart @ V3) @ V1))) @ cNIL)))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (^[V5]: ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (V4 @ V5))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (^[V5]: ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (^[V6]: ((V4 @ V6) @ V5))))))))))))))))))
(TCRAMER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ (cdet @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((c= @ ((cmatrix_vector_mul @ V2) @ V0)) @ V1)) @ ((c= @ V0) @ (clambda @ (^[V3]: ((creal_div @ (cdet @ (clambda @ (^[V4]: (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V3)) @ ((c$ @ V1) @ V4)) @ ((c$ @ ((c$ @ V2) @ V4)) @ V5)))))))) @ (cdet @ V2))))))))))))))
(TFRECHET_DERIVATIVE_CONST_AT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cfrechet_derivative @ (^[V2]: V0)) @ (cat @ V1))) @ (^[V2]: (cvec @ (cNUMERAL @ c_0)))))))))
(THAS_INTEGRAL_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (((chas_integral @ (^[V3]: V0)) @ ((c% @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ V0)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))
(TINTEGRABLE_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((cintegrable_on @ (^[V3]: V0)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))
(TDOT_MATRIX_VECTOR_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cdot @ ((cmatrix_vector_mul @ V1) @ V0)) @ ((cmatrix_vector_mul @ V2) @ V3))) @ ((c$ @ ((c$ @ ((cmatrix_mul @ (crowvector @ V0)) @ ((cmatrix_mul @ ((cmatrix_mul @ (ctransp @ V1)) @ V2)) @ (ccolumnvector @ V3)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))
(TMATRIX_MUL_VSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_vector_mul @ V1) @ V0)) @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V2]: ((c% @ ((c$ @ V0) @ V2)) @ ((ccolumn @ V2) @ V1))))))))))
(TMATRIX_VECTOR_COLUMN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_vector_mul @ V1) @ V0)) @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V2]: ((c% @ ((c$ @ V0) @ V2)) @ ((c$ @ (ctransp @ V1)) @ V2))))))))))
(TBALL_SUBSET_OPEN_MAP_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cbounded @ V3)) @ ((c/__caret__ @ ((ccontinuous_on @ V2) @ (cclosure @ V3))) @ ((c/__caret__ @ (copen @ ((cIMAGE @ V2) @ (cinterior @ V3)))) @ ((c/__caret__ @ ((cIN @ V0) @ V3)) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ (cfrontier @ V3))) @ ((creal_le @ V1) @ (cvector_norm @ ((cvector_sub @ (V2 @ V4)) @ (V2 @ V0))))))))))))) @ ((cSUBSET @ (cball @ ((c__comma__ @ (V2 @ V0)) @ V1))) @ ((cIMAGE @ V2) @ V3))))))))))))
(TINTEGRAL_SPLIT_SIGNED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((creal_le @ ((c$ @ V0) @ V1)) @ ((c$ @ V3) @ V1))) @ ((cintegrable_on @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V1)) @ ((creal_max @ ((c$ @ V3) @ V1)) @ V2)) @ ((c$ @ V3) @ V5)))))) @ cNIL)))))))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL))) @ V4)) @ ((cvector_add @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V1)) @ V2) @ ((c$ @ V3) @ V5)))))) @ cNIL))) @ V4)) @ ((c% @ (((cCOND @ ((creal_lt @ ((c$ @ V3) @ V1)) @ V2)) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V1)) @ ((creal_min @ ((c$ @ V3) @ V1)) @ V2)) @ ((c$ @ V0) @ V5))))) @ (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V1)) @ ((creal_max @ ((c$ @ V3) @ V1)) @ V2)) @ ((c$ @ V3) @ V5)))))) @ cNIL))) @ V4))))))))))))))))
(THAS_BOUNDED_SETVARIATION_TRANSLATION2_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chas_bounded_setvariation_on @ (^[V3]: (V1 @ ((cIMAGE @ (^[V4]: ((cvector_add @ V0) @ V4))) @ V3)))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ (cvector_neg @ V0)) @ V3))) @ V2))) @ ((chas_bounded_setvariation_on @ V1) @ V2)))))))))
(TURYSOHN_LOCAL_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V1)) @ ((c/__caret__ @ ((cclosed_in @ ((csubtopology @ ceuclidean) @ V2)) @ V4)) @ ((c/__caret__ @ ((c= @ ((cINTER @ V1) @ V4)) @ cEMPTY)) @ (c~ @ ((c= @ V0) @ V3)))))) @ (c? @ (^[V5]: ((c/__caret__ @ ((ccontinuous_on @ V5) @ V2)) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((cIN @ (V5 @ V6)) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V3)) @ cNIL))))))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((c= @ ((c= @ (V5 @ V6)) @ V0)) @ ((cIN @ V6) @ V1)))))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ V2)) @ ((c= @ ((c= @ (V5 @ V6)) @ V3)) @ ((cIN @ V6) @ V4))))))))))))))))))))))
(TURYSOHN_STRONG,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ ((c/__caret__ @ (cclosed @ V3)) @ ((c/__caret__ @ ((c= @ ((cINTER @ V1) @ V3)) @ cEMPTY)) @ (c~ @ ((c= @ V0) @ V2)))))) @ (c? @ (^[V4]: ((c/__caret__ @ ((ccontinuous_on @ V4) @ cUNIV)) @ ((c/__caret__ @ (c! @ (^[V5]: ((cIN @ (V4 @ V5)) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c= @ ((c= @ (V4 @ V5)) @ V0)) @ ((cIN @ V5) @ V1))))) @ (c! @ (^[V5]: ((c= @ ((c= @ (V4 @ V5)) @ V2)) @ ((cIN @ V5) @ V3)))))))))))))))))))
(TCONTINUOUS_AT_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((ccontinuous @ V1) @ (cat @ V0))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (copen @ V2)) @ ((cIN @ (V1 @ V0)) @ V2))) @ (c? @ (^[V3]: ((c/__caret__ @ (copen @ V3)) @ ((c/__caret__ @ ((cIN @ V0) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((cIN @ (V1 @ V4)) @ V2)))))))))))))))))
(TLINEAR_COMPONENTWISE_EXPANSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (clinear @ V1)) @ ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ (V1 @ V0)) @ V2)) @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V3]: ((creal_mul @ ((c$ @ V0) @ V3)) @ ((c$ @ (V1 @ (cbasis @ V3))) @ V2))))))))))))))
(TLIM_TRANSFORM_AWAY_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V4) @ V0))) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V5) @ V4))) @ (c~ @ ((c= @ V5) @ V0)))) @ ((c= @ (V1 @ V5)) @ (V2 @ V5)))))) @ (((c--> @ V1) @ V3) @ (cat @ V4))))) @ (((c--> @ V2) @ V3) @ (cat @ V4))))))))))))))
(TLIM_TRANSFORM_AWAY_WITHIN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V4) @ V0))) @ ((c/__caret__ @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V6) @ V5)) @ ((c/__caret__ @ (c~ @ ((c= @ V6) @ V4))) @ (c~ @ ((c= @ V6) @ V0))))) @ ((c= @ (V1 @ V6)) @ (V2 @ V6)))))) @ (((c--> @ V1) @ V3) @ ((cwithin @ (cat @ V4)) @ V5))))) @ (((c--> @ V2) @ V3) @ ((cwithin @ (cat @ V4)) @ V5))))))))))))))))
(TIN_CONVEX_HULL_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ ((cIN @ V0) @ ((chull @ cconvex) @ V2)))) @ ((cIN @ (V1 @ V0)) @ ((chull @ cconvex) @ ((cIMAGE @ V1) @ V2)))))))))))
(TIN_AFFINE_HULL_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (clinear @ V1)) @ ((cIN @ V0) @ ((chull @ caffine) @ V2)))) @ ((cIN @ (V1 @ V0)) @ ((chull @ caffine) @ ((cIMAGE @ V1) @ V2)))))))))))
(TCONTINUOUS_AT_AVOID,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((ccontinuous @ V1) @ (cat @ V0))) @ (c~ @ ((c= @ (V1 @ V0)) @ V2)))) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (cdistance @ ((c__comma__ @ V0) @ V4))) @ V3)) @ (c~ @ ((c= @ (V1 @ V4)) @ V2))))))))))))))))
(TADJOINT_WORKS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (clinear @ V1)) @ ((c= @ ((cdot @ (V1 @ V0)) @ V2)) @ ((cdot @ V0) @ ((cadjoint @ V1) @ V2)))))))))))
(TLIM_AT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((c--> @ V1) @ V2) @ (cat @ V0))) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdistance @ ((c__comma__ @ V5) @ V0)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V5) @ V0))) @ V4))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ (V1 @ V5)) @ V2))) @ V3))))))))))))))))))
(TSET_VARIATION_TRANSLATION2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cset_variation @ ((cIMAGE @ (^[V3]: ((cvector_add @ (cvector_neg @ V0)) @ V3))) @ V1)) @ (^[V3]: (V2 @ ((cIMAGE @ (^[V4]: ((cvector_add @ V0) @ V4))) @ V3))))) @ ((cset_variation @ V1) @ V2)))))))))
(TCONTINUOUS_WITHIN_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((ccontinuous @ V2) @ ((cwithin @ (cat @ V0)) @ V1))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (copen @ V3)) @ ((cIN @ (V2 @ V0)) @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ (copen @ V4)) @ ((c/__caret__ @ ((cIN @ V0) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V4)) @ ((cIN @ V5) @ V1))) @ ((cIN @ (V2 @ V5)) @ V3)))))))))))))))))))
(THAS_DERIVATIVE_ZERO_UNIQUE_STRONG_CONVEX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cconvex @ V2)) @ ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((c/__caret__ @ ((c= @ (V3 @ V0)) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ ((cDIFF @ V2) @ V1))) @ (((chas_derivative @ V3) @ (^[V7]: (cvec @ (cNUMERAL @ c_0)))) @ ((cwithin @ (cat @ V6)) @ V2))))))))))) @ ((c==> @ ((cIN @ V4) @ V2)) @ ((c= @ (V3 @ V4)) @ V5))))))))))))))))
(THAS_DERIVATIVE_ZERO_UNIQUE_STRONG_CONNECTED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (cconnected @ V2)) @ ((c/__caret__ @ (copen @ V2)) @ ((c/__caret__ @ (cCOUNTABLE @ V1)) @ ((c/__caret__ @ ((ccontinuous_on @ V3) @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((c/__caret__ @ ((c= @ (V3 @ V0)) @ V5)) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ ((cDIFF @ V2) @ V1))) @ (((chas_derivative @ V3) @ (^[V7]: (cvec @ (cNUMERAL @ c_0)))) @ ((cwithin @ (cat @ V6)) @ V2)))))))))))) @ ((c==> @ ((cIN @ V4) @ V2)) @ ((c= @ (V3 @ V4)) @ V5))))))))))))))))
(TNORM_LE_PASTECART_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cvector_norm @ V1)) @ (cvector_norm @ ((cpastecart @ V0) @ V1))))))))
(TNORM_LE_PASTECART_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cvector_norm @ V0)) @ (cvector_norm @ ((cpastecart @ V0) @ V1))))))))
(THOMEOMORPHIC_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((chomeomorphic @ ((cINSERT @ V0) @ cEMPTY)) @ ((cINSERT @ V1) @ cEMPTY)))))))
(TPASTECART_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpastecart @ (cvector_neg @ V0)) @ (cvector_neg @ V1))) @ (cvector_neg @ ((cpastecart @ V0) @ V1))))))))
(TPASTECART_AS_ORTHOGONAL_SUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpastecart @ V0) @ V1)) @ ((cvector_add @ ((cpastecart @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ ((cpastecart @ (cvec @ (cNUMERAL @ c_0))) @ V1))))))))
(TLIMPT_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((climit_point_of @ V0) @ V2)) @ ((climit_point_of @ V1) @ V3))) @ ((climit_point_of @ ((cpastecart @ V0) @ V1)) @ ((cPCROSS @ V2) @ V3))))))))))))
(THOMEOMORPHIC_ONE_POINT_COMPACTIFICATIONS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (ccompact @ V2)) @ ((c/__caret__ @ (ccompact @ V3)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((c/__caret__ @ ((cIN @ V1) @ V3)) @ ((chomeomorphic @ ((cDELETE @ V2) @ V0)) @ ((cDELETE @ V3) @ V1))))))) @ ((chomeomorphic @ V2) @ V3)))))))))))
(TPCROSS_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cPCROSS @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V3)) @ cNIL)))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cpastecart @ V0) @ V1)) @ ((cpastecart @ V2) @ V3))) @ cNIL))))))))))))
(THAS_INTEGRAL_SEPARATE_SIDES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V4) @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV))))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V6)) @ (c? @ (^[V7]: ((c/__caret__ @ (cgauge @ V7)) @ (c! @ (^[V8]: (c! @ (^[V9]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V8) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cGSPEC @ (^[V10]: (c? @ (^[V11]: (((cSETSPEC @ V10) @ ((creal_le @ ((c$ @ V11) @ V2)) @ V3)) @ V11)))))))) @ ((c/__caret__ @ ((cfine @ V7) @ V8)) @ ((c/__caret__ @ ((ctagged_division_of @ V9) @ ((cINTER @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cGSPEC @ (^[V10]: (c? @ (^[V11]: (((cSETSPEC @ V10) @ ((creal_ge @ ((c$ @ V11) @ V2)) @ V3)) @ V11)))))))) @ ((cfine @ V7) @ V9))))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cvector_add @ ((cvsum @ V8) @ (cGABS @ (^[V10]: (c! @ (^[V11]: (c! @ (^[V12]: ((cGEQ @ (V10 @ ((c__comma__ @ V11) @ V12))) @ ((c% @ (ccontent @ V12)) @ (V4 @ V11))))))))))) @ ((cvsum @ V9) @ (cGABS @ (^[V10]: (c! @ (^[V11]: (c! @ (^[V12]: ((cGEQ @ (V10 @ ((c__comma__ @ V11) @ V12))) @ ((c% @ (ccontent @ V12)) @ (V4 @ V11)))))))))))) @ V5))) @ V6))))))))))))))))))))))))))
(TINTEGRAL_COMBINE_TAGGED_DIVISION_BOTTOMUP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cIN @ ((c__comma__ @ V4) @ V5)) @ V2)) @ ((cintegrable_on @ V3) @ V5)))))))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V3)) @ ((cvsum @ V2) @ (cGABS @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((cGEQ @ (V4 @ ((c__comma__ @ V5) @ V6))) @ ((cintegral @ V6) @ V3))))))))))))))))))))
(TINTEGRAL_COMBINE_TAGGED_DIVISION_TOPDOWN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((ctagged_division_of @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V3)) @ ((cvsum @ V2) @ (cGABS @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((cGEQ @ (V4 @ ((c__comma__ @ V5) @ V6))) @ ((cintegral @ V6) @ V3))))))))))))))))))))
(TVSUM_CONTENT_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((ctagged_division_of @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))) @ ((c= @ ((cvsum @ V2) @ (cGABS @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((cGEQ @ (V4 @ ((c__comma__ @ V5) @ V6))) @ ((c% @ (ccontent @ V6)) @ (V3 @ V5))))))))))) @ (cvec @ (cNUMERAL @ c_0)))))))))))))
(THAS_BOUNDED_SETVARIATION_WORKS_ON_INTERVAL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chas_bounded_setvariation_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: ((c==> @ ((cdivision_of @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((creal_le @ ((csum @ V4) @ (^[V5]: (cvector_norm @ (V2 @ V5))))) @ V3))))) @ ((creal_le @ ((cset_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)) @ V3))))))))))))
(THAS_BOUNDED_SETVARIATION_WORKS_ON_INTERVAL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((chas_bounded_setvariation_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (c! @ (^[V3]: ((c==> @ ((cdivision_of @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((creal_le @ ((csum @ V3) @ (^[V4]: (cvector_norm @ (V2 @ V4))))) @ ((cset_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)))))))))))))
(TSET_VARIATION_ON_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cset_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)) @ (csup @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((cdivision_of @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((csum @ V4) @ (^[V5]: (cvector_norm @ (V2 @ V5))))))))))))))))))
(THAS_BOUNDED_SETVARIATION_ON_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chas_bounded_setvariation_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (c? @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((cdivision_of @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((creal_le @ ((csum @ V4) @ (^[V5]: (cvector_norm @ (V2 @ V5))))) @ V3))))))))))))))
(TSET_VARIATION_UBOUND_ON_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((cdivision_of @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((creal_le @ ((csum @ V4) @ (^[V5]: (cvector_norm @ (V2 @ V5))))) @ V3)))))) @ ((creal_le @ ((cset_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)) @ V3)))))))))))
(TEQUIINTEGRABLE_DIVISION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cdivision_of @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c= @ ((cequiintegrable_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V2)) @ ((cequiintegrable_on @ V3) @ V4)))))))))))))))
(TFINE_DIVISION_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cgauge @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((ctagged_division_of @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cfine @ V2) @ V3))))))))))))
(THENSTOCK_LEMMA_PART2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((c/__caret__ @ (cgauge @ V2)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cfine @ V2) @ V6))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cvsum @ V6) @ (cGABS @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((cGEQ @ (V7 @ ((c__comma__ @ V8) @ V9))) @ ((c% @ (ccontent @ V9)) @ (V4 @ V8))))))))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V4)))) @ V5)))))))) @ ((c==> @ ((c/__caret__ @ ((ctagged_partial_division_of @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cfine @ V2) @ V3))) @ ((creal_le @ ((csum @ V3) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ (cvector_norm @ ((cvector_sub @ ((c% @ (ccontent @ V8)) @ (V4 @ V7))) @ ((cintegral @ V8) @ V4)))))))))))) @ ((creal_mul @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ (creal_of_num @ (cdimindex @ cUNIV))) @ V5))))))))))))))))))
(THENSTOCK_LEMMA_PART1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((c/__caret__ @ (cgauge @ V2)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cfine @ V2) @ V6))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cvsum @ V6) @ (cGABS @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((cGEQ @ (V7 @ ((c__comma__ @ V8) @ V9))) @ ((c% @ (ccontent @ V9)) @ (V4 @ V8))))))))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V4)))) @ V5)))))))) @ ((c==> @ ((c/__caret__ @ ((ctagged_partial_division_of @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cfine @ V2) @ V3))) @ ((creal_le @ (cvector_norm @ ((cvsum @ V3) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ ((cvector_sub @ ((c% @ (ccontent @ V8)) @ (V4 @ V7))) @ ((cintegral @ V8) @ V4)))))))))))) @ V5))))))))))))))))
(TABSOLUTELY_INTEGRABLE_SET_VARIATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cabsolutely_integrable_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c= @ ((cset_variation @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (^[V3]: ((cintegral @ V3) @ V2)))) @ (cdrop @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (^[V3]: (clift @ (cvector_norm @ (V2 @ V3)))))))))))))))
(TINTEGRAL_REFLECT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (cvector_neg @ V1)) @ (cvector_neg @ V0))) @ cNIL))) @ (^[V3]: (V2 @ (cvector_neg @ V3))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)))))))))
(TINTEGRABLE_CAUCHY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cintegrable_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (c! @ (^[V3]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ (cgauge @ V4)) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((cfine @ V4) @ V5)) @ ((c/__caret__ @ ((ctagged_division_of @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cfine @ V4) @ V6))))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cvsum @ V5) @ (cGABS @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((cGEQ @ (V7 @ ((c__comma__ @ V8) @ V9))) @ ((c% @ (ccontent @ V9)) @ (V2 @ V8))))))))))) @ ((cvsum @ V6) @ (cGABS @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((cGEQ @ (V7 @ ((c__comma__ @ V8) @ V9))) @ ((c% @ (ccontent @ V9)) @ (V2 @ V8))))))))))))) @ V3))))))))))))))))))))
(THENSTOCK_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((cintegrable_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ (c? @ (^[V4]: ((c/__caret__ @ (cgauge @ V4)) @ (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ctagged_partial_division_of @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cfine @ V4) @ V5))) @ ((creal_lt @ ((csum @ V5) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ (cvector_norm @ ((cvector_sub @ ((c% @ (ccontent @ V8)) @ (V2 @ V7))) @ ((cintegral @ V8) @ V2)))))))))))) @ V3))))))))))))))))))
(TINDEFINITE_INTEGRAL_UNIFORMLY_CONTINUOUS_EXPLICIT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3))) @ (c? @ (^[V4]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V8) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((creal_le @ (cvector_norm @ ((cvector_sub @ V7) @ V5))) @ V4)) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ V8) @ V6))) @ V4))))))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V7) @ V8)) @ cNIL))) @ V2)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V5) @ V6)) @ cNIL))) @ V2)))) @ V3)))))))))))))))))))))))
(TRSUM_COMPONENT_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V5)) @ ((c/__caret__ @ ((c<= @ V5) @ (cdimindex @ cUNIV))) @ (c! @ (^[V6]: ((c==> @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((creal_le @ ((c$ @ (V2 @ V6)) @ V5)) @ ((c$ @ (V4 @ V6)) @ V5))))))))) @ ((creal_le @ ((c$ @ ((cvsum @ V3) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ ((c% @ (ccontent @ V8)) @ (V2 @ V7))))))))))) @ V5)) @ ((c$ @ ((cvsum @ V3) @ (cGABS @ (^[V6]: (c! @ (^[V7]: (c! @ (^[V8]: ((cGEQ @ (V6 @ ((c__comma__ @ V7) @ V8))) @ ((c% @ (ccontent @ V8)) @ (V4 @ V7))))))))))) @ V5))))))))))))))))
(THAS_INTEGRAL_RESTRICT_CLOSED_SUBINTERVALS_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c= @ (((chas_integral @ (^[V6]: (((cCOND @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))) @ (V2 @ V6)) @ (cvec @ (cNUMERAL @ c_0))))) @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (((chas_integral @ V2) @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))))))))))))))))
(THAS_INTEGRAL_RESTRICT_OPEN_SUBINTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V2) @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))) @ (((chas_integral @ (^[V6]: (((cCOND @ ((cIN @ V6) @ (copen_interval @ ((c__comma__ @ V0) @ V1)))) @ (V2 @ V6)) @ (cvec @ (cNUMERAL @ c_0))))) @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))))))))))))))))
(THAS_INTEGRAL_RESTRICT_CLOSED_SUBINTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ (((chas_integral @ V2) @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL))))) @ (((chas_integral @ (^[V6]: (((cCOND @ ((cIN @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (V2 @ V6)) @ (cvec @ (cNUMERAL @ c_0))))) @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V4) @ V5)) @ cNIL)))))))))))))))))
(TINTEGRABLE_SUBINTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))) @ ((cintegrable_on @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V3) @ V4)) @ cNIL)))))))))))))))
(TSET_VARIATION_GE_FUNCTION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((chas_bounded_setvariation_on @ V3) @ V2)) @ ((c/__caret__ @ ((cSUBSET @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)) @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ cEMPTY))))) @ ((creal_le @ (cvector_norm @ (V3 @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))) @ ((cset_variation @ V2) @ V3))))))))))))
(TCONTENT_PASTECART,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cpastecart @ V0) @ V2)) @ ((cpastecart @ V1) @ V3))) @ cNIL)))) @ ((creal_mul @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))))))))))))))
(TPASTECART_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cvector_sub @ ((cpastecart @ V0) @ V2)) @ ((cpastecart @ V1) @ V3))) @ ((cpastecart @ ((cvector_sub @ V0) @ V1)) @ ((cvector_sub @ V2) @ V3))))))))))))
(TPASTECART_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cvector_add @ ((cpastecart @ V0) @ V2)) @ ((cpastecart @ V1) @ V3))) @ ((cpastecart @ ((cvector_add @ V0) @ V1)) @ ((cvector_add @ V2) @ V3))))))))))))
(TPASTECART_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cpastecart @ V0) @ V2)) @ ((cpastecart @ V1) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ V3))))))))))))
(TINTEGRAL_PASTECART_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((ccontinuous_on @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cpastecart @ V0) @ V2)) @ ((cpastecart @ V1) @ V3))) @ cNIL)))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cpastecart @ V0) @ V2)) @ ((cpastecart @ V1) @ V3))) @ cNIL))) @ V4)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (^[V5]: ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (^[V6]: (V4 @ ((cpastecart @ V5) @ V6)))))))))))))))))))
(TINTEGRAL_PASTECART_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cpastecart @ V0) @ V2)) @ ((cpastecart @ V1) @ V3))) @ cNIL))) @ (^[V5]: V4))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (^[V5]: ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ (^[V6]: V4))))))))))))))))
(TINTEGRAL_INTERVALS_INCLUSION_EXCLUSION_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((cIN @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL))) @ V3)) @ ((cvsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cSUBSET @ V5) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ V5)))))) @ (^[V4]: ((c% @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ V4))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (clambda @ (^[V5]: (((cCOND @ ((cIN @ V5) @ V4)) @ ((c$ @ V0) @ V5)) @ ((c$ @ V1) @ V5))))) @ V2)) @ cNIL))) @ V3)))))))))))))))
(TINTEGRAL_INTERVALS_INCLUSION_EXCLUSION_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL)))) @ ((cIN @ V1) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V2)) @ cNIL))))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V3)) @ ((cvsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((cSUBSET @ V5) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ V5)))))) @ (^[V4]: ((c% @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ V4))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ (clambda @ (^[V5]: (((cCOND @ ((cIN @ V5) @ V4)) @ ((c$ @ V1) @ V5)) @ ((c$ @ V2) @ V5)))))) @ cNIL))) @ V3)))))))))))))))
(TINTEGRAL_INTERVALS_DIFF_INCLUSION_EXCLUSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL)))) @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL)))))) @ ((c= @ ((cvector_sub @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V4)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V3)) @ cNIL))) @ V4))) @ ((cvsum @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ (c~ @ ((c= @ V6) @ cEMPTY))) @ ((cSUBSET @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))) @ V6)))))) @ (^[V5]: ((c% @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V5)) @ ((creal_lt @ ((c$ @ V2) @ V7)) @ ((c$ @ V3) @ V7)))) @ V7)))))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (clambda @ (^[V6]: (((cCOND @ ((cIN @ V6) @ V5)) @ ((creal_min @ ((c$ @ V3) @ V6)) @ ((c$ @ V2) @ V6))) @ ((c$ @ V1) @ V6))))) @ (clambda @ (^[V6]: (((cCOND @ ((cIN @ V6) @ V5)) @ ((creal_max @ ((c$ @ V3) @ V6)) @ ((c$ @ V2) @ V6))) @ ((c$ @ V3) @ V6)))))) @ cNIL))) @ V4)))))))))))))))))
(TINTEGRAL_INTERVALS_INCLUSION_EXCLUSION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL)))) @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ cNIL)))))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))) @ V4)) @ ((cvsum @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((cSUBSET @ V6) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ V6)))))) @ (^[V5]: ((c% @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cCARD @ (cGSPEC @ (^[V6]: (c? @ (^[V7]: (((cSETSPEC @ V6) @ ((c/__caret__ @ ((cIN @ V7) @ V5)) @ ((creal_lt @ ((c$ @ V2) @ V7)) @ ((c$ @ V3) @ V7)))) @ V7)))))))) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ (clambda @ (^[V6]: (((cCOND @ ((cIN @ V6) @ V5)) @ ((creal_min @ ((c$ @ V3) @ V6)) @ ((c$ @ V2) @ V6))) @ ((c$ @ V1) @ V6))))) @ (clambda @ (^[V6]: (((cCOND @ ((cIN @ V6) @ V5)) @ ((creal_max @ ((c$ @ V3) @ V6)) @ ((c$ @ V2) @ V6))) @ ((c$ @ V3) @ V6)))))) @ cNIL))) @ V4)))))))))))))))))
(TINDEFINITE_INTEGRAL_CONTINUOUS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cintegrable_on @ V4) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5))))) @ (c? @ (^[V6]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V6)) @ (c! @ (^[V7]: (c! @ (^[V8]: ((c==> @ ((c/__caret__ @ ((cIN @ V7) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((cIN @ V8) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c/__caret__ @ ((creal_le @ (cvector_norm @ ((cvector_sub @ V7) @ V2))) @ V6)) @ ((creal_le @ (cvector_norm @ ((cvector_sub @ V8) @ V3))) @ V6))))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V7) @ V8)) @ cNIL))) @ V4)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V2) @ V3)) @ cNIL))) @ V4)))) @ V5)))))))))))))))))))))))
(TFARKAS_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ ((cmatrix_vector_mul @ V1) @ V2)) @ V0)) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V2) @ V3))))))))) @ (c~ @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ ((cdot @ V0) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ ((cmatrix_vector_mul @ (ctransp @ V1)) @ V2)) @ V3)))))))))))))))
(TDOT_LMUL_MATRIX,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ ((cvector_matrix_mul @ V0) @ V1)) @ V2)) @ ((cdot @ V0) @ ((cmatrix_vector_mul @ V1) @ V2))))))))))
(TMATRIX_VECTOR_MUL_IN_COLUMNSPACE,(c! @ (^[V0]: (c! @ (^[V1]: ((cIN @ ((cmatrix_vector_mul @ V1) @ V0)) @ (cspan @ (ccolumns @ V1))))))))
(TMATRIX_VECTOR_MUL_TRANSP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_vector_mul @ V1) @ V0)) @ ((cvector_matrix_mul @ V0) @ (ctransp @ V1))))))))
(TMATRIX_VECTOR_MUL_SUB_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_vector_mul @ V1) @ ((cvector_sub @ V0) @ V2))) @ ((cvector_sub @ ((cmatrix_vector_mul @ V1) @ V0)) @ ((cmatrix_vector_mul @ V1) @ V2))))))))))
(TMATRIX_VECTOR_MUL_ADD_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_vector_mul @ V1) @ ((cvector_add @ V0) @ V2))) @ ((cvector_add @ ((cmatrix_vector_mul @ V1) @ V0)) @ ((cmatrix_vector_mul @ V1) @ V2))))))))))
(TcollinearSymmetry_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (ccollinear @ ((cINSERT @ V2) @ ((cINSERT @ V1) @ ((cINSERT @ V0) @ cEMPTY))))) @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))))
(TcollinearSymmetry_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (ccollinear @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))) @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))))
(TcollinearSymmetry_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (ccollinear @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ cEMPTY))))) @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))))
(TcollinearSymmetry_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (ccollinear @ ((cINSERT @ V1) @ ((cINSERT @ V0) @ ((cINSERT @ V2) @ cEMPTY))))) @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))))
(TcollinearSymmetry_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V2) @ ((cINSERT @ V1) @ cEMPTY))))) @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))))
(TNoncollinear_3ImpliesDistinct_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ (ccollinear @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ cEMPTY)))))) @ (c~ @ ((c= @ V1) @ V2))))))))))
(TNoncollinear_3ImpliesDistinct_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ (ccollinear @ ((cINSERT @ V1) @ ((cINSERT @ V0) @ ((cINSERT @ V2) @ cEMPTY)))))) @ (c~ @ ((c= @ V1) @ V2))))))))))
(TNoncollinear_3ImpliesDistinct_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY)))))) @ (c~ @ ((c= @ V1) @ V2))))))))))
(THYPERPLANE_EQUIV_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((chyperplane_equiv @ V1) @ V2) @ V0)) @ (((chyperplane_equiv @ V1) @ V0) @ V3))) @ (((chyperplane_equiv @ V1) @ V2) @ V3)))))))))))
(TTARSKI_AXIOM_6_EUCLIDEAN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cbetween @ V1) @ ((c__comma__ @ V0) @ V0))) @ ((c= @ V0) @ V1)))))))
(TTARSKI_AXIOM_3_EUCLIDEAN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (cdistance @ ((c__comma__ @ V1) @ V2))) @ (cdistance @ ((c__comma__ @ V0) @ V0)))) @ ((c= @ V1) @ V2)))))))))
(TTARSKI_AXIOM_2_EUCLIDEAN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (cdistance @ ((c__comma__ @ V2) @ V3)))) @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (cdistance @ ((c__comma__ @ V4) @ V5))))) @ ((c= @ (cdistance @ ((c__comma__ @ V2) @ V3))) @ (cdistance @ ((c__comma__ @ V4) @ V5)))))))))))))))))
(TINTEGRAL_OPEN_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cintegral @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ V2)) @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)))))))))
(TMEASURABLE_CBALL,(c! @ (^[V0]: (c! @ (^[V1]: (cmeasurable @ (ccball @ ((c__comma__ @ V0) @ V1))))))))
(TMEASURABLE_BALL,(c! @ (^[V0]: (c! @ (^[V1]: (cmeasurable @ (cball @ ((c__comma__ @ V0) @ V1))))))))
(TABSOLUTELY_INTEGRABLE_ON_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cabsolutely_integrable_on @ (^[V2]: V0)) @ V1)) @ ((c__caret__/ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (cmeasurable @ V1))))))))
(TNEGLIGIBLE_INTERVAL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnegligible @ (copen_interval @ ((c__comma__ @ V0) @ V1)))) @ ((c= @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ cEMPTY)))))))
(TNEGLIGIBLE_INTERVAL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cnegligible @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((c= @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ cEMPTY)))))))
(TABSOLUTELY_INTEGRABLE_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((cabsolutely_integrable_on @ (^[V3]: V0)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL))))))))))
(TDROP_INDICATOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdrop @ ((cindicator @ V1) @ V0))) @ (((cCOND @ ((cIN @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TINTEGRAL_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (^[V3]: V2))) @ ((c% @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ V2)))))))))
(TINTEGRAL_REFL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V0)) @ cNIL))) @ V1)) @ (cvec @ (cNUMERAL @ c_0))))))))
(TINTEGRAL_NULL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ ((cintegral @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)) @ (cvec @ (cNUMERAL @ c_0)))))))))))
(THAS_INTEGRAL_INTEGRABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((chas_integral @ V1) @ V0) @ V2)) @ ((cintegrable_on @ V1) @ V2)))))))))
(Thas_integral,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((chas_integral @ V2) @ V3) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (c! @ (^[V4]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ (cgauge @ V5)) @ (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((ctagged_division_of @ V6) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ ((cfine @ V5) @ V6))) @ ((creal_lt @ (cvector_norm @ ((cvector_sub @ ((cvsum @ V6) @ (cGABS @ (^[V7]: (c! @ (^[V8]: (c! @ (^[V9]: ((cGEQ @ (V7 @ ((c__comma__ @ V8) @ V9))) @ ((c% @ (ccontent @ V9)) @ (V2 @ V8))))))))))) @ V3))) @ V4))))))))))))))))))))
(TTAGGED_DIVISION_OF_SELF,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ ((ctagged_division_of @ ((cINSERT @ ((c__comma__ @ V0) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))) @ cEMPTY)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TDIVISION_OF_CONTENT_0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((cdivision_of @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))) @ ((c==> @ ((cIN @ V3) @ V2)) @ ((c= @ (ccontent @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))))
(TELEMENTARY_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((cdivision_of @ V2) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))))
(TDIVISION_OF_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ cEMPTY))) @ ((cdivision_of @ ((cINSERT @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ cEMPTY)) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))))))))
(TCONTENT_LT_NZ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))) @ (c~ @ ((c= @ (ccontent @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))
(THAS_VECTOR_DERIVATIVE_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (((chas_vector_derivative @ (^[V2]: V0)) @ (cvec @ (cNUMERAL @ c_0))) @ V1))))))
(THAS_DERIVATIVE_ZERO_CONNECTED_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (copen @ V1)) @ ((c/__caret__ @ (cconnected @ V1)) @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ ((c/__caret__ @ ((c= @ (V2 @ V0)) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ (((chas_derivative @ V2) @ (^[V6]: (cvec @ (cNUMERAL @ c_0)))) @ (cat @ V5)))))))))) @ ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ V4))))))))))))))
(THAS_DERIVATIVE_ZERO_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cconvex @ V1)) @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ ((c/__caret__ @ ((c= @ (V2 @ V0)) @ V4)) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ (((chas_derivative @ V2) @ (^[V6]: (cvec @ (cNUMERAL @ c_0)))) @ ((cwithin @ (cat @ V5)) @ V1))))))))) @ ((c==> @ ((cIN @ V3) @ V1)) @ ((c= @ (V2 @ V3)) @ V4))))))))))))))
(TDIFFERENTIABLE_ON_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((cdifferentiable_on @ (^[V2]: V0)) @ V1))))))
(TDIFFERENTIABLE_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((cdifferentiable @ (^[V2]: V0)) @ V1))))))
(THAS_DERIVATIVE_CONST,(c! @ (^[V0]: (c! @ (^[V1]: (((chas_derivative @ (^[V2]: V0)) @ (^[V2]: (cvec @ (cNUMERAL @ c_0)))) @ V1))))))
(TCONTINUOUS_ON_INTERVAL_BIJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((ccontinuous_on @ ((cinterval_bij @ ((c__comma__ @ V0) @ V1)) @ ((c__comma__ @ V2) @ V3))) @ V4))))))))))))
(TINTERVAL_BIJ_AFFINE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cinterval_bij @ ((c__comma__ @ V3) @ V2)) @ ((c__comma__ @ V1) @ V0))) @ (^[V4]: ((cvector_add @ (clambda @ (^[V5]: ((creal_mul @ ((creal_div @ ((creal_sub @ ((c$ @ V0) @ V5)) @ ((c$ @ V1) @ V5))) @ ((creal_sub @ ((c$ @ V2) @ V5)) @ ((c$ @ V3) @ V5)))) @ ((c$ @ V4) @ V5))))) @ (clambda @ (^[V5]: ((creal_sub @ ((c$ @ V1) @ V5)) @ ((creal_mul @ ((creal_div @ ((creal_sub @ ((c$ @ V0) @ V5)) @ ((c$ @ V1) @ V5))) @ ((creal_sub @ ((c$ @ V2) @ V5)) @ ((c$ @ V3) @ V5)))) @ ((c$ @ V3) @ V5)))))))))))))))))
(TPOLYHEDRON_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (cpolyhedron @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
(TPOLYTOPE_SING,(c! @ (^[V0]: (cpolytope @ ((cINSERT @ V0) @ cEMPTY)))))
(TPOLYTOPE_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: (cpolytope @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
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(TEXTREME_POINT_OF_CONVEX_HULL_AFFINE_INDEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ (caffine_dependent @ V1))) @ ((c= @ ((cextreme_point_of @ V0) @ ((chull @ cconvex) @ V1))) @ ((cIN @ V0) @ V1))))))))
(TEXTREME_POINT_OF_INTER_SUPPORTING_HYPERPLANE_GE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((creal_ge @ ((cdot @ V0) @ V4)) @ V1))))) @ ((c= @ ((cINTER @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V0) @ V5)) @ V1)) @ V5))))))) @ ((cINSERT @ V2) @ cEMPTY)))) @ ((cextreme_point_of @ V2) @ V3)))))))))))
(TEXTREME_POINT_OF_INTER_SUPPORTING_HYPERPLANE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c! @ (^[V4]: ((c==> @ ((cIN @ V4) @ V3)) @ ((creal_le @ ((cdot @ V0) @ V4)) @ V1))))) @ ((c= @ ((cINTER @ V3) @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c= @ ((cdot @ V0) @ V5)) @ V1)) @ V5))))))) @ ((cINSERT @ V2) @ cEMPTY)))) @ ((cextreme_point_of @ V2) @ V3)))))))))))
(TEXTREME_POINT_OF_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cextreme_point_of @ V0) @ V1)) @ ((cextreme_point_of @ V0) @ V2))) @ ((cextreme_point_of @ V0) @ ((cINTER @ V1) @ V2))))))))))
(TEXTREME_POINT_OF_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cextreme_point_of @ V0) @ ((cINSERT @ V1) @ cEMPTY))) @ ((c= @ V0) @ V1)))))))
(TEXTREME_POINT_OF_EMPTY,(c! @ (^[V0]: (c~ @ ((cextreme_point_of @ V0) @ cEMPTY)))))
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(TINSIDE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinside @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ (cinside @ V1))))))))
(TCOMPACT_SEGMENT,(c! @ (^[V0]: (c! @ (^[V1]: (ccompact @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
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(TCONNECTED_SEGMENT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (cconnected @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
(TPATH_CONNECTED_SEGMENT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (cpath_connected @ (copen_segment @ ((c__comma__ @ V0) @ V1))))))))
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(TCONVEX_SEGMENT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (cconvex @ (copen_segment @ ((c__comma__ @ V0) @ V1))))))))
(TCONVEX_SEGMENT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (cconvex @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
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(TPATH_COMPONENT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V0) @ ((cpath_component @ V1) @ V2))) @ ((c= @ ((cpath_component @ V1) @ V0)) @ ((cpath_component @ V1) @ V2))))))))))
(TPATH_COMPONENT_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpath_component @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V1)) @ ((cvector_add @ V0) @ V2))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ ((cpath_component @ V1) @ V2))))))))))
(TPATH_COMPONENT_EMPTY,(c! @ (^[V0]: ((c= @ ((cpath_component @ cEMPTY) @ V0)) @ cEMPTY))))
(TPATH_COMPONENT_EQ_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cpath_component @ V1) @ V0)) @ cEMPTY)) @ (c~ @ ((cIN @ V0) @ V1))))))))
(TPATH_COMPONENT_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ ((cpath_component @ V1) @ V0)) @ V1))))))
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(TLINEPATH_REFL,(c! @ (^[V0]: ((c= @ (clinepath @ ((c__comma__ @ V0) @ V0))) @ (^[V1]: V0)))))
(TARC_LINEPATH_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (carc @ (clinepath @ ((c__comma__ @ V0) @ V1)))) @ (c~ @ ((c= @ V0) @ V1))))))))
(TSIMPLE_PATH_LINEPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ V1))) @ (csimple_path @ (clinepath @ ((c__comma__ @ V0) @ V1)))))))))
(TARC_LINEPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ V1))) @ (carc @ (clinepath @ ((c__comma__ @ V0) @ V1)))))))))
(TREVERSEPATH_LINEPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (creversepath @ (clinepath @ ((c__comma__ @ V1) @ V0)))) @ (clinepath @ ((c__comma__ @ V0) @ V1))))))))
(TPATH_IMAGE_LINEPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpath_image @ (clinepath @ ((c__comma__ @ V0) @ V1)))) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
(TPATH_LINEPATH,(c! @ (^[V0]: (c! @ (^[V1]: (cpath @ (clinepath @ ((c__comma__ @ V0) @ V1))))))))
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(TPATHFINISH_LINEPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpathfinish @ (clinepath @ ((c__comma__ @ V0) @ V1)))) @ V1))))))
(TPATHSTART_LINEPATH,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpathstart @ (clinepath @ ((c__comma__ @ V1) @ V0)))) @ V1))))))
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(Tlinepath,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (clinepath @ ((c__comma__ @ V0) @ V1))) @ (^[V2]: ((cvector_add @ ((c% @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cdrop @ V2))) @ V0)) @ ((c% @ (cdrop @ V2)) @ V1)))))))))
(TSHIFTPATH_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cshiftpath @ V1) @ ((co @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((co @ (^[V3]: ((cvector_add @ V0) @ V3))) @ ((cshiftpath @ V1) @ V2))))))))))
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(TPATH_IMAGE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpath_image @ ((co @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ (cpath_image @ V1))))))))
(TPATHFINISH_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpathfinish @ ((co @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cvector_add @ V0) @ (cpathfinish @ V1))))))))
(TPATHSTART_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cpathstart @ ((co @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cvector_add @ V0) @ (cpathstart @ V1))))))))
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(TRELATIVE_INTERIOR_SING,(c! @ (^[V0]: ((c= @ (crelative_interior @ ((cINSERT @ V0) @ cEMPTY))) @ ((cINSERT @ V0) @ cEMPTY)))))
(TBETWEEN_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cbetween @ ((cvector_add @ V0) @ V1)) @ ((c__comma__ @ ((cvector_add @ V0) @ V2)) @ ((cvector_add @ V0) @ V3)))) @ ((cbetween @ V1) @ ((c__comma__ @ V2) @ V3))))))))))))
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(TCONVEX_CONE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cconvex_cone @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((cIN @ V1) @ V2)))) @ ((cIN @ ((cvector_add @ V0) @ V1)) @ V2)))))))))
(TCLOSER_POINT_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((creal_gt @ ((cdot @ ((cvector_sub @ V2) @ V1)) @ ((cvector_sub @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c? @ (^[V3]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c/__caret__ @ ((creal_le @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ ((cvector_add @ V1) @ ((c% @ V3) @ ((cvector_sub @ V0) @ V1)))) @ V2))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))))))))))))
(TDIST_INCREASES_ONLINE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c__caret__/ @ ((creal_gt @ (cdistance @ ((c__comma__ @ V1) @ ((cvector_add @ V2) @ V0)))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))) @ ((creal_gt @ (cdistance @ ((c__comma__ @ V1) @ ((cvector_sub @ V2) @ V0)))) @ (cdistance @ ((c__comma__ @ V1) @ V2))))))))))))
(TCONVEX_HULL_3_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chull @ cconvex) @ ((cINSERT @ V2) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((creal_le @ ((creal_add @ V4) @ V5)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((cvector_add @ V2) @ ((cvector_add @ ((c% @ V4) @ ((cvector_sub @ V0) @ V2))) @ ((c% @ V5) @ ((cvector_sub @ V1) @ V2)))))))))))))))))))
(TCONVEX_HULL_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V6)) @ ((c= @ ((creal_add @ V4) @ ((creal_add @ V5) @ V6))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cvector_add @ ((c% @ V4) @ V0)) @ ((cvector_add @ ((c% @ V5) @ V1)) @ ((c% @ V6) @ V2))))))))))))))))))))
(TCONVEX_HULL_2_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ cconvex) @ ((cINSERT @ V1) @ ((cINSERT @ V0) @ cEMPTY)))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((creal_le @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cvector_add @ V1) @ ((c% @ V3) @ ((cvector_sub @ V0) @ V1))))))))))))))
(TCONVEX_HULL_2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ cconvex) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V4)) @ ((c= @ ((creal_add @ V3) @ V4)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((cvector_add @ ((c% @ V3) @ V0)) @ ((c% @ V4) @ V1)))))))))))))))
(TCONVEX_HULL_SING,(c! @ (^[V0]: ((c= @ ((chull @ cconvex) @ ((cINSERT @ V0) @ cEMPTY))) @ ((cINSERT @ V0) @ cEMPTY)))))
(TCONVEX_DISTANCE,(c! @ (^[V0]: (c! @ (^[V1]: ((cconvex_on @ (^[V2]: (cdistance @ ((c__comma__ @ V0) @ V2)))) @ V1))))))
(TAFFINE_HULL_3_IMP_COLLINEAR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V2) @ ((chull @ caffine) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))) @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))))))))))
(TCOPLANAR_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (ccoplanar @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY)))))))))))
(TCOPLANAR_2,(c! @ (^[V0]: (c! @ (^[V1]: (ccoplanar @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY))))))))
(TCOPLANAR_SING,(c! @ (^[V0]: (ccoplanar @ ((cINSERT @ V0) @ cEMPTY)))))
(TAFFINE_DEPENDENT_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (caffine_dependent @ V1)) @ (caffine_dependent @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TAFFINE_DEPENDENT_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (caffine_dependent @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (caffine_dependent @ V1)))))))
(TCONIC_HALFSPACE_GE,(c! @ (^[V0]: (cconic @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((creal_ge @ ((cdot @ V0) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V2)))))))))
(TCONIC_HALFSPACE_LE,(c! @ (^[V0]: (cconic @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((creal_le @ ((cdot @ V0) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ V2)))))))))
(TCONVEX_HALFSPACE_GT,(c! @ (^[V0]: (c! @ (^[V1]: (cconvex @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_gt @ ((cdot @ V0) @ V3)) @ V1)) @ V3)))))))))))
(TCONVEX_HALFSPACE_LT,(c! @ (^[V0]: (c! @ (^[V1]: (cconvex @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_lt @ ((cdot @ V0) @ V3)) @ V1)) @ V3)))))))))))
(TCONVEX_HALFSPACE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (cconvex @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_le @ ((cdot @ V0) @ V3)) @ V1)) @ V3)))))))))))
(TCONVEX_SING,(c! @ (^[V0]: (cconvex @ ((cINSERT @ V0) @ cEMPTY)))))
(TCONVEX_CONTAINS_SEGMENT_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cconvex @ V2)) @ ((c= @ ((cSUBSET @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((cIN @ V1) @ V2)))))))))))
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(TAFFINE_HULL_SING,(c! @ (^[V0]: ((c= @ ((chull @ caffine) @ ((cINSERT @ V0) @ cEMPTY))) @ ((cINSERT @ V0) @ cEMPTY)))))
(TAFFINE_HULL_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((chull @ caffine) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V3) @ ((c= @ ((creal_add @ V4) @ ((creal_add @ V5) @ V6))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cvector_add @ ((c% @ V4) @ V0)) @ ((cvector_add @ ((c% @ V5) @ V1)) @ ((c% @ V6) @ V2))))))))))))))))))))
(TAFFINE_HULL_2_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ caffine) @ ((cINSERT @ V1) @ ((cINSERT @ V0) @ cEMPTY)))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((cIN @ V3) @ cUNIV)) @ ((cvector_add @ V1) @ ((c% @ V3) @ ((cvector_sub @ V0) @ V1))))))))))))))
(TAFFINE_HULL_2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ caffine) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c= @ ((creal_add @ V3) @ V4)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((cvector_add @ ((c% @ V3) @ V0)) @ ((c% @ V4) @ V1)))))))))))))))
(TAFFINE_HULL_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((chull @ caffine) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ ((chull @ caffine) @ V1))))))))
(TAFFINE_HYPERPLANE,(c! @ (^[V0]: (c! @ (^[V1]: (caffine @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ ((cdot @ V0) @ V3)) @ V1)) @ V3)))))))))))
(TAFFINE_SING,(c! @ (^[V0]: (caffine @ ((cINSERT @ V0) @ cEMPTY)))))
(TSETDIST_SING_IN_SET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V0) @ V1)) @ ((c= @ (csetdist @ ((c__comma__ @ ((cINSERT @ V0) @ cEMPTY)) @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TSETDIST_EQ_0_CLOSED,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cclosed @ V1)) @ ((c= @ ((c= @ (csetdist @ ((c__comma__ @ ((cINSERT @ V0) @ cEMPTY)) @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c__caret__/ @ ((c= @ V1) @ cEMPTY)) @ ((cIN @ V0) @ V1)))))))))
(TSETDIST_SINGS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csetdist @ ((c__comma__ @ ((cINSERT @ V0) @ cEMPTY)) @ ((cINSERT @ V1) @ cEMPTY)))) @ (cdistance @ ((c__comma__ @ V0) @ V1))))))))
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(TCLOSEST_POINT_EXISTS_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cclosed @ V1)) @ (c~ @ ((c= @ V1) @ cEMPTY)))) @ ((cIN @ ((cclosest_point @ V1) @ V0)) @ V1)))))))
(TSERIES_TERMS_TOZERO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((csums @ V2) @ V0) @ (cfrom @ V1))) @ (((c--> @ V2) @ (cvec @ (cNUMERAL @ c_0))) @ csequentially)))))))))
(TSUMS_SUMMABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (((csums @ V2) @ V0) @ V1)) @ ((csummable @ V1) @ V2)))))))))
(TVECTOR_EQ_AFFINITY,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c~ @ ((c= @ V1) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((c= @ V0) @ ((cvector_add @ ((c% @ V1) @ V3)) @ V2))) @ ((c= @ ((cvector_add @ ((c% @ (creal_inv @ V1)) @ V0)) @ (cvector_neg @ ((c% @ (creal_inv @ V1)) @ V2)))) @ V3))))))))))))
(TVECTOR_AFFINITY_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c~ @ ((c= @ V2) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((c= @ ((cvector_add @ ((c% @ V2) @ V0)) @ V3)) @ V1)) @ ((c= @ V0) @ ((cvector_add @ ((c% @ (creal_inv @ V2)) @ V1)) @ (cvector_neg @ ((c% @ (creal_inv @ V2)) @ V3)))))))))))))))
(TLIMPT_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((climit_point_of @ ((cvector_add @ V0) @ V1)) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ V2))) @ ((climit_point_of @ V1) @ V2)))))))))
(TCOUNTABLE_OPEN_INTERVAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cCOUNTABLE @ (copen_interval @ ((c__comma__ @ V0) @ V1)))) @ ((c= @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ cEMPTY)))))))
(TUNCOUNTABLE_INTERVAL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ cEMPTY))) @ (c~ @ (cCOUNTABLE @ (copen_interval @ ((c__comma__ @ V0) @ V1))))))))))
(TUNCOUNTABLE_INTERVAL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ (copen_interval @ ((c__comma__ @ V0) @ V1))) @ cEMPTY))) @ (c~ @ (cCOUNTABLE @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))))
(TCOLLINEAR_DIST_IN_OPEN_SEGMENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))) @ ((c/__caret__ @ ((creal_lt @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V0) @ V2))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))) @ ((cIN @ V0) @ (copen_segment @ ((c__comma__ @ V1) @ V2)))))))))))
(TCOLLINEAR_DIST_IN_CLOSED_SEGMENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))) @ ((c/__caret__ @ ((creal_le @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))) @ ((creal_le @ (cdistance @ ((c__comma__ @ V0) @ V2))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))) @ ((cIN @ V0) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TSEGMENT_TRANSLATION_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (copen_segment @ ((c__comma__ @ ((cvector_add @ V0) @ V1)) @ ((cvector_add @ V0) @ V2)))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ (copen_segment @ ((c__comma__ @ V1) @ V2)))))))))))
(TSEGMENT_TRANSLATION_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ ((cvector_add @ V0) @ V1)) @ ((cvector_add @ V0) @ V2))) @ cNIL))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
(TSEGMENT_CLOSED_OPEN,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ ((cUNION @ (copen_segment @ ((c__comma__ @ V0) @ V1))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))))
(TENDS_NOT_IN_SEGMENT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((cIN @ V1) @ (copen_segment @ ((c__comma__ @ V0) @ V1)))))))))
(TENDS_NOT_IN_SEGMENT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((cIN @ V0) @ (copen_segment @ ((c__comma__ @ V0) @ V1)))))))))
(TENDS_IN_SEGMENT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cIN @ V1) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
(TENDS_IN_SEGMENT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cIN @ V0) @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))))))))
(TSEGMENT_REFL_conjunct1,(c! @ (^[V0]: ((c= @ (copen_segment @ ((c__comma__ @ V0) @ V0))) @ cEMPTY))))
(TSEGMENT_REFL_conjunct0,(c! @ (^[V0]: ((c= @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V0)) @ cNIL))) @ ((cINSERT @ V0) @ cEMPTY)))))
(Tsegment_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (copen_segment @ ((c__comma__ @ V0) @ V1))) @ ((cDIFF @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))))
(Tsegment_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((creal_le @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cvector_add @ ((c% @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c% @ V3) @ V1)))))))))))))
(Topen_segment,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (copen_segment @ ((c__comma__ @ V0) @ V1))) @ ((cDIFF @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))))))))
(Tclosed_segment,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cclosed_segment @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ cNIL))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V3)) @ ((creal_le @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((cvector_add @ ((c% @ ((creal_sub @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3)) @ V0)) @ ((c% @ V3) @ V1)))))))))))))
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(TINTERVAL_TRANSLATION_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ ((cvector_add @ V0) @ V1)) @ ((cvector_add @ V0) @ V2))) @ cNIL))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ (cclosed_interval @ ((cCONS @ ((c__comma__ @ V1) @ V2)) @ cNIL)))))))))))
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(TCONTINUOUS_AT_ID,(c! @ (^[V0]: ((ccontinuous @ (^[V1]: V1)) @ (cat @ V0)))))
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(TUNIFORMLY_CONTINUOUS_ON_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((cuniformly_continuous_on @ (^[V2]: V0)) @ V1))))))
(TCONTINUOUS_ON_CONST,(c! @ (^[V0]: (c! @ (^[V1]: ((ccontinuous_on @ (^[V2]: V0)) @ V1))))))
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(TBALL_EQ_EMPTY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cball @ ((c__comma__ @ V0) @ V1))) @ cEMPTY)) @ ((creal_le @ V1) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TOPEN_CONTAINS_BALL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (copen @ V1)) @ ((c= @ ((cIN @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V2)) @ ((cSUBSET @ (cball @ ((c__comma__ @ V0) @ V2))) @ V1)))))))))))
(TCENTRE_IN_BALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ (cball @ ((c__comma__ @ V0) @ V1)))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)))))))
(TOPEN_BALL,(c! @ (^[V0]: (c! @ (^[V1]: (copen @ (cball @ ((c__comma__ @ V0) @ V1))))))))
(TCBALL_DIFF_SPHERE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDIFF @ (ccball @ ((c__comma__ @ V0) @ V1))) @ (csphere @ ((c__comma__ @ V0) @ V1)))) @ (cball @ ((c__comma__ @ V0) @ V1))))))))
(TSPHERE_UNION_BALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cUNION @ (csphere @ ((c__comma__ @ V0) @ V1))) @ (cball @ ((c__comma__ @ V0) @ V1)))) @ (ccball @ ((c__comma__ @ V0) @ V1))))))))
(TBALL_UNION_SPHERE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cUNION @ (cball @ ((c__comma__ @ V0) @ V1))) @ (csphere @ ((c__comma__ @ V0) @ V1)))) @ (ccball @ ((c__comma__ @ V0) @ V1))))))))
(TCBALL_DIFF_BALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cDIFF @ (ccball @ ((c__comma__ @ V0) @ V1))) @ (cball @ ((c__comma__ @ V0) @ V1)))) @ (csphere @ ((c__comma__ @ V0) @ V1))))))))
(TSPHERE_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (csphere @ ((c__comma__ @ ((cvector_add @ V0) @ V1)) @ V2))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ (csphere @ ((c__comma__ @ V1) @ V2)))))))))))
(TCBALL_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (ccball @ ((c__comma__ @ ((cvector_add @ V0) @ V1)) @ V2))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ (ccball @ ((c__comma__ @ V1) @ V2)))))))))))
(TBALL_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cball @ ((c__comma__ @ ((cvector_add @ V0) @ V1)) @ V2))) @ ((cIMAGE @ (^[V3]: ((cvector_add @ V0) @ V3))) @ (cball @ ((c__comma__ @ V1) @ V2)))))))))))
(TSPHERE_SUBSET_CBALL,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ (csphere @ ((c__comma__ @ V0) @ V1))) @ (ccball @ ((c__comma__ @ V0) @ V1))))))))
(TBALL_SUBSET_CBALL,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ (cball @ ((c__comma__ @ V0) @ V1))) @ (ccball @ ((c__comma__ @ V0) @ V1))))))))
(TCENTRE_IN_CBALL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ (ccball @ ((c__comma__ @ V0) @ V1)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)))))))
(TCBALL_TRIVIAL,(c! @ (^[V0]: ((c= @ (ccball @ ((c__comma__ @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((cINSERT @ V0) @ cEMPTY)))))
(TBALL_TRIVIAL,(c! @ (^[V0]: ((c= @ (cball @ ((c__comma__ @ V0) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ cEMPTY))))
(TIN_SPHERE_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ (csphere @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))) @ ((c= @ (cvector_norm @ V0)) @ V1)))))))
(TIN_CBALL_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ (ccball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))) @ ((creal_le @ (cvector_norm @ V0)) @ V1)))))))
(TIN_BALL_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ (cball @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V1)))) @ ((creal_lt @ (cvector_norm @ V0)) @ V1)))))))
(TIN_SPHERE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ V1) @ (csphere @ ((c__comma__ @ V0) @ V2)))) @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ V2)))))))))
(TIN_CBALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ V1) @ (ccball @ ((c__comma__ @ V0) @ V2)))) @ ((creal_le @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ V2)))))))))
(TIN_BALL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ V1) @ (cball @ ((c__comma__ @ V0) @ V2)))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ V2)))))))))
(Tsphere,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csphere @ ((c__comma__ @ V0) @ V1))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V3))) @ V1)) @ V3)))))))))))
(Tcball,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccball @ ((c__comma__ @ V0) @ V1))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_le @ (cdistance @ ((c__comma__ @ V0) @ V3))) @ V1)) @ V3)))))))))))
(Tball,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cball @ ((c__comma__ @ V0) @ V1))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (((cSETSPEC @ V2) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V0) @ V3))) @ V1)) @ V3)))))))))))
(TCOLLINEAR_TRANSLATION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (ccollinear @ V1)) @ (ccollinear @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))))))))
(TCOLLINEAR_TRANSLATION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccollinear @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1))) @ (ccollinear @ V1)))))))
(TCOLLINEAR_MIDPOINT,(c! @ (^[V0]: (c! @ (^[V1]: (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ (cmidpoint @ ((c__comma__ @ V0) @ V1))) @ ((cINSERT @ V1) @ cEMPTY)))))))))
(TBETWEEN_MIDPOINT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cbetween @ (cmidpoint @ ((c__comma__ @ V1) @ V0))) @ ((c__comma__ @ V0) @ V1)))))))
(TBETWEEN_MIDPOINT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cbetween @ (cmidpoint @ ((c__comma__ @ V0) @ V1))) @ ((c__comma__ @ V0) @ V1)))))))
(TMIDPOINT_EQ_ENDPOINT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cmidpoint @ ((c__comma__ @ V0) @ V1))) @ V1)) @ ((c= @ V0) @ V1)))))))
(TMIDPOINT_EQ_ENDPOINT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cmidpoint @ ((c__comma__ @ V0) @ V1))) @ V0)) @ ((c= @ V0) @ V1)))))))
(TMIDPOINT_EQ_ENDPOINT_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V1) @ (cmidpoint @ ((c__comma__ @ V0) @ V1)))) @ ((c= @ V0) @ V1)))))))
(TMIDPOINT_EQ_ENDPOINT_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ (cmidpoint @ ((c__comma__ @ V0) @ V1)))) @ ((c= @ V0) @ V1)))))))
(TDIST_MIDPOINT_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdistance @ ((c__comma__ @ (cmidpoint @ ((c__comma__ @ V0) @ V1))) @ V1))) @ ((creal_div @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TDIST_MIDPOINT_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdistance @ ((c__comma__ @ (cmidpoint @ ((c__comma__ @ V0) @ V1))) @ V0))) @ ((creal_div @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TDIST_MIDPOINT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdistance @ ((c__comma__ @ V1) @ (cmidpoint @ ((c__comma__ @ V0) @ V1))))) @ ((creal_div @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TDIST_MIDPOINT_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdistance @ ((c__comma__ @ V0) @ (cmidpoint @ ((c__comma__ @ V0) @ V1))))) @ ((creal_div @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TMIDPOINT_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmidpoint @ ((c__comma__ @ V1) @ V0))) @ (cmidpoint @ ((c__comma__ @ V0) @ V1))))))))
(TMIDPOINT_REFL,(c! @ (^[V0]: ((c= @ (cmidpoint @ ((c__comma__ @ V0) @ V0))) @ V0))))
(Tmidpoint,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmidpoint @ ((c__comma__ @ V0) @ V1))) @ ((c% @ (creal_inv @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((cvector_add @ V0) @ V1))))))))
(TCOLLINEAR_DIST_BETWEEN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))) @ ((c/__caret__ @ ((creal_le @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))) @ ((creal_le @ (cdistance @ ((c__comma__ @ V0) @ V2))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))) @ ((cbetween @ V0) @ ((c__comma__ @ V1) @ V2))))))))))
(TBETWEEN_TRANS_2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cbetween @ V1) @ ((c__comma__ @ V0) @ V2))) @ ((cbetween @ V3) @ ((c__comma__ @ V1) @ V0)))) @ ((cbetween @ V1) @ ((c__comma__ @ V2) @ V3))))))))))))
(TBETWEEN_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cbetween @ V0) @ ((c__comma__ @ V2) @ V3))) @ ((cbetween @ V1) @ ((c__comma__ @ V0) @ V3)))) @ ((cbetween @ V1) @ ((c__comma__ @ V2) @ V3))))))))))))
(TBETWEEN_ANTISYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cbetween @ V1) @ ((c__comma__ @ V2) @ V0))) @ ((cbetween @ V2) @ ((c__comma__ @ V1) @ V0)))) @ ((c= @ V1) @ V2)))))))))
(TBETWEEN_SYM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cbetween @ V0) @ ((c__comma__ @ V2) @ V1))) @ ((cbetween @ V0) @ ((c__comma__ @ V1) @ V2))))))))))
(TBETWEEN_REFL_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cbetween @ V0) @ ((c__comma__ @ V1) @ V1))) @ ((c= @ V0) @ V1)))))))
(TBETWEEN_REFL_conjunct2,(c! @ (^[V0]: ((cbetween @ V0) @ ((c__comma__ @ V0) @ V0)))))
(TBETWEEN_REFL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((cbetween @ V1) @ ((c__comma__ @ V0) @ V1)))))))
(TBETWEEN_REFL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((cbetween @ V0) @ ((c__comma__ @ V0) @ V1)))))))
(Tbetween,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cbetween @ V1) @ ((c__comma__ @ V0) @ V2))) @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V2))) @ ((creal_add @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (cdistance @ ((c__comma__ @ V1) @ V2))))))))))))
(TCOLLINEAR_LEMMA_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccollinear @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ ((cINSERT @ V1) @ ((cINSERT @ V0) @ cEMPTY))))) @ ((c__caret__/ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0)))) @ (c? @ (^[V2]: ((c= @ V0) @ ((c% @ V2) @ V1)))))))))))
(TCOLLINEAR_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (ccollinear @ ((cINSERT @ V0) @ ((cINSERT @ V2) @ ((cINSERT @ V1) @ cEMPTY))))) @ (ccollinear @ ((cINSERT @ (cvec @ (cNUMERAL @ c_0))) @ ((cINSERT @ ((cvector_sub @ V0) @ V2)) @ ((cINSERT @ ((cvector_sub @ V1) @ V2)) @ cEMPTY))))))))))))
(TCOLLINEAR_SING,(c! @ (^[V0]: (ccollinear @ ((cINSERT @ V0) @ cEMPTY)))))
(TDIST_TRIANGLE_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ (cdistance @ ((c__comma__ @ V1) @ V0))) @ ((creal_add @ (cdistance @ ((c__comma__ @ V1) @ V2))) @ (cdistance @ ((c__comma__ @ V2) @ V0))))) @ ((c= @ ((c% @ (cvector_norm @ ((cvector_sub @ V1) @ V2))) @ ((cvector_sub @ V2) @ V0))) @ ((c% @ (cvector_norm @ ((cvector_sub @ V2) @ V0))) @ ((cvector_sub @ V1) @ V2)))))))))))
(TINFNORM_LE_NORM,(c! @ (^[V0]: ((creal_le @ (cinfnorm @ V0)) @ (cvector_norm @ V0)))))
(TINFNORM_POS_LT,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cinfnorm @ V0))) @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))))))
(TREAL_ABS_INFNORM,(c! @ (^[V0]: ((c= @ (creal_abs @ (cinfnorm @ V0))) @ (cinfnorm @ V0)))))
(TREAL_ABS_SUB_INFNORM,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (creal_abs @ ((creal_sub @ (cinfnorm @ V0)) @ (cinfnorm @ V1)))) @ (cinfnorm @ ((cvector_sub @ V0) @ V1))))))))
(TINFNORM_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinfnorm @ ((cvector_sub @ V1) @ V0))) @ (cinfnorm @ ((cvector_sub @ V0) @ V1))))))))
(TINFNORM_NEG,(c! @ (^[V0]: ((c= @ (cinfnorm @ (cvector_neg @ V0))) @ (cinfnorm @ V0)))))
(TINFNORM_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cinfnorm @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))
(TINFNORM_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cinfnorm @ ((cvector_add @ V0) @ V1))) @ ((creal_add @ (cinfnorm @ V0)) @ (cinfnorm @ V1))))))))
(TINFNORM_POS_LE,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cinfnorm @ V0)))))
(TINFNORM_SET_IMAGE,(c! @ (^[V0]: ((c= @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (creal_abs @ ((c$ @ V0) @ V2)))))))) @ ((cIMAGE @ (^[V1]: (creal_abs @ ((c$ @ V0) @ V1)))) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))))))
(TSUBSPACE_ORTHOGONAL_TO_VECTOR,(c! @ (^[V0]: (csubspace @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((corthogonal @ V0) @ V2)) @ V2)))))))))
(TTRANSP_ROWVECTOR,(c! @ (^[V0]: ((c= @ (ctransp @ (crowvector @ V0))) @ (ccolumnvector @ V0)))))
(TTRANSP_COLUMNVECTOR,(c! @ (^[V0]: ((c= @ (ctransp @ (ccolumnvector @ V0))) @ (crowvector @ V0)))))
(TSPAN_EQ_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cspan @ ((cINSERT @ V0) @ V1))) @ (cspan @ V1))) @ ((cIN @ V0) @ (cspan @ V1))))))))
(TDIM_SING,(c! @ (^[V0]: ((c= @ (cdim @ ((cINSERT @ V0) @ cEMPTY))) @ (((cCOND @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (cNUMERAL @ c_0)) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TDEPENDENT_SING,(c! @ (^[V0]: ((c= @ (cdependent @ ((cINSERT @ V0) @ cEMPTY))) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))
(TINDEPENDENT_SING,(c! @ (^[V0]: ((c= @ (cindependent @ ((cINSERT @ V0) @ cEMPTY))) @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))))))
(TIN_SPAN_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ (cspan @ V1))) @ (c~ @ ((cIN @ V0) @ (cspan @ ((cDELETE @ V1) @ V2)))))) @ ((cIN @ V2) @ (cspan @ ((cINSERT @ V0) @ ((cDELETE @ V1) @ V2))))))))))))
(TSPAN_3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cspan @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ ((cINSERT @ V2) @ cEMPTY))))) @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V3) @ ((c/__caret__ @ ((cIN @ V4) @ cUNIV)) @ ((c/__caret__ @ ((cIN @ V5) @ cUNIV)) @ ((cIN @ V6) @ cUNIV)))) @ ((cvector_add @ ((c% @ V4) @ V0)) @ ((cvector_add @ ((c% @ V5) @ V1)) @ ((c% @ V6) @ V2))))))))))))))))))))
(TSPAN_2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cspan @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ cEMPTY)))) @ (cGSPEC @ (^[V2]: (c? @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V2) @ ((c/__caret__ @ ((cIN @ V3) @ cUNIV)) @ ((cIN @ V4) @ cUNIV))) @ ((cvector_add @ ((c% @ V3) @ V0)) @ ((c% @ V4) @ V1)))))))))))))))
(TSPAN_SING,(c! @ (^[V0]: ((c= @ (cspan @ ((cINSERT @ V0) @ cEMPTY))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cIN @ V2) @ cUNIV)) @ ((c% @ V2) @ V0))))))))))
(TSUBSPACE_TRANSLATION_SELF,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V1)) @ ((cIN @ V0) @ V1))) @ ((c= @ ((cIMAGE @ (^[V2]: ((cvector_add @ V0) @ V2))) @ V1)) @ V1)))))))
(TSPAN_ADD_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V0) @ (cspan @ V2))) @ ((c= @ ((cIN @ ((cvector_add @ V0) @ V1)) @ (cspan @ V2))) @ ((cIN @ V1) @ (cspan @ V2)))))))))))
(TSPAN_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ (cspan @ V2))) @ ((cIN @ V1) @ (cspan @ V2)))) @ ((cIN @ ((cvector_sub @ V0) @ V1)) @ (cspan @ V2))))))))))
(TSPAN_NEG_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ (cvector_neg @ V0)) @ (cspan @ V1))) @ ((cIN @ V0) @ (cspan @ V1))))))))
(TSPAN_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V0) @ (cspan @ V1))) @ ((cIN @ (cvector_neg @ V0)) @ (cspan @ V1))))))))
(TSPAN_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ (cspan @ V2))) @ ((cIN @ V1) @ (cspan @ V2)))) @ ((cIN @ ((cvector_add @ V0) @ V1)) @ (cspan @ V2))))))))))
(TSPAN_SUPERSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V0) @ V1)) @ ((cIN @ V0) @ (cspan @ V1))))))))
(TSPAN_CLAUSES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ (cspan @ V2))) @ ((cIN @ V1) @ (cspan @ V2)))) @ ((cIN @ ((cvector_add @ V0) @ V1)) @ (cspan @ V2))))))))))
(TSPAN_CLAUSES_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V0) @ (cspan @ V2))) @ ((cIN @ ((c% @ V1) @ V0)) @ (cspan @ V2))))))))))
(TSPAN_CLAUSES_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((cIN @ V0) @ V1)) @ ((cIN @ V0) @ (cspan @ V1))))))))
(TSUBSPACE_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (csubspace @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((cIN @ V1) @ V2)))) @ ((cIN @ ((cvector_sub @ V0) @ V1)) @ V2)))))))))
(TSUBSPACE_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (csubspace @ V1)) @ ((cIN @ V0) @ V1))) @ ((cIN @ (cvector_neg @ V0)) @ V1)))))))
(TSUBSPACE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (csubspace @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((cIN @ V1) @ V2)))) @ ((cIN @ ((cvector_add @ V0) @ V1)) @ V2)))))))))
(TDIST_PASTECART_CANCEL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cdistance @ ((c__comma__ @ ((cpastecart @ V0) @ V1)) @ ((cpastecart @ V0) @ V2)))) @ (cdistance @ ((c__comma__ @ V1) @ V2))))))))))
(TDIST_PASTECART_CANCEL_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (cdistance @ ((c__comma__ @ ((cpastecart @ V0) @ V2)) @ ((cpastecart @ V1) @ V2)))) @ (cdistance @ ((c__comma__ @ V0) @ V1))))))))))
(TNORM_PASTECART_0_conjunct1,(c! @ (^[V0]: ((c= @ (cvector_norm @ ((cpastecart @ (cvec @ (cNUMERAL @ c_0))) @ V0))) @ (cvector_norm @ V0)))))
(TNORM_PASTECART_0_conjunct0,(c! @ (^[V0]: ((c= @ (cvector_norm @ ((cpastecart @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ (cvector_norm @ V0)))))
(TNORM_PASTECART_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cvector_norm @ ((cpastecart @ V0) @ V1))) @ ((creal_add @ (cvector_norm @ V0)) @ (cvector_norm @ V1))))))))
(TNORM_PASTECART,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cvector_norm @ ((cpastecart @ V0) @ V1))) @ (csqrt @ ((creal_add @ ((creal_pow @ (cvector_norm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))))))
(TSQNORM_PASTECART,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_pow @ (cvector_norm @ ((cpastecart @ V0) @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_add @ ((creal_pow @ (cvector_norm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TDOT_PASTECART,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cdot @ ((cpastecart @ V0) @ V2)) @ ((cpastecart @ V1) @ V3))) @ ((creal_add @ ((cdot @ V0) @ V1)) @ ((cdot @ V2) @ V3))))))))))))
(TPASTECART_EQ_VEC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ ((cpastecart @ V0) @ V1)) @ (cvec @ V2))) @ ((c/__caret__ @ ((c= @ V0) @ (cvec @ V2))) @ ((c= @ V1) @ (cvec @ V2)))))))))))
(TLINEAR_LIFT_DOT,(c! @ (^[V0]: (clinear @ (^[V1]: (clift @ ((cdot @ V0) @ V1)))))))
(TBILINEAR_RSUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cbilinear @ V1)) @ ((c= @ ((V1 @ V2) @ ((cvector_sub @ V0) @ V3))) @ ((cvector_sub @ ((V1 @ V2) @ V0)) @ ((V1 @ V2) @ V3)))))))))))))
(TBILINEAR_LSUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cbilinear @ V1)) @ ((c= @ ((V1 @ ((cvector_sub @ V0) @ V2)) @ V3)) @ ((cvector_sub @ ((V1 @ V0) @ V3)) @ ((V1 @ V2) @ V3)))))))))))))
(TBILINEAR_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cbilinear @ V1)) @ ((c= @ ((V1 @ V2) @ ((cvector_add @ V0) @ V3))) @ ((cvector_add @ ((V1 @ V2) @ V0)) @ ((V1 @ V2) @ V3)))))))))))))
(TBILINEAR_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cbilinear @ V1)) @ ((c= @ ((V1 @ ((cvector_add @ V0) @ V2)) @ V3)) @ ((cvector_add @ ((V1 @ V0) @ V3)) @ ((V1 @ V2) @ V3)))))))))))))
(TSYMMETRIC_LINEAR_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V2)) @ ((cIN @ (cvector_neg @ V3)) @ V2))))) @ (clinear @ V1))) @ ((c==> @ ((cIN @ V0) @ ((cIMAGE @ V1) @ V2))) @ ((cIN @ (cvector_neg @ V0)) @ ((cIMAGE @ V1) @ V2)))))))))))
(TLINEAR_SUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (clinear @ V1)) @ ((c= @ (V1 @ ((cvector_sub @ V0) @ V2))) @ ((cvector_sub @ (V1 @ V0)) @ (V1 @ V2)))))))))))
(TLINEAR_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (clinear @ V1)) @ ((c= @ (V1 @ ((cvector_add @ V0) @ V2))) @ ((cvector_add @ (V1 @ V0)) @ (V1 @ V2)))))))))))
(TORTHOGONAL_CLAUSES_conjunct9,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((corthogonal @ V1) @ V0)) @ ((corthogonal @ V2) @ V0))) @ ((corthogonal @ ((cvector_sub @ V1) @ V2)) @ V0)))))))))
(TORTHOGONAL_CLAUSES_conjunct8,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((corthogonal @ V1) @ V0)) @ ((corthogonal @ V2) @ V0))) @ ((corthogonal @ ((cvector_add @ V1) @ V2)) @ V0)))))))))
(TORTHOGONAL_CLAUSES_conjunct7,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((corthogonal @ V1) @ V0)) @ ((corthogonal @ (cvector_neg @ V1)) @ V0)))))))
(TORTHOGONAL_CLAUSES_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((corthogonal @ V0) @ V1)) @ ((corthogonal @ V0) @ V2))) @ ((corthogonal @ V0) @ ((cvector_sub @ V1) @ V2))))))))))
(TORTHOGONAL_CLAUSES_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((corthogonal @ V0) @ V1)) @ ((corthogonal @ V0) @ V2))) @ ((corthogonal @ V0) @ ((cvector_add @ V1) @ V2))))))))))
(TORTHOGONAL_CLAUSES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((corthogonal @ V0) @ V1)) @ ((corthogonal @ V0) @ (cvector_neg @ V1))))))))
(TORTHOGONAL_CLAUSES_conjunct6,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((corthogonal @ V1) @ V0)) @ ((corthogonal @ ((c% @ V2) @ V1)) @ V0)))))))))
(TORTHOGONAL_CLAUSES_conjunct5,(c! @ (^[V0]: ((corthogonal @ (cvec @ (cNUMERAL @ c_0))) @ V0))))
(TORTHOGONAL_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((corthogonal @ V0) @ V1)) @ ((corthogonal @ V0) @ ((c% @ V2) @ V1))))))))))
(TORTHOGONAL_CLAUSES_conjunct0,(c! @ (^[V0]: ((corthogonal @ V0) @ (cvec @ (cNUMERAL @ c_0))))))
(TORTHOGONAL_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((corthogonal @ V0) @ (cvector_neg @ V1))) @ ((corthogonal @ V0) @ V1)))))))
(TORTHOGONAL_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((corthogonal @ (cvector_neg @ V0)) @ V1)) @ ((corthogonal @ V0) @ V1)))))))
(TORTHOGONAL_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((corthogonal @ V1) @ V0)) @ ((corthogonal @ V0) @ V1)))))))
(TORTHOGONAL_REFL,(c! @ (^[V0]: ((c= @ ((corthogonal @ V0) @ V0)) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))
(TORTHOGONAL_0_conjunct0,(c! @ (^[V0]: ((corthogonal @ (cvec @ (cNUMERAL @ c_0))) @ V0))))
(TORTHOGONAL_0_conjunct1,(c! @ (^[V0]: ((corthogonal @ V0) @ (cvec @ (cNUMERAL @ c_0))))))
(Torthogonal,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((corthogonal @ V0) @ V1)) @ ((c= @ ((cdot @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TVECTOR_EQ_RDOT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c= @ ((cdot @ V0) @ V2)) @ ((cdot @ V1) @ V2))))) @ ((c= @ V0) @ V1)))))))
(TVECTOR_EQ_LDOT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c= @ ((cdot @ V2) @ V0)) @ ((cdot @ V2) @ V1))))) @ ((c= @ V0) @ V1)))))))
(TDIST_0_conjunct1,(c! @ (^[V0]: ((c= @ (cdistance @ ((c__comma__ @ (cvec @ (cNUMERAL @ c_0))) @ V0))) @ (cvector_norm @ V0)))))
(TDIST_0_conjunct0,(c! @ (^[V0]: ((c= @ (cdistance @ ((c__comma__ @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ (cvector_norm @ V0)))))
(TDIST_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (cdistance @ ((c__comma__ @ V2) @ V3)))) @ ((c= @ ((creal_pow @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cdistance @ ((c__comma__ @ V2) @ V3))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))
(TDIST_LE_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_le @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ V1)))))))
(TDIST_TRIANGLE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((creal_le @ (cdistance @ ((c__comma__ @ ((cvector_add @ V0) @ V2)) @ ((cvector_add @ V1) @ V3)))) @ ((creal_add @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (cdistance @ ((c__comma__ @ V2) @ V3)))))))))))))
(TDIST_TRIANGLE_HALF_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ ((creal_div @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V0) @ V2))) @ ((creal_div @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V1) @ V2))) @ V3)))))))))))
(TDIST_TRIANGLE_HALF_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((creal_lt @ (cdistance @ ((c__comma__ @ V1) @ V0))) @ ((creal_div @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V2) @ V0))) @ ((creal_div @ V3) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V1) @ V2))) @ V3)))))))))))
(TDIST_TRIANGLE_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_lt @ ((creal_add @ (cdistance @ ((c__comma__ @ V1) @ V0))) @ (cdistance @ ((c__comma__ @ V2) @ V0)))) @ V3)) @ ((creal_lt @ (cdistance @ ((c__comma__ @ V1) @ V2))) @ V3)))))))))))
(TDIST_TRIANGLE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((creal_le @ ((creal_add @ (cdistance @ ((c__comma__ @ V1) @ V0))) @ (cdistance @ ((c__comma__ @ V2) @ V0)))) @ V3)) @ ((creal_le @ (cdistance @ ((c__comma__ @ V1) @ V2))) @ V3)))))))))))
(TDIST_NZ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c~ @ ((c= @ V0) @ V1))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdistance @ ((c__comma__ @ V0) @ V1)))))))))
(TDIST_POS_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((c= @ V0) @ V1))) @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdistance @ ((c__comma__ @ V0) @ V1)))))))))
(TDIST_EQ_0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ V1)))))))
(TDIST_TRIANGLE_ALT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((creal_le @ (cdistance @ ((c__comma__ @ V0) @ V2))) @ ((creal_add @ (cdistance @ ((c__comma__ @ V1) @ V0))) @ (cdistance @ ((c__comma__ @ V1) @ V2)))))))))))
(TDIST_POS_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cdistance @ ((c__comma__ @ V0) @ V1))))))))
(TDIST_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdistance @ ((c__comma__ @ V1) @ V0))) @ (cdistance @ ((c__comma__ @ V0) @ V1))))))))
(TDIST_REFL,(c! @ (^[V0]: ((c= @ (cdistance @ ((c__comma__ @ V0) @ V0))) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TVECTOR_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V1) @ V0)) @ ((c/__caret__ @ ((c= @ ((cdot @ V1) @ V1)) @ ((cdot @ V1) @ V0))) @ ((c= @ ((cdot @ V0) @ V0)) @ ((cdot @ V1) @ V1)))))))))
(TDOT_NORM_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ V0) @ V1)) @ ((creal_div @ ((creal_sub @ ((creal_add @ ((creal_pow @ (cvector_norm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_pow @ (cvector_norm @ ((cvector_sub @ V0) @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TDOT_NORM_NEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ V0) @ V1)) @ ((creal_div @ ((creal_sub @ ((creal_add @ ((creal_pow @ (cvector_norm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_pow @ (cvector_norm @ ((cvector_sub @ V0) @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TDOT_NORM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ V0) @ V1)) @ ((creal_div @ ((creal_sub @ ((creal_sub @ ((creal_pow @ (cvector_norm @ ((cvector_add @ V0) @ V1))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ (cvector_norm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_pow @ (cvector_norm @ V1)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))
(TDOT_SQUARE_NORM,(c! @ (^[V0]: ((c= @ ((cdot @ V0) @ V0)) @ ((creal_pow @ (cvector_norm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))
(TNORM_EQ_1,(c! @ (^[V0]: ((c= @ ((c= @ (cvector_norm @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cdot @ V0) @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TNORM_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cvector_norm @ V0)) @ (cvector_norm @ V1))) @ ((c= @ ((cdot @ V0) @ V0)) @ ((cdot @ V1) @ V1))))))))
(TNORM_LT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_lt @ (cvector_norm @ V0)) @ (cvector_norm @ V1))) @ ((creal_lt @ ((cdot @ V0) @ V0)) @ ((cdot @ V1) @ V1))))))))
(TNORM_LE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((creal_le @ (cvector_norm @ V0)) @ (cvector_norm @ V1))) @ ((creal_le @ ((cdot @ V0) @ V0)) @ ((cdot @ V1) @ V1))))))))
(TREAL_ABS_SUB_NORM,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (creal_abs @ ((creal_sub @ (cvector_norm @ V0)) @ (cvector_norm @ V1)))) @ (cvector_norm @ ((cvector_sub @ V0) @ V1))))))))
(TNORM_TRIANGLE_LT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((creal_lt @ ((creal_add @ (cvector_norm @ V0)) @ (cvector_norm @ V1))) @ V2)) @ ((creal_lt @ (cvector_norm @ ((cvector_add @ V0) @ V1))) @ V2)))))))))
(TNORM_TRIANGLE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((creal_le @ ((creal_add @ (cvector_norm @ V0)) @ (cvector_norm @ V1))) @ V2)) @ ((creal_le @ (cvector_norm @ ((cvector_add @ V0) @ V1))) @ V2)))))))))
(TNORM_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: ((creal_le @ (cvector_norm @ ((cvector_add @ V0) @ V1))) @ ((creal_add @ (cvector_norm @ V0)) @ (cvector_norm @ V1))))))))
(TREAL_ABS_NORM,(c! @ (^[V0]: ((c= @ (creal_abs @ (cvector_norm @ V0))) @ (cvector_norm @ V0)))))
(TVECTOR_MUL_RCANCEL_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ ((c% @ V1) @ V0)) @ ((c% @ V2) @ V0)))) @ ((c= @ V1) @ V2)))))))))
(TNORM_LE_0,(c! @ (^[V0]: ((c= @ ((creal_le @ (cvector_norm @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))
(TNORM_EQ_0_IMP,(c! @ (^[V0]: ((c==> @ ((c= @ (cvector_norm @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))
(TNORM_POW_2,(c! @ (^[V0]: ((c= @ ((creal_pow @ (cvector_norm @ V0)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((cdot @ V0) @ V0)))))
(TNORM_POS_LT,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cvector_norm @ V0))) @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))))))
(TNORM_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cvector_norm @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))
(TNORM_EQ_0_DOT,(c! @ (^[V0]: ((c= @ ((c= @ (cvector_norm @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c= @ ((cdot @ V0) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TNORM_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cvector_norm @ ((cvector_sub @ V1) @ V0))) @ (cvector_norm @ ((cvector_sub @ V0) @ V1))))))))
(TNORM_NEG,(c! @ (^[V0]: ((c= @ (cvector_norm @ (cvector_neg @ V0))) @ (cvector_norm @ V0)))))
(TNORM_POS_LE,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ (cvector_norm @ V0)))))
(Tdist,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdistance @ ((c__comma__ @ V0) @ V1))) @ (cvector_norm @ ((cvector_sub @ V0) @ V1))))))))
(Tvector_norm,(c! @ (^[V0]: ((c= @ (cvector_norm @ V0)) @ (csqrt @ ((cdot @ V0) @ V0))))))
(TFORALL_DOT_EQ_0_conjunct1,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c= @ ((cdot @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))
(TFORALL_DOT_EQ_0_conjunct0,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: ((c= @ ((cdot @ V1) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))
(TDOT_POS_LT,(c! @ (^[V0]: ((c= @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cdot @ V0) @ V0))) @ (c~ @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0))))))))
(TDOT_POS_LE,(c! @ (^[V0]: ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((cdot @ V0) @ V0)))))
(TDOT_RZERO,(c! @ (^[V0]: ((c= @ ((cdot @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TDOT_LZERO,(c! @ (^[V0]: ((c= @ ((cdot @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))))
(TDOT_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ V0) @ (cvector_neg @ V1))) @ (creal_neg @ ((cdot @ V0) @ V1))))))))
(TDOT_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ (cvector_neg @ V0)) @ V1)) @ (creal_neg @ ((cdot @ V0) @ V1))))))))
(TDOT_RSUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ V1) @ ((cvector_sub @ V0) @ V2))) @ ((creal_sub @ ((cdot @ V1) @ V0)) @ ((cdot @ V1) @ V2))))))))))
(TDOT_LSUB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ ((cvector_sub @ V0) @ V1)) @ V2)) @ ((creal_sub @ ((cdot @ V0) @ V2)) @ ((cdot @ V1) @ V2))))))))))
(TDOT_RADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ V1) @ ((cvector_add @ V0) @ V2))) @ ((creal_add @ ((cdot @ V1) @ V0)) @ ((cdot @ V1) @ V2))))))))))
(TDOT_LADD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cdot @ ((cvector_add @ V0) @ V1)) @ V2)) @ ((creal_add @ ((cdot @ V0) @ V2)) @ ((cdot @ V1) @ V2))))))))))
(TDOT_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cdot @ V1) @ V0)) @ ((cdot @ V0) @ V1)))))))
(TVECTOR_NEG_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cvector_neg @ V0)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cvec @ (cNUMERAL @ c_0)))))))
(TVECTOR_SUB_LZERO,(c! @ (^[V0]: ((c= @ ((cvector_sub @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ (cvector_neg @ V0)))))
(TVECTOR_NEG_MINUS1,(c! @ (^[V0]: ((c= @ (cvector_neg @ V0)) @ ((c% @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)))))
(TVECTOR_SUB_RZERO,(c! @ (^[V0]: ((c= @ ((cvector_sub @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ V0))))
(TVECTOR_EQ_ADDR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cvector_add @ V0) @ V1)) @ V0)) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TVECTOR_SUB_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c% @ V1) @ ((cvector_sub @ V0) @ V2))) @ ((cvector_sub @ ((c% @ V1) @ V0)) @ ((c% @ V1) @ V2))))))))))
(TVECTOR_ADD_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c% @ V1) @ ((cvector_add @ V0) @ V2))) @ ((cvector_add @ ((c% @ V1) @ V0)) @ ((c% @ V1) @ V2))))))))))
(TVECTOR_MUL_LZERO,(c! @ (^[V0]: ((c= @ ((c% @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))
(TVECTOR_MUL_LID,(c! @ (^[V0]: ((c= @ ((c% @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ V0))))
(TVECTOR_SUB_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cvector_sub @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ V1)))))))
(TVECTOR_ADD_RINV,(c! @ (^[V0]: ((c= @ ((cvector_add @ V0) @ (cvector_neg @ V0))) @ (cvec @ (cNUMERAL @ c_0))))))
(TVECTOR_ADD_LINV,(c! @ (^[V0]: ((c= @ ((cvector_add @ (cvector_neg @ V0)) @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))
(TVECTOR_SUB_REFL,(c! @ (^[V0]: ((c= @ ((cvector_sub @ V0) @ V0)) @ (cvec @ (cNUMERAL @ c_0))))))
(TVECTOR_ADD_RID,(c! @ (^[V0]: ((c= @ ((cvector_add @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ V0))))
(TVECTOR_ADD_LID,(c! @ (^[V0]: ((c= @ ((cvector_add @ (cvec @ (cNUMERAL @ c_0))) @ V0)) @ V0))))
(TDET_4,(c! @ (^[V0]: ((c= @ (cdet @ V0)) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))))))))))))))))))
(TEULER_ROTOINVERSION_THEOREM,(c! @ (^[V0]: ((c==> @ (crotoinversion_matrix @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ (cvector_neg @ V1)))))))))
(TEULER_ROTATION_THEOREM,(c! @ (^[V0]: ((c==> @ (crotation_matrix @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ V1))))))))
(TDET_3,(c! @ (^[V0]: ((c= @ (cdet @ V0)) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))))) @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((creal_sub @ ((creal_sub @ ((creal_sub @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0)))))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))))))))
(TDET_2,(c! @ (^[V0]: ((c= @ (cdet @ V0)) @ ((creal_sub @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TROTATION_MATRIX_2,(c! @ (^[V0]: ((c= @ (crotation_matrix @ V0)) @ ((c/__caret__ @ ((c= @ ((creal_add @ ((creal_pow @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((c= @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c= @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_neg @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TORTHOGONAL_MATRIX_2_ALT,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ ((c= @ ((creal_add @ ((creal_pow @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c__caret__/ @ ((c/__caret__ @ ((c= @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((c= @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (creal_neg @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((c/__caret__ @ ((c= @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_neg @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ ((c= @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TORTHOGONAL_MATRIX_2,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ ((c= @ ((creal_add @ ((creal_pow @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ ((c= @ ((creal_add @ ((creal_pow @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ ((creal_pow @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((creal_add @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ ((creal_mul @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))))) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))
(TDET_1,(c! @ (^[V0]: ((c= @ (cdet @ V0)) @ ((c$ @ ((c$ @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TMATRIX_MUL_LZERO,(c! @ (^[V0]: ((c= @ ((cmatrix_mul @ (cmat @ (cNUMERAL @ c_0))) @ V0)) @ (cmat @ (cNUMERAL @ c_0))))))
(TRANK_MUL_LE_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ (crank @ ((cmatrix_mul @ V1) @ V0))) @ (crank @ V1)))))))
(TMATRIX_SUB_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_mul @ V1) @ ((cmatrix_sub @ V0) @ V2))) @ ((cmatrix_sub @ ((cmatrix_mul @ V1) @ V0)) @ ((cmatrix_mul @ V1) @ V2))))))))))
(TMATRIX_ADD_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_mul @ V1) @ ((cmatrix_add @ V0) @ V2))) @ ((cmatrix_add @ ((cmatrix_mul @ V1) @ V0)) @ ((cmatrix_mul @ V1) @ V2))))))))))
(TSYMMETRIC_MATRIX_IMP_DIAGONALIZABLE,(c! @ (^[V0]: ((c==> @ ((c= @ (ctransp @ V0)) @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (corthogonal_matrix @ V1)) @ (cdiagonal_matrix @ ((cmatrix_mul @ (ctransp @ V1)) @ ((cmatrix_mul @ V0) @ V1))))))))))
(TSYMMETRIC_MATRIX_DIAGONALIZABLE_EXPLICIT,(c! @ (^[V0]: ((c==> @ ((c= @ (ctransp @ V0)) @ V0)) @ (c? @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ (corthogonal_matrix @ V1)) @ ((c= @ ((cmatrix_mul @ (ctransp @ V1)) @ ((cmatrix_mul @ V0) @ V1))) @ (clambda @ (^[V3]: (clambda @ (^[V4]: (((cCOND @ ((c= @ V3) @ V4)) @ (V2 @ V3)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))))))
(TCOFACTOR_COFACTOR,(c! @ (^[V0]: ((c==> @ ((c<= @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ (cdimindex @ cUNIV))) @ ((c= @ (ccofactor @ (ccofactor @ V0))) @ ((c%% @ ((creal_pow @ (cdet @ V0)) @ ((c- @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V0))))))
(TMATRIX_MUL_LINV,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((cmatrix_mul @ (cmatrix_inv @ V0)) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TMATRIX_MUL_RINV,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((cmatrix_mul @ V0) @ (cmatrix_inv @ V0))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TCOFACTOR_MATRIX_INV,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (ccofactor @ V0)) @ ((c%% @ (cdet @ V0)) @ (ctransp @ (cmatrix_inv @ V0))))))))
(TORTHOGONAL_MATRIX_INV,(c! @ (^[V0]: ((c==> @ (corthogonal_matrix @ V0)) @ ((c= @ (cmatrix_inv @ V0)) @ (ctransp @ V0))))))
(TTRANSP_DIAGONAL_MATRIX,(c! @ (^[V0]: ((c==> @ (cdiagonal_matrix @ V0)) @ ((c= @ (ctransp @ V0)) @ V0)))))
(TDET_DEPENDENT_ROWS,(c! @ (^[V0]: ((c==> @ (cdependent @ (crows @ V0))) @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TDET_DEPENDENT_COLUMNS,(c! @ (^[V0]: ((c==> @ (cdependent @ (ccolumns @ V0))) @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TINTEGER_DET,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))))) @ (cinteger @ ((c$ @ ((c$ @ V0) @ V1)) @ V2)))))))) @ (cinteger @ (cdet @ V0))))))
(TDET_UPPERTRIANGULAR,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c< @ V2) @ V1)))))) @ ((c= @ ((c$ @ ((c$ @ V0) @ V1)) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ ((c= @ (cdet @ V0)) @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V1]: ((c$ @ ((c$ @ V0) @ V1)) @ V1))))))))
(TDET_LOWERTRIANGULAR,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c< @ V1) @ V2)))))) @ ((c= @ ((c$ @ ((c$ @ V0) @ V1)) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ ((c= @ (cdet @ V0)) @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V1]: ((c$ @ ((c$ @ V0) @ V1)) @ V1))))))))
(TDET_DIAGONAL,(c! @ (^[V0]: ((c==> @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V1) @ V2))))))) @ ((c= @ ((c$ @ ((c$ @ V0) @ V1)) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))) @ ((c= @ (cdet @ V0)) @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V1]: ((c$ @ ((c$ @ V0) @ V1)) @ V1))))))))
(TTRACE_TRANSP,(c! @ (^[V0]: ((c= @ (ctrace @ (ctransp @ V0))) @ (ctrace @ V0)))))
(Ttrace,(c! @ (^[V0]: ((c= @ (ctrace @ V0)) @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V1]: ((c$ @ ((c$ @ V0) @ V1)) @ V1)))))))
(TDET_TRANSP,(c! @ (^[V0]: ((c= @ (cdet @ (ctransp @ V0))) @ (cdet @ V0)))))
(TDET_NEG,(c! @ (^[V0]: ((c= @ (cdet @ (cmatrix_neg @ V0))) @ ((creal_mul @ ((creal_pow @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cdimindex @ cUNIV))) @ (cdet @ V0))))))
(TDET_COFACTOR,(c! @ (^[V0]: ((c= @ (cdet @ (ccofactor @ V0))) @ ((creal_pow @ (cdet @ V0)) @ ((c- @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(Tdet,(c! @ (^[V0]: ((c= @ (cdet @ V0)) @ ((csum @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((cpermutes @ V2) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV)))) @ V2)))))) @ (^[V1]: ((creal_mul @ (csign @ V1)) @ ((cproduct @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V2]: ((c$ @ ((c$ @ V0) @ V2)) @ (V1 @ V2)))))))))))
(TRANK_COFACTOR,(c! @ (^[V0]: ((c= @ (crank @ (ccofactor @ V0))) @ (((cCOND @ ((c= @ (crank @ V0)) @ (cdimindex @ cUNIV))) @ (cdimindex @ cUNIV)) @ (((cCOND @ ((c= @ (crank @ V0)) @ ((c- @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ c_0)))))))
(TMPOW_1,(c! @ (^[V0]: ((c= @ ((cmpow @ V0) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))
(Tmpow_conjunct0,(c! @ (^[V0]: ((c= @ ((cmpow @ V0) @ (cNUMERAL @ c_0))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))))
(TMATRIX_MUL_LEFT_COFACTOR,(c! @ (^[V0]: ((c= @ ((cmatrix_mul @ (ctransp @ (ccofactor @ V0))) @ V0)) @ ((c%% @ (cdet @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TMATRIX_MUL_RIGHT_COFACTOR,(c! @ (^[V0]: ((c= @ ((cmatrix_mul @ V0) @ (ctransp @ (ccofactor @ V0)))) @ ((c%% @ (cdet @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TMATRIX_NEG_NEG,(c! @ (^[V0]: ((c= @ (cmatrix_neg @ (cmatrix_neg @ V0))) @ V0))))
(TCOFACTOR_TRANSP,(c! @ (^[V0]: ((c= @ (ccofactor @ (ctransp @ V0))) @ (ctransp @ (ccofactor @ V0))))))
(TCOFACTOR_COLUMN,(c! @ (^[V0]: ((c= @ (ccofactor @ V0)) @ (clambda @ (^[V1]: (clambda @ (^[V2]: (cdet @ (clambda @ (^[V3]: (clambda @ (^[V4]: (((cCOND @ ((c= @ V4) @ V2)) @ (((cCOND @ ((c= @ V3) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c$ @ ((c$ @ V0) @ V3)) @ V4)))))))))))))))
(TCOFACTOR_ROW,(c! @ (^[V0]: ((c= @ (ccofactor @ V0)) @ (clambda @ (^[V1]: (clambda @ (^[V2]: (cdet @ (clambda @ (^[V3]: (clambda @ (^[V4]: (((cCOND @ ((c= @ V3) @ V1)) @ (((cCOND @ ((c= @ V4) @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c$ @ ((c$ @ V0) @ V3)) @ V4)))))))))))))))
(Tcofactor,(c! @ (^[V0]: ((c= @ (ccofactor @ V0)) @ (clambda @ (^[V1]: (clambda @ (^[V2]: (cdet @ (clambda @ (^[V3]: (clambda @ (^[V4]: (((cCOND @ ((c/__caret__ @ ((c= @ V3) @ V1)) @ ((c= @ V4) @ V2))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (((cCOND @ ((c__caret__/ @ ((c= @ V3) @ V1)) @ ((c= @ V4) @ V2))) @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ ((c$ @ V0) @ V3)) @ V4))))))))))))))))
(TDET_EQ_0_RANK,(c! @ (^[V0]: ((c= @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c< @ (crank @ V0)) @ (cdimindex @ cUNIV))))))
(TDET_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ (c~ @ (cinvertible @ V0))))))
(TRANK_COFACTOR_EQ_FULL,(c! @ (^[V0]: ((c= @ ((c= @ (crank @ (ccofactor @ V0))) @ (cdimindex @ cUNIV))) @ ((c__caret__/ @ ((c= @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ (crank @ V0)) @ (cdimindex @ cUNIV)))))))
(TRANK_COFACTOR_EQ_1,(c! @ (^[V0]: ((c= @ ((c= @ (crank @ (ccofactor @ V0))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c__caret__/ @ ((c= @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((c= @ (crank @ V0)) @ ((c- @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TRANK_EQ_FULL_DET,(c! @ (^[V0]: ((c= @ ((c= @ (crank @ V0)) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TSYMMETRIC_MATRIX,(c! @ (^[V0]: ((c= @ ((c= @ (ctransp @ V0)) @ V0)) @ ((c= @ (cadjoint @ (^[V1]: ((cmatrix_vector_mul @ V0) @ V1)))) @ (^[V1]: ((cmatrix_vector_mul @ V0) @ V1)))))))
(TSYMMETRIC_MATRIX_EQ_DIAGONALIZABLE,(c! @ (^[V0]: ((c= @ ((c= @ (ctransp @ V0)) @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ (corthogonal_matrix @ V1)) @ (cdiagonal_matrix @ ((cmatrix_mul @ (ctransp @ V1)) @ ((cmatrix_mul @ V0) @ V1))))))))))
(TCOFACTOR_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (ccofactor @ V0)) @ (cmat @ (cNUMERAL @ c_0)))) @ ((c< @ (crank @ V0)) @ ((c- @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TORTHOGONAL_MATRIX_TRANSP,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ (ctransp @ V0))) @ (corthogonal_matrix @ V0)))))
(TORTHOGONAL_MATRIX,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c= @ ((cmatrix_mul @ (ctransp @ V0)) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TORTHOGONAL_MATRIX_ALT,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c= @ ((cmatrix_mul @ V0) @ (ctransp @ V0))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TORTHOGONAL_MATRIX_ORTHONORMAL_ROWS_PAIRWISE,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ ((c= @ (cCARD @ (crows @ V0))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cvector_norm @ ((crow @ V1) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cpairwise @ corthogonal) @ (crows @ V0))))))))
(TORTHOGONAL_MATRIX_ORTHONORMAL_COLUMNS_PAIRWISE,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ ((c= @ (cCARD @ (ccolumns @ V0))) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cvector_norm @ ((ccolumn @ V1) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cpairwise @ corthogonal) @ (ccolumns @ V0))))))))
(TORTHOGONAL_MATRIX_ORTHONORMAL_ROWS_SPAN,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ ((c= @ (cspan @ (crows @ V0))) @ cUNIV)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cvector_norm @ ((crow @ V1) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cpairwise @ corthogonal) @ (crows @ V0))))))))
(TORTHOGONAL_MATRIX_ORTHONORMAL_COLUMNS_SPAN,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ ((c= @ (cspan @ (ccolumns @ V0))) @ cUNIV)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cvector_norm @ ((ccolumn @ V1) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cpairwise @ corthogonal) @ (ccolumns @ V0))))))))
(Torthogonal_matrix,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ ((c= @ ((cmatrix_mul @ (ctransp @ V0)) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cmatrix_mul @ V0) @ (ctransp @ V0))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TORTHOGONAL_MATRIX_ORTHONORMAL_ROWS_INDEXED,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cvector_norm @ ((crow @ V1) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cpairwise @ (^[V1]: (^[V2]: ((corthogonal @ ((crow @ V1) @ V0)) @ ((crow @ V2) @ V0))))) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))))))
(TORTHOGONAL_MATRIX_ORTHONORMAL_ROWS,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cvector_norm @ ((crow @ V1) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V1) @ V2))))))) @ ((corthogonal @ ((crow @ V1) @ V0)) @ ((crow @ V2) @ V0))))))))))))
(TORTHOGONAL_MATRIX_ORTHONORMAL_COLUMNS_INDEXED,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cvector_norm @ ((ccolumn @ V1) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ ((cpairwise @ (^[V1]: (^[V2]: ((corthogonal @ ((ccolumn @ V1) @ V0)) @ ((ccolumn @ V2) @ V0))))) @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))))))))
(TORTHOGONAL_MATRIX_ORTHONORMAL_COLUMNS,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cvector_norm @ ((ccolumn @ V1) @ V0))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V1) @ V2))))))) @ ((corthogonal @ ((ccolumn @ V1) @ V0)) @ ((ccolumn @ V2) @ V0))))))))))))
(TORTHOGONAL_MATRIX_TRANSFORMATION,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ (corthogonal_transformation @ (^[V1]: ((cmatrix_vector_mul @ V0) @ V1)))))))
(TINVERTIBLE_COFACTOR,(c! @ (^[V0]: ((c= @ (cinvertible @ (ccofactor @ V0))) @ ((c__caret__/ @ ((c= @ (cdimindex @ cUNIV)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cinvertible @ V0))))))
(TINVERTIBLE_DET_NZ,(c! @ (^[V0]: ((c= @ (cinvertible @ V0)) @ (c~ @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))
(TINVERTIBLE_LEFT_INVERSE,(c! @ (^[V0]: ((c= @ (cinvertible @ V0)) @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TINVERTIBLE_RIGHT_INVERSE,(c! @ (^[V0]: ((c= @ (cinvertible @ V0)) @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(THOMOGENEOUS_LINEAR_EQUATIONS_DET,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0))))))) @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))
(TNEARBY_INVERTIBLE_MATRIX,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((creal_lt @ (creal_abs @ V2)) @ V1))) @ (cinvertible @ ((cmatrix_add @ V0) @ ((c%% @ V2) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))))))
(TCHARACTERISTIC_POLYNOMIAL,(c! @ (^[V0]: (c? @ (^[V1]: ((c/__caret__ @ ((c= @ (V1 @ (cdimindex @ cUNIV))) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ (c! @ (^[V2]: ((c= @ (cdet @ ((cmatrix_sub @ ((c%% @ V2) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0))) @ ((csum @ ((c.. @ (cNUMERAL @ c_0)) @ (cdimindex @ cUNIV))) @ (^[V3]: ((creal_mul @ (V1 @ V3)) @ ((creal_pow @ V2) @ V3)))))))))))))
(TSYMMETRIC_MATRIX_ORTHOGONAL_EIGENVECTORS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ ((c= @ (ctransp @ V0)) @ V0)) @ ((c/__caret__ @ ((c= @ ((cmatrix_vector_mul @ V0) @ V3)) @ ((c% @ V1) @ V3))) @ ((c/__caret__ @ ((c= @ ((cmatrix_vector_mul @ V0) @ V4)) @ ((c% @ V2) @ V4))) @ (c~ @ ((c= @ V1) @ V2)))))) @ ((corthogonal @ V3) @ V4)))))))))))))
(TORTHOGONAL_MATRIX_ORTHOGONAL_EIGENVECTORS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (corthogonal_matrix @ V0)) @ ((c/__caret__ @ ((c= @ ((cmatrix_vector_mul @ V0) @ V3)) @ ((c% @ V1) @ V3))) @ ((c/__caret__ @ ((c= @ ((cmatrix_vector_mul @ V0) @ V4)) @ ((c% @ V2) @ V4))) @ (c~ @ ((c= @ V1) @ V2)))))) @ ((corthogonal @ V3) @ V4)))))))))))))
(TDET_COFACTOR_EXPANSION,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ (cdet @ V0)) @ ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V2]: ((creal_mul @ ((c$ @ ((c$ @ V0) @ V1)) @ V2)) @ ((c$ @ ((c$ @ (ccofactor @ V0)) @ V1)) @ V2)))))))))))
(Tmpow_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmpow @ V0) @ (cSUC @ V1))) @ ((cmatrix_mul @ V0) @ ((cmpow @ V0) @ V1))))))))
(TMATRIX_INV_UNIQUE_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cmatrix_inv @ V0)) @ V1)))))))
(TMATRIX_INV_UNIQUE_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cmatrix_inv @ V0)) @ V1)))))))
(TSYMMETRIC_MATRIX_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ (ctransp @ V1)) @ V1)) @ ((c= @ (ctransp @ V0)) @ V0))) @ ((c= @ ((c= @ (ctransp @ ((cmatrix_mul @ V1) @ V0))) @ ((cmatrix_mul @ V1) @ V0))) @ ((c= @ ((cmatrix_mul @ V1) @ V0)) @ ((cmatrix_mul @ V0) @ V1)))))))))
(TMATRIX_INV_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cinvertible @ V1)) @ (cinvertible @ V0))) @ ((c= @ (cmatrix_inv @ ((cmatrix_mul @ V1) @ V0))) @ ((cmatrix_mul @ (cmatrix_inv @ V0)) @ (cmatrix_inv @ V1)))))))))
(TTRACE_CONJUGATE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cinvertible @ V0)) @ ((c= @ (ctrace @ ((cmatrix_mul @ (cmatrix_inv @ V0)) @ ((cmatrix_mul @ V1) @ V0)))) @ (ctrace @ V1))))))))
(TTRACE_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctrace @ ((cmatrix_sub @ V0) @ V1))) @ ((creal_sub @ (ctrace @ V0)) @ (ctrace @ V1))))))))
(TTRACE_MUL_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctrace @ ((cmatrix_mul @ V1) @ V0))) @ (ctrace @ ((cmatrix_mul @ V0) @ V1))))))))
(TTRACE_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctrace @ ((cmatrix_add @ V0) @ V1))) @ ((creal_add @ (ctrace @ V0)) @ (ctrace @ V1))))))))
(TDET_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdet @ ((cmatrix_mul @ V0) @ V1))) @ ((creal_mul @ (cdet @ V0)) @ (cdet @ V1))))))))
(TMATRIX_MUL_VSUM_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (clambda @ (^[V2]: ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V3]: ((c% @ ((c$ @ ((c$ @ V0) @ V2)) @ V3)) @ ((c$ @ V1) @ V3))))))))))))
(TCOFACTOR_MATRIX_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccofactor @ ((cmatrix_mul @ V0) @ V1))) @ ((cmatrix_mul @ (ccofactor @ V0)) @ (ccofactor @ V1))))))))
(TMATRIX_LEFT_RIGHT_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TMATRIX_RIGHT_INVERSE_COFACTOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (c~ @ ((c= @ (cdet @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ V0) @ ((c%% @ (creal_inv @ (cdet @ V1))) @ (ctransp @ (ccofactor @ V1)))))))))))
(TCRAMER_MATRIX_RIGHT_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (c~ @ ((c= @ (cdet @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ V0) @ (clambda @ (^[V2]: (clambda @ (^[V3]: ((creal_div @ (cdet @ (clambda @ (^[V4]: (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V2)) @ (((cCOND @ ((c= @ V4) @ V3)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c$ @ ((c$ @ V1) @ V4)) @ V5)))))))) @ (cdet @ V1))))))))))))))
(TMATRIX_LEFT_INVERSE_COFACTOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (c~ @ ((c= @ (cdet @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ V0) @ ((c%% @ (creal_inv @ (cdet @ V1))) @ (ctransp @ (ccofactor @ V1)))))))))))
(TCRAMER_MATRIX_LEFT_INVERSE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c/__caret__ @ (c~ @ ((c= @ (cdet @ V1)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ V0) @ (clambda @ (^[V2]: (clambda @ (^[V3]: ((creal_div @ (cdet @ (clambda @ (^[V4]: (clambda @ (^[V5]: (((cCOND @ ((c= @ V5) @ V3)) @ (((cCOND @ ((c= @ V4) @ V2)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_of_num @ (cNUMERAL @ c_0)))) @ ((c$ @ ((c$ @ V1) @ V5)) @ V4)))))))) @ (cdet @ V1))))))))))))))
(TINVERTIBLE_MATRIX_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinvertible @ ((cmatrix_mul @ V0) @ V1))) @ ((c/__caret__ @ (cinvertible @ V0)) @ (cinvertible @ V1))))))))
(TMATRIX_MUL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ ((cmatrix_mul @ V1) @ V0)) @ V2)) @ ((cmatrix_vector_mul @ (ctransp @ V0)) @ ((c$ @ V1) @ V2)))))))))))
(TCRAMER_MATRIX_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ (cdet @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((c= @ ((cmatrix_mul @ V2) @ V0)) @ V1)) @ ((c= @ V0) @ (clambda @ (^[V3]: (clambda @ (^[V4]: ((creal_div @ (cdet @ (clambda @ (^[V5]: (clambda @ (^[V6]: (((cCOND @ ((c= @ V6) @ V3)) @ ((c$ @ ((c$ @ V1) @ V5)) @ V4)) @ ((c$ @ ((c$ @ V2) @ V5)) @ V6)))))))) @ (cdet @ V2))))))))))))))))
(TCRAMER_MATRIX_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((c= @ (cdet @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ ((c= @ ((cmatrix_mul @ V0) @ V2)) @ V1)) @ ((c= @ V0) @ (clambda @ (^[V3]: (clambda @ (^[V4]: ((creal_div @ (cdet @ (clambda @ (^[V5]: (clambda @ (^[V6]: (((cCOND @ ((c= @ V6) @ V4)) @ ((c$ @ ((c$ @ V1) @ V3)) @ V5)) @ ((c$ @ ((c$ @ V2) @ V6)) @ V5)))))))) @ (cdet @ V2))))))))))))))))
(TSYMMETRIX_MATRIX_CONJUGATE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (ctransp @ V0)) @ V0)) @ ((c= @ (ctransp @ ((cmatrix_mul @ (ctransp @ V1)) @ ((cmatrix_mul @ V0) @ V1)))) @ ((cmatrix_mul @ (ctransp @ V1)) @ ((cmatrix_mul @ V0) @ V1)))))))))
(TINVERTIBLE_IMP_SQUARE_MATRIX,(c! @ (^[V0]: ((c==> @ (cinvertible @ V0)) @ ((c= @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))))))
(TMATRIX_INV_conjunct1,(c! @ (^[V0]: ((c==> @ (cinvertible @ V0)) @ ((c= @ ((cmatrix_mul @ (cmatrix_inv @ V0)) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(TMATRIX_INV_conjunct0,(c! @ (^[V0]: ((c==> @ (cinvertible @ V0)) @ ((c= @ ((cmatrix_mul @ V0) @ (cmatrix_inv @ V0))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))
(Trows,(c! @ (^[V0]: ((c= @ (crows @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((crow @ V2) @ V0))))))))))
(TCOLUMNS_TRANSP,(c! @ (^[V0]: ((c= @ (ccolumns @ (ctransp @ V0))) @ (crows @ V0)))))
(TADJOINT_MATRIX,(c! @ (^[V0]: ((c= @ (cadjoint @ (^[V1]: ((cmatrix_vector_mul @ V0) @ V1)))) @ (^[V1]: ((cmatrix_vector_mul @ (ctransp @ V0)) @ V1))))))
(TROWS_TRANSP,(c! @ (^[V0]: ((c= @ (crows @ (ctransp @ V0))) @ (ccolumns @ V0)))))
(Tcolumns,(c! @ (^[V0]: ((c= @ (ccolumns @ V0)) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((ccolumn @ V2) @ V0))))))))))
(TMATRIX_MUL_RZERO,(c! @ (^[V0]: ((c= @ ((cmatrix_mul @ V0) @ (cmat @ (cNUMERAL @ c_0)))) @ (cmat @ (cNUMERAL @ c_0))))))
(TMATRIX_MUL_LTRANSP_DOT_COLUMN,(c! @ (^[V0]: ((c= @ ((cmatrix_mul @ (ctransp @ V0)) @ V0)) @ (clambda @ (^[V1]: (clambda @ (^[V2]: ((cdot @ ((ccolumn @ V1) @ V0)) @ ((ccolumn @ V2) @ V0))))))))))
(TMATRIX_SUB_LZERO,(c! @ (^[V0]: ((c= @ ((cmatrix_sub @ (cmat @ (cNUMERAL @ c_0))) @ V0)) @ (cmatrix_neg @ V0)))))
(TMATRIX_SUB_RZERO,(c! @ (^[V0]: ((c= @ ((cmatrix_sub @ V0) @ (cmat @ (cNUMERAL @ c_0)))) @ V0))))
(TMATRIX_MUL_RID,(c! @ (^[V0]: ((c= @ ((cmatrix_mul @ V0) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0))))
(TMATRIX_MUL_LID,(c! @ (^[V0]: ((c= @ ((cmatrix_mul @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ V0))))
(TTRANSP_TRANSP,(c! @ (^[V0]: ((c= @ (ctransp @ (ctransp @ V0))) @ V0))))
(TMATRIX_NEG_MINUS1,(c! @ (^[V0]: ((c= @ (cmatrix_neg @ V0)) @ ((c%% @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ V0)))))
(TMATRIX_OF_MATRIX_VECTOR_MUL,(c! @ (^[V0]: ((c= @ (cmatrix @ (^[V1]: ((cmatrix_vector_mul @ V0) @ V1)))) @ V0))))
(TTRANSP_MATRIX_NEG,(c! @ (^[V0]: ((c= @ (ctransp @ (cmatrix_neg @ V0))) @ (cmatrix_neg @ (ctransp @ V0))))))
(Tmatrix_inv,(c! @ (^[V0]: ((c= @ (cmatrix_inv @ V0)) @ (c__at__ @ (^[V1]: ((c/__caret__ @ ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TMATRIX_MUL_RTRANSP_DOT_ROW,(c! @ (^[V0]: ((c= @ ((cmatrix_mul @ V0) @ (ctransp @ V0))) @ (clambda @ (^[V1]: (clambda @ (^[V2]: ((cdot @ ((crow @ V1) @ V0)) @ ((crow @ V2) @ V0))))))))))
(TMATRIX_NEG_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (cmatrix_neg @ V0)) @ (cmat @ (cNUMERAL @ c_0)))) @ ((c= @ V0) @ (cmat @ (cNUMERAL @ c_0)))))))
(TINVERTIBLE_NEG,(c! @ (^[V0]: ((c= @ (cinvertible @ (cmatrix_neg @ V0))) @ (cinvertible @ V0)))))
(Tinvertible,(c! @ (^[V0]: ((c= @ (cinvertible @ V0)) @ (c? @ (^[V1]: ((c/__caret__ @ ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TINVERTIBLE_TRANSP,(c! @ (^[V0]: ((c= @ (cinvertible @ (ctransp @ V0))) @ (cinvertible @ V0)))))
(Tdiagonal_matrix,(c! @ (^[V0]: ((c= @ (cdiagonal_matrix @ V0)) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c/__caret__ @ ((c<= @ V1) @ (cdimindex @ cUNIV))) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c/__caret__ @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ (c~ @ ((c= @ V1) @ V2))))))) @ ((c= @ ((c$ @ ((c$ @ V0) @ V1)) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))
(TRIGHT_INVERTIBLE_TRANSP,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ (ctransp @ V0)) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TLEFT_INVERTIBLE_TRANSP,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V1) @ (ctransp @ V0))) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TMATRIX_LEFT_INVERTIBLE_SPAN_ROWS,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((c= @ (cspan @ (crows @ V0))) @ cUNIV)))))
(TMATRIX_LEFT_INVERTIBLE_INDEPENDENT_COLUMNS,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c! @ (^[V1]: ((c==> @ ((c= @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V2]: ((c% @ (V1 @ V2)) @ ((ccolumn @ V2) @ V0))))) @ (cvec @ (cNUMERAL @ c_0)))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))
(TMATRIX_LEFT_INVERTIBLE_KER,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c! @ (^[V1]: ((c==> @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))))))))
(TMATRIX_LEFT_INVERTIBLE_INJECTIVE,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ ((cmatrix_vector_mul @ V0) @ V2))) @ ((c= @ V1) @ V2))))))))))
(TMATRIX_RIGHT_INVERTIBLE_SPAN_COLUMNS,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ ((c= @ (cspan @ (ccolumns @ V0))) @ cUNIV)))))
(TMATRIX_RIGHT_INVERTIBLE_INDEPENDENT_ROWS,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c! @ (^[V1]: ((c==> @ ((c= @ ((cvsum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V2]: ((c% @ (V1 @ V2)) @ ((crow @ V2) @ V0))))) @ (cvec @ (cNUMERAL @ c_0)))) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ (V1 @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0)))))))))))))
(TMATRIX_RIGHT_INVERTIBLE_SURJECTIVE,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))))) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ ((cmatrix_vector_mul @ V0) @ V2)) @ V1)))))))))
(TMATRIX_VECTOR_MUL_LINEAR,(c! @ (^[V0]: (clinear @ (^[V1]: ((cmatrix_vector_mul @ V0) @ V1))))))
(TFINITE_ROWS,(c! @ (^[V0]: (cFINITE @ (crows @ V0)))))
(TFINITE_COLUMNS,(c! @ (^[V0]: (cFINITE @ (ccolumns @ V0)))))
(TMATRIX_CMUL_SUB_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c%% @ V1) @ ((cmatrix_sub @ V0) @ V2))) @ ((cmatrix_sub @ ((c%% @ V1) @ V0)) @ ((c%% @ V1) @ V2))))))))))
(TMATRIX_CMUL_ADD_LDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c%% @ V1) @ ((cmatrix_add @ V0) @ V2))) @ ((cmatrix_add @ ((c%% @ V1) @ V0)) @ ((c%% @ V1) @ V2))))))))))
(TMATRIX_NEG_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c$ @ ((c$ @ (cmatrix_neg @ V0)) @ V1)) @ V2)) @ (creal_neg @ ((c$ @ ((c$ @ V0) @ V1)) @ V2))))))))))
(TTRANSP_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c$ @ ((c$ @ (ctransp @ V0)) @ V2)) @ V1)) @ ((c$ @ ((c$ @ V0) @ V1)) @ V2)))))))))
(TMATRIX_VECTOR_MUL_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V1)) @ ((c<= @ V1) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ ((cmatrix_vector_mul @ V0) @ V2)) @ V1)) @ ((cdot @ ((c$ @ V0) @ V1)) @ V2))))))))))
(TMSUM_MATRIX_LMUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((cmsum @ V1) @ (^[V3]: ((cmatrix_mul @ V0) @ (V2 @ V3))))) @ ((cmatrix_mul @ V0) @ ((cmsum @ V1) @ V2)))))))))))
(Tmatrix_vector_mul,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ (clambda @ (^[V2]: ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V3]: ((creal_mul @ ((c$ @ ((c$ @ V0) @ V2)) @ V3)) @ ((c$ @ V1) @ V3))))))))))))
(TMATRIX_MUL_DOT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ (clambda @ (^[V2]: ((cdot @ ((c$ @ V0) @ V2)) @ V1)))))))))
(TDOT_ROWVECTOR_COLUMNVECTOR,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ccolumnvector @ ((cmatrix_vector_mul @ V0) @ V1))) @ ((cmatrix_mul @ V0) @ (ccolumnvector @ V1))))))))
(Tvector_matrix_mul,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_matrix_mul @ V1) @ V0)) @ (clambda @ (^[V2]: ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V3]: ((creal_mul @ ((c$ @ ((c$ @ V0) @ V3)) @ V2)) @ ((c$ @ V1) @ V3))))))))))))
(TFARKAS_LEMMA_ALT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((creal_le @ ((c$ @ ((cmatrix_vector_mul @ V0) @ V2)) @ V3)) @ ((c$ @ V1) @ V3)))))))) @ (c~ @ (c? @ (^[V2]: ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V3)) @ ((c<= @ V3) @ (cdimindex @ cUNIV)))) @ ((creal_le @ (creal_of_num @ (cNUMERAL @ c_0))) @ ((c$ @ V2) @ V3)))))) @ ((c/__caret__ @ ((c= @ ((cvector_matrix_mul @ V2) @ V0)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((creal_lt @ ((cdot @ V1) @ V2)) @ (creal_of_num @ (cNUMERAL @ c_0))))))))))))))
(TMATRIX_MUL_LNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_mul @ (cmatrix_neg @ V0)) @ V1)) @ (cmatrix_neg @ ((cmatrix_mul @ V0) @ V1))))))))
(TMATRIX_MUL_RNEG,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_mul @ V0) @ (cmatrix_neg @ V1))) @ (cmatrix_neg @ ((cmatrix_mul @ V0) @ V1))))))))
(Tmatrix_mul,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (clambda @ (^[V2]: (clambda @ (^[V3]: ((csum @ ((c.. @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cdimindex @ cUNIV))) @ (^[V4]: ((creal_mul @ ((c$ @ ((c$ @ V0) @ V2)) @ V4)) @ ((c$ @ ((c$ @ V1) @ V4)) @ V3))))))))))))))
(TRANK_SYLVESTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ ((c+ @ (crank @ V0)) @ (crank @ V1))) @ ((c+ @ (crank @ ((cmatrix_mul @ V0) @ V1))) @ (cdimindex @ cUNIV))))))))
(TRANK_MUL_LE_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ (crank @ ((cmatrix_mul @ V0) @ V1))) @ (crank @ V1)))))))
(TMATRIX_VECTOR_MUL_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_vector_mul @ V0) @ ((cmatrix_vector_mul @ V1) @ V2))) @ ((cmatrix_vector_mul @ ((cmatrix_mul @ V0) @ V1)) @ V2)))))))))
(TMATRIX_MUL_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_mul @ V0) @ ((cmatrix_mul @ V1) @ V2))) @ ((cmatrix_mul @ ((cmatrix_mul @ V0) @ V1)) @ V2)))))))))
(TMATRIX_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_sub @ V0) @ V1)) @ ((cmatrix_add @ V0) @ (cmatrix_neg @ V1))))))))
(TMATRIX_ADD_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmatrix_add @ V1) @ V0)) @ ((cmatrix_add @ V0) @ V1)))))))
(TMATRIX_NEG_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmatrix_neg @ ((cmatrix_sub @ V1) @ V0))) @ ((cmatrix_sub @ V0) @ V1)))))))
(TMATRIX_NEG_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cmatrix_neg @ ((cmatrix_add @ V0) @ V1))) @ ((cmatrix_add @ (cmatrix_neg @ V0)) @ (cmatrix_neg @ V1))))))))
(TTRANSP_MATRIX_SUB,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctransp @ ((cmatrix_sub @ V0) @ V1))) @ ((cmatrix_sub @ (ctransp @ V0)) @ (ctransp @ V1))))))))
(TTRANSP_MATRIX_ADD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctransp @ ((cmatrix_add @ V0) @ V1))) @ ((cmatrix_add @ (ctransp @ V0)) @ (ctransp @ V1))))))))
(TMATRIX_EQUAL_COLUMNS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ ((ccolumn @ V2) @ V0)) @ ((ccolumn @ V2) @ V1)))))))))))
(TMATRIX_EQUAL_ROWS,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ ((crow @ V2) @ V0)) @ ((crow @ V2) @ V1)))))))))))
(TMATRIX_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ ((cmatrix_vector_mul @ V0) @ V2)) @ ((cmatrix_vector_mul @ V1) @ V2))))))))))
(TMATRIX_SUB_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c$ @ ((c$ @ ((cmatrix_sub @ V0) @ V1)) @ V2)) @ V3)) @ ((creal_sub @ ((c$ @ ((c$ @ V0) @ V2)) @ V3)) @ ((c$ @ ((c$ @ V1) @ V2)) @ V3))))))))))))
(TMATRIX_ADD_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c$ @ ((c$ @ ((cmatrix_add @ V0) @ V1)) @ V2)) @ V3)) @ ((creal_add @ ((c$ @ ((c$ @ V0) @ V2)) @ V3)) @ ((c$ @ ((c$ @ V1) @ V2)) @ V3))))))))))))
(TMATRIX_SUB_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_mul @ ((cmatrix_sub @ V0) @ V1)) @ V2)) @ ((cmatrix_sub @ ((cmatrix_mul @ V0) @ V2)) @ ((cmatrix_mul @ V1) @ V2))))))))))
(TMATRIX_ADD_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_mul @ ((cmatrix_add @ V0) @ V1)) @ V2)) @ ((cmatrix_add @ ((cmatrix_mul @ V0) @ V2)) @ ((cmatrix_mul @ V1) @ V2))))))))))
(TMATRIX_ADD_AC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_add @ ((cmatrix_add @ V0) @ V1)) @ V2)) @ ((cmatrix_add @ V0) @ ((cmatrix_add @ V1) @ V2))))))))))
(TMATRIX_ADD_AC_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_add @ V1) @ ((cmatrix_add @ V0) @ V2))) @ ((cmatrix_add @ V0) @ ((cmatrix_add @ V1) @ V2))))))))))
(TMATRIX_ADD_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_add @ V0) @ ((cmatrix_add @ V1) @ V2))) @ ((cmatrix_add @ ((cmatrix_add @ V0) @ V1)) @ V2)))))))))
(TMATRIX_INV_UNIQUE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ ((c= @ ((cmatrix_mul @ V0) @ V1)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ ((cmatrix_mul @ V1) @ V0)) @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))))) @ ((c= @ (cmatrix_inv @ V0)) @ V1)))))))
(TMATRIX_TRIVIAL_LINEAR_EQUATIONS,(c! @ (^[V0]: ((c==> @ ((c< @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0))))))))))
(TMATRIX_NONFULL_LINEAR_EQUATIONS,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (crank @ V0)) @ (cdimindex @ cUNIV)))) @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0))))))))))
(TRANK_NULLSPACE,(c! @ (^[V0]: ((c= @ ((c+ @ (crank @ V0)) @ (cdim @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c= @ ((cmatrix_vector_mul @ V0) @ V2)) @ (cvec @ (cNUMERAL @ c_0)))) @ V2)))))))) @ (cdimindex @ cUNIV)))))
(TRANK_TRANSP,(c! @ (^[V0]: ((c= @ (crank @ (ctransp @ V0))) @ (crank @ V0)))))
(TRANK_DIM_IM,(c! @ (^[V0]: ((c= @ (crank @ V0)) @ (cdim @ ((cIMAGE @ (^[V1]: ((cmatrix_vector_mul @ V0) @ V1))) @ cUNIV))))))
(Trank,(c! @ (^[V0]: ((c= @ (crank @ V0)) @ (cdim @ (ccolumns @ V0))))))
(TRANK_ROW,(c! @ (^[V0]: ((c= @ (crank @ V0)) @ (cdim @ (crows @ V0))))))
(TRANK_GRAM,(c! @ (^[V0]: ((c= @ (crank @ ((cmatrix_mul @ (ctransp @ V0)) @ V0))) @ (crank @ V0)))))
(TCOLUMNS_IMAGE_BASIS,(c! @ (^[V0]: ((c= @ (ccolumns @ V0)) @ ((cIMAGE @ (^[V1]: ((cmatrix_vector_mul @ V0) @ V1))) @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ (cbasis @ V2)))))))))))
(TMATRIX_VECTOR_MUL_RZERO,(c! @ (^[V0]: ((c= @ ((cmatrix_vector_mul @ V0) @ (cvec @ (cNUMERAL @ c_0)))) @ (cvec @ (cNUMERAL @ c_0))))))
(TMATRIX_CMUL_LID,(c! @ (^[V0]: ((c= @ ((c%% @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0)) @ V0))))
(TFULL_RANK_SURJECTIVE,(c! @ (^[V0]: ((c= @ ((c= @ (crank @ V0)) @ (cdimindex @ cUNIV))) @ (c! @ (^[V1]: (c? @ (^[V2]: ((c= @ ((cmatrix_vector_mul @ V0) @ V2)) @ V1)))))))))
(TFULL_RANK_INJECTIVE,(c! @ (^[V0]: ((c= @ ((c= @ (crank @ V0)) @ (cdimindex @ cUNIV))) @ (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ ((cmatrix_vector_mul @ V0) @ V2))) @ ((c= @ V1) @ V2))))))))))
(TRANK_EQ_0,(c! @ (^[V0]: ((c= @ ((c= @ (crank @ V0)) @ (cNUMERAL @ c_0))) @ ((c= @ V0) @ (cmat @ (cNUMERAL @ c_0)))))))
(TMATRIX_NONFULL_LINEAR_EQUATIONS_EQ,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: ((c/__caret__ @ (c~ @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0))))) @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0))))))) @ (c~ @ ((c= @ (crank @ V0)) @ (cdimindex @ cUNIV)))))))
(TRANK_BOUND,(c! @ (^[V0]: ((c<= @ (crank @ V0)) @ ((cMIN @ (cdimindex @ cUNIV)) @ (cdimindex @ cUNIV))))))
(TDIM_ROWS_LE_DIM_COLUMNS,(c! @ (^[V0]: ((c<= @ (cdim @ (crows @ V0))) @ (cdim @ (ccolumns @ V0))))))
(TMATRIX_FULL_LINEAR_EQUATIONS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ (crank @ V0)) @ (cdimindex @ cUNIV))) @ (c? @ (^[V2]: ((c= @ ((cmatrix_vector_mul @ V0) @ V2)) @ V1)))))))))
(TVECTOR_MATRIX_MUL_TRANSP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cvector_matrix_mul @ V1) @ V0)) @ ((cmatrix_vector_mul @ (ctransp @ V0)) @ V1)))))))
(TNULLSPACE_INTER_ROWSPACE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((cIN @ V1) @ (cspan @ (crows @ V0))))) @ ((c= @ V1) @ (cvec @ (cNUMERAL @ c_0)))))))))
(TMATRIX_VECTOR_MUL_INJECTIVE_ON_ROWSPACE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V1) @ (cspan @ (crows @ V0)))) @ ((c/__caret__ @ ((cIN @ V2) @ (cspan @ (crows @ V0)))) @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ ((cmatrix_vector_mul @ V0) @ V2))))) @ ((c= @ V1) @ V2)))))))))
(TORTHOGONAL_NULLSPACE_ROWSPACE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c= @ ((cmatrix_vector_mul @ V0) @ V1)) @ (cvec @ (cNUMERAL @ c_0)))) @ ((cIN @ V2) @ (cspan @ (crows @ V0))))) @ ((corthogonal @ V1) @ V2)))))))))
(TSYLVESTER_DETERMINANT_IDENTITY,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cdet @ ((cmatrix_add @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cmatrix_mul @ V1) @ V0)))) @ (cdet @ ((cmatrix_add @ (cmat @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cmatrix_mul @ V0) @ V1)))))))))
(TTRANSP_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (ctransp @ V0)) @ (ctransp @ V1))) @ ((c= @ V0) @ V1)))))))
(TRANK_TRIANGLE,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ (crank @ ((cmatrix_add @ V0) @ V1))) @ ((c+ @ (crank @ V0)) @ (crank @ V1))))))))
(TMATRIX_VECTOR_MUL_SUB_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_vector_mul @ ((cmatrix_sub @ V0) @ V1)) @ V2)) @ ((cvector_sub @ ((cmatrix_vector_mul @ V0) @ V2)) @ ((cmatrix_vector_mul @ V1) @ V2))))))))))
(TMATRIX_VECTOR_MUL_ADD_RDISTRIB,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cmatrix_vector_mul @ ((cmatrix_add @ V0) @ V1)) @ V2)) @ ((cvector_add @ ((cmatrix_vector_mul @ V0) @ V2)) @ ((cmatrix_vector_mul @ V1) @ V2))))))))))
(TORTHOGONAL_ROTATION_OR_ROTOINVERSION,(c! @ (^[V0]: ((c= @ (corthogonal_matrix @ V0)) @ ((c__caret__/ @ (crotation_matrix @ V0)) @ (crotoinversion_matrix @ V0))))))
(Trotoinversion_matrix,(c! @ (^[V0]: ((c= @ (crotoinversion_matrix @ V0)) @ ((c/__caret__ @ (corthogonal_matrix @ V0)) @ ((c= @ (cdet @ V0)) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(Trotation_matrix,(c! @ (^[V0]: ((c= @ (crotation_matrix @ V0)) @ ((c/__caret__ @ (corthogonal_matrix @ V0)) @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))
(TDET_ORTHOGONAL_MATRIX,(c! @ (^[V0]: ((c==> @ (corthogonal_matrix @ V0)) @ ((c__caret__/ @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))) @ ((c= @ (cdet @ V0)) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0))))))))))
(TORTHOGONAL_MATRIX_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (corthogonal_matrix @ V0)) @ (corthogonal_matrix @ V1))) @ (corthogonal_matrix @ ((cmatrix_mul @ V0) @ V1))))))))
(TMATRIX_INV_COFACTOR,(c! @ (^[V0]: ((c==> @ (c~ @ ((c= @ (cdet @ V0)) @ (creal_of_num @ (cNUMERAL @ c_0))))) @ ((c= @ (cmatrix_inv @ V0)) @ ((c%% @ (creal_inv @ (cdet @ V0))) @ (ctransp @ (ccofactor @ V0))))))))
(TMATRIX_TRANSP_MUL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctransp @ ((cmatrix_mul @ V1) @ V0))) @ ((cmatrix_mul @ (ctransp @ V0)) @ (ctransp @ V1))))))))
(TMATRIX_CMUL_LZERO,(c! @ (^[V0]: ((c= @ ((c%% @ (creal_of_num @ (cNUMERAL @ c_0))) @ V0)) @ (cmat @ (cNUMERAL @ c_0))))))
(TMATRIX_SUB_REFL,(c! @ (^[V0]: ((c= @ ((cmatrix_sub @ V0) @ V0)) @ (cmat @ (cNUMERAL @ c_0))))))
(TMATRIX_ADD_RNEG,(c! @ (^[V0]: ((c= @ ((cmatrix_add @ V0) @ (cmatrix_neg @ V0))) @ (cmat @ (cNUMERAL @ c_0))))))
(TMATRIX_ADD_LNEG,(c! @ (^[V0]: ((c= @ ((cmatrix_add @ (cmatrix_neg @ V0)) @ V0)) @ (cmat @ (cNUMERAL @ c_0))))))
(TMATRIX_ADD_RID,(c! @ (^[V0]: ((c= @ ((cmatrix_add @ V0) @ (cmat @ (cNUMERAL @ c_0)))) @ V0))))
(TMATRIX_ADD_LID,(c! @ (^[V0]: ((c= @ ((cmatrix_add @ (cmat @ (cNUMERAL @ c_0))) @ V0)) @ V0))))
(Tsndcart,(c! @ (^[V0]: ((c= @ (csndcart @ V0)) @ (clambda @ (^[V1]: ((c$ @ V0) @ ((c+ @ V1) @ (cdimindex @ cUNIV)))))))))
(Tfstcart,(c! @ (^[V0]: ((c= @ (cfstcart @ V0)) @ (clambda @ (^[V1]: ((c$ @ V0) @ V1)))))))
(TCART_EQ_FULL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c= @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2))))))))))
(TFSTCART_PASTECART,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cfstcart @ ((cpastecart @ V1) @ V0))) @ V1))))))
(Tpastecart,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpastecart @ V0) @ V1)) @ (clambda @ (^[V2]: (((cCOND @ ((c<= @ V2) @ (cdimindex @ cUNIV))) @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ ((c- @ V2) @ (cdimindex @ cUNIV))))))))))))
(TSNDCART_PASTECART,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csndcart @ ((cpastecart @ V0) @ V1))) @ V1))))))
(Tcart_tybij_conjunct0,(c! @ (^[V0]: ((c= @ (cmk_cart @ (cdest_cart @ V0))) @ V0))))
(TCART_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c<= @ (cNUMERAL @ (cBIT1 @ c_0))) @ V2)) @ ((c<= @ V2) @ (cdimindex @ cUNIV)))) @ ((c= @ ((c$ @ V0) @ V2)) @ ((c$ @ V1) @ V2)))))))))))
(TPASTECART_IN_PCROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cIN @ ((cpastecart @ V0) @ V2)) @ ((cPCROSS @ V1) @ V3))) @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ ((cIN @ V2) @ V3))))))))))))
(TPASTECART_EQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ ((c/__caret__ @ ((c= @ (cfstcart @ V0)) @ (cfstcart @ V1))) @ ((c= @ (csndcart @ V0)) @ (csndcart @ V1)))))))))
(TPASTECART_FST_SND,(c! @ (^[V0]: ((c= @ ((cpastecart @ (cfstcart @ V0)) @ (csndcart @ V0))) @ V0))))
(TLAMBDA_ETA,(c! @ (^[V0]: ((c= @ (clambda @ (^[V1]: ((c$ @ V0) @ V1)))) @ V0))))
(Tfinite_index,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c$ @ V0) @ V1)) @ ((cdest_cart @ V0) @ (cfinite_index @ V1))))))))
(TBOOL_CASES_AX,(c! @ (^[V0]: ((c__caret__/ @ ((c= @ V0) @ cT)) @ ((c= @ V0) @ cF)))))
(TEXCLUDED_MIDDLE,(c! @ (^[V0]: ((c__caret__/ @ V0) @ (c~ @ V0)))))
(TAND_INV2,(c! @ (^[V0]: ((c==> @ ((c==> @ (c~ @ V0)) @ cF)) @ ((c==> @ ((c==> @ V0) @ cF)) @ cF)))))
(TIMP_F,(c! @ (^[V0]: ((c==> @ ((c==> @ V0) @ cF)) @ (c~ @ V0)))))
(TEQT_Imp2,(c! @ (^[V0]: ((c==> @ ((c= @ V0) @ cT)) @ V0))))
(TAND_INV_IMP,(c! @ (^[V0]: ((c==> @ (c~ @ V0)) @ ((c==> @ V0) @ cF)))))
(TEQF_Imp1,(c! @ (^[V0]: ((c==> @ (c~ @ V0)) @ ((c= @ V0) @ cF)))))
(TEQT_Imp1,(c! @ (^[V0]: ((c==> @ V0) @ ((c= @ V0) @ cT)))))
(Tbset_conjunct8,(c! @ (^[V0]: ((c= @ (cbset @ (cNox @ V0))) @ cEMPTY))))
(Taset_conjunct8,(c! @ (^[V0]: ((c= @ (caset @ (cNox @ V0))) @ cEMPTY))))
(Tplusinf_conjunct8,(c! @ (^[V0]: ((c= @ (cplusinf @ (cNox @ V0))) @ (cNox @ V0)))))
(Tmirror_conjunct8,(c! @ (^[V0]: ((c= @ (cmirror @ (cNox @ V0))) @ (cNox @ V0)))))
(Tminusinf_conjunct8,(c! @ (^[V0]: ((c= @ (cminusinf @ (cNox @ V0))) @ (cNox @ V0)))))
(TCOND_T_F,(c! @ (^[V0]: ((c= @ (((cCOND @ V0) @ cT) @ cF)) @ V0))))
(TCOND_RIGHT_F,(c! @ (^[V0]: ((c= @ (((cCOND @ V0) @ V0) @ cF)) @ V0))))
(TT_OR,(c! @ (^[V0]: ((c= @ ((c__caret__/ @ cT) @ V0)) @ cT))))
(TF_OR,(c! @ (^[V0]: ((c= @ ((c__caret__/ @ cF) @ V0)) @ V0))))
(TOR_T,(c! @ (^[V0]: ((c= @ ((c__caret__/ @ V0) @ cT)) @ cT))))
(TOR_F,(c! @ (^[V0]: ((c= @ ((c__caret__/ @ V0) @ cF)) @ V0))))
(TDISJ_ACI_conjunct3,(c! @ (^[V0]: ((c= @ ((c__caret__/ @ V0) @ V0)) @ V0))))
(TNOT_ELIM2,(c! @ (^[V0]: ((c= @ ((c==> @ (c~ @ V0)) @ cF)) @ V0))))
(TIMP_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((c==> @ cT) @ V0)) @ V0))))
(TIMP_CLAUSES_conjunct2,(c! @ (^[V0]: ((c= @ ((c==> @ cF) @ V0)) @ cT))))
(TIMP_CLAUSES_conjunct1,(c! @ (^[V0]: ((c= @ ((c==> @ V0) @ cT)) @ cT))))
(TIMP_F_EQ_F,(c! @ (^[V0]: ((c= @ ((c==> @ V0) @ cF)) @ ((c= @ V0) @ cF)))))
(TIMP_CLAUSES_conjunct4,(c! @ (^[V0]: ((c= @ ((c==> @ V0) @ cF)) @ (c~ @ V0)))))
(TIMP_CLAUSES_conjunct3,(c! @ (^[V0]: ((c= @ ((c==> @ V0) @ V0)) @ cT))))
(TEQ_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((c= @ cT) @ V0)) @ V0))))
(TEQ_CLAUSES_conjunct2,(c! @ (^[V0]: ((c= @ ((c= @ cF) @ V0)) @ (c~ @ V0)))))
(TEQ_T,(c! @ (^[V0]: ((c= @ ((c= @ V0) @ cT)) @ V0))))
(TEQ_F,(c! @ (^[V0]: ((c= @ ((c= @ V0) @ cF)) @ (((cCOND @ V0) @ cF) @ cT)))))
(TEQ_CLAUSES_conjunct3,(c! @ (^[V0]: ((c= @ ((c= @ V0) @ cF)) @ (c~ @ V0)))))
(TAND_INV,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ (c~ @ V0)) @ V0)) @ cF))))
(TAND_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ cT) @ V0)) @ V0))))
(TAND_CLAUSES_conjunct2,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ cF) @ V0)) @ cF))))
(TAND_CLAUSES_conjunct1,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ V0) @ cT)) @ V0))))
(TAND_CLAUSES_conjunct3,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ V0) @ cF)) @ cF))))
(TAND_CLAUSES_conjunct4,(c! @ (^[V0]: ((c= @ ((c/__caret__ @ V0) @ V0)) @ V0))))
(TNOT_NOT,(c! @ (^[V0]: ((c= @ (c~ @ (c~ @ V0))) @ V0))))
(TEXISTS_SIMP,(c! @ (^[V0]: ((c= @ (c? @ (^[V1]: V0))) @ V0))))
(TFORALL_SIMP,(c! @ (^[V0]: ((c= @ (c! @ (^[V1]: V0))) @ V0))))
(Tone_tydef_conjunct1,(c! @ (^[V0]: ((c= @ V0) @ ((c= @ (cone_REP @ (cone_ABS @ V0))) @ V0)))))
(TNOT_AND,(c! @ (^[V0]: (c~ @ ((c/__caret__ @ V0) @ (c~ @ V0))))))
(TNUMSUM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cNUMSUM @ V0) @ V1)) @ (((cCOND @ V0) @ (cSUC @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))) @ ((c* @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0)))) @ V1))))))))
(TNUMSUM_DEST_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cNUMRIGHT @ ((cNUMSUM @ V0) @ V1))) @ V1))))))
(TNORM_VSUM_TRIVIAL_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((creal_lt @ (creal_of_num @ (cNUMERAL @ c_0))) @ V5)) @ ((c= @ ((c==> @ V0) @ ((creal_lt @ (cvector_norm @ ((cvsum @ ((cINTER @ V1) @ ((c.. @ V2) @ V3))) @ V4))) @ V5))) @ ((c==> @ V0) @ ((c__caret__/ @ ((c< @ V3) @ V2)) @ ((creal_lt @ (cvector_norm @ ((cvsum @ ((cINTER @ V1) @ ((c.. @ V2) @ V3))) @ V4))) @ V5))))))))))))))))))
(TRIGHT_OR_EXISTS_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c__caret__/ @ V0) @ (c? @ (^[V2]: (V1 @ V2))))) @ (c? @ (^[V2]: ((c__caret__/ @ V0) @ (V1 @ V2))))))))))
(TRIGHT_OR_FORALL_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c__caret__/ @ V0) @ (c! @ (^[V2]: (V1 @ V2))))) @ (c! @ (^[V2]: ((c__caret__/ @ V0) @ (V1 @ V2))))))))))
(TRIGHT_IMP_EXISTS_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c==> @ V0) @ (c? @ (^[V2]: (V1 @ V2))))) @ (c? @ (^[V2]: ((c==> @ V0) @ (V1 @ V2))))))))))
(TRIGHT_IMP_FORALL_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c==> @ V0) @ (c! @ (^[V2]: (V1 @ V2))))) @ (c! @ (^[V2]: ((c==> @ V0) @ (V1 @ V2))))))))))
(TRIGHT_AND_EXISTS_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ V0) @ (c? @ (^[V2]: (V1 @ V2))))) @ (c? @ (^[V2]: ((c/__caret__ @ V0) @ (V1 @ V2))))))))))
(TRIGHT_AND_FORALL_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ V0) @ (c! @ (^[V2]: (V1 @ V2))))) @ (c! @ (^[V2]: ((c/__caret__ @ V0) @ (V1 @ V2))))))))))
(TRIGHT_EXISTS_IMP_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c==> @ V0) @ (V1 @ V2))))) @ ((c==> @ V0) @ (c? @ (^[V2]: (V1 @ V2))))))))))
(TRIGHT_EXISTS_AND_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c/__caret__ @ V0) @ (V1 @ V2))))) @ ((c/__caret__ @ V0) @ (c? @ (^[V2]: (V1 @ V2))))))))))
(TRIGHT_FORALL_OR_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c__caret__/ @ V0) @ (V1 @ V2))))) @ ((c__caret__/ @ V0) @ (c! @ (^[V2]: (V1 @ V2))))))))))
(TRIGHT_FORALL_IMP_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ V0) @ (V1 @ V2))))) @ ((c==> @ V0) @ (c! @ (^[V2]: (V1 @ V2))))))))))
(TCOND_ABS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (^[V3]: (((cCOND @ V0) @ (V1 @ V3)) @ (V2 @ V3)))) @ (((cCOND @ V0) @ V1) @ V2)))))))))
(TCOND_RATOR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((cCOND @ V0) @ V1) @ V2) @ V3)) @ (((cCOND @ V0) @ (V1 @ V3)) @ (V2 @ V3))))))))))))
(TCOND_COMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c$ @ (((cCOND @ V0) @ V1) @ V2)) @ V3)) @ (((cCOND @ V0) @ ((c$ @ V1) @ V3)) @ ((c$ @ V2) @ V3))))))))))))
(TMONO_NOT,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c==> @ V1) @ V0)) @ ((c==> @ (c~ @ V0)) @ (c~ @ V1))))))))
(TEQ_IMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ V0) @ V1)) @ ((c==> @ V0) @ V1)))))))
(TAND1_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ V1) @ V0)) @ V1))))))
(TAND2_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ V0) @ V1)) @ V1))))))
(TOR_INTRO_THM2,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ V1) @ ((c__caret__/ @ V0) @ V1)))))))
(TAND_INTRO_THM_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ V1) @ ((c==> @ V0) @ V1)))))))
(TOR_INTRO_THM1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ V0) @ ((c__caret__/ @ V0) @ V1)))))))
(TAND_INTRO_THM_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ V0) @ ((c==> @ V1) @ V1)))))))
(TTRIV_OR_FORALL_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c__caret__/ @ (c! @ (^[V2]: V0))) @ (c! @ (^[V2]: V1)))) @ (c! @ (^[V2]: ((c__caret__/ @ V0) @ V1)))))))))
(TDISJ_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c__caret__/ @ V1) @ V0)) @ ((c__caret__/ @ V0) @ V1)))))))
(TDISJ_ACI_conjunct4,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c__caret__/ @ V0) @ ((c__caret__/ @ V0) @ V1))) @ ((c__caret__/ @ V0) @ V1)))))))
(TOR_DUAL3,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c==> @ (c~ @ ((c__caret__/ @ (c~ @ V0)) @ V1))) @ cF)) @ ((c==> @ V0) @ ((c==> @ (c~ @ V1)) @ cF))))))))
(TOR_DUAL2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c==> @ (c~ @ ((c__caret__/ @ V0) @ V1))) @ cF)) @ ((c==> @ ((c==> @ V0) @ cF)) @ ((c==> @ (c~ @ V1)) @ cF))))))))
(TOR_DUAL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c==> @ (c~ @ ((c__caret__/ @ V0) @ V1))) @ cF)) @ ((c==> @ (c~ @ V0)) @ ((c==> @ (c~ @ V1)) @ cF))))))))
(TCONTRAPOS_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c==> @ (c~ @ V1)) @ (c~ @ V0))) @ ((c==> @ V0) @ V1)))))))
(TIMP_DISJ_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c==> @ V0) @ V1)) @ ((c__caret__/ @ (c~ @ V0)) @ V1)))))))
(TOR_IMP_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V1) @ ((c__caret__/ @ V0) @ V1))) @ ((c==> @ V0) @ V1)))))))
(TEQ_IMP_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V1) @ V0)) @ ((c/__caret__ @ ((c==> @ V1) @ V0)) @ ((c==> @ V0) @ V1))))))))
(TEQ_EXPAND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ V0) @ V1)) @ ((c__caret__/ @ ((c/__caret__ @ V0) @ V1)) @ ((c/__caret__ @ (c~ @ V0)) @ (c~ @ V1)))))))))
(TI_BOOL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cI_BOOL @ V0)) @ (cI_BOOL @ V1))) @ ((c= @ V0) @ V1)))))))
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(TCONJ_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c/__caret__ @ V1) @ V0)) @ ((c/__caret__ @ V0) @ V1)))))))
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(TTRIV_EXISTS_AND_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c? @ (^[V2]: ((c/__caret__ @ V0) @ V1)))) @ ((c/__caret__ @ (c? @ (^[V2]: V0))) @ (c? @ (^[V2]: V1)))))))))
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(TTRIV_FORALL_IMP_THM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: ((c==> @ V0) @ V1)))) @ ((c==> @ (c? @ (^[V2]: V0))) @ (c! @ (^[V2]: V1)))))))))
(TNUMSUM_INJ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ ((cNUMSUM @ V0) @ V2)) @ ((cNUMSUM @ V1) @ V3))) @ ((c/__caret__ @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ V3))))))))))))
(TOR_ELIM_THM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c__caret__/ @ V1) @ V0)) @ ((c==> @ ((c==> @ V0) @ V2)) @ ((c==> @ ((c==> @ V1) @ V2)) @ V2))))))))))
(TAND_IMP_INTRO,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c= @ V2) @ V1)) @ V0)) @ ((c==> @ V0) @ ((c==> @ V1) @ V2))))))))))
(TCOND_EXPAND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cCOND @ V1) @ V0) @ V2)) @ ((c/__caret__ @ ((c__caret__/ @ (c~ @ V1)) @ V0)) @ ((c__caret__/ @ V1) @ V2))))))))))
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(TDISJ_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c__caret__/ @ V0) @ ((c__caret__/ @ V1) @ V2))) @ ((c__caret__/ @ ((c__caret__/ @ V0) @ V1)) @ V2)))))))))
(TAND_IMP3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c==> @ ((c/__caret__ @ (c~ @ V0)) @ V1)) @ V2)) @ ((c==> @ ((c= @ V0) @ cF)) @ ((c==> @ V1) @ V2))))))))))
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(TAND_IMP2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c==> @ ((c/__caret__ @ V0) @ V1)) @ V2)) @ ((c==> @ ((c= @ V0) @ cT)) @ ((c==> @ V1) @ V2))))))))))
(TAND_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c==> @ ((c/__caret__ @ V0) @ V1)) @ V2)) @ ((c==> @ V0) @ ((c==> @ V1) @ V2))))))))))
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(TIMP_NOT_EQ_EQ_EQ_OR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c==> @ (c~ @ V1)) @ ((c= @ V0) @ V2))) @ ((c= @ ((c__caret__/ @ V1) @ V0)) @ ((c__caret__/ @ V1) @ V2))))))))))
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(TIMP_EQ_EQ_EQ_NOT_OR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c==> @ V1) @ ((c= @ V0) @ V2))) @ ((c= @ ((c__caret__/ @ (c~ @ V1)) @ V0)) @ ((c__caret__/ @ (c~ @ V1)) @ V2))))))))))
(TIMP_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c==> @ V0) @ ((c==> @ V1) @ V2))) @ ((c==> @ ((c/__caret__ @ V0) @ V1)) @ V2)))))))))
(TRIGHT_AND_OVER_OR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ ((c__caret__/ @ V0) @ V1)) @ V2)) @ ((c__caret__/ @ ((c/__caret__ @ V0) @ V2)) @ ((c/__caret__ @ V1) @ V2))))))))))
(TCONJ_ASSOC_NORM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ ((c/__caret__ @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ V0) @ ((c/__caret__ @ V1) @ V2))))))))))
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(TCONJ_ACI_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ V1) @ ((c/__caret__ @ V0) @ V2))) @ ((c/__caret__ @ V0) @ ((c/__caret__ @ V1) @ V2))))))))))
(TCONJ_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c/__caret__ @ V0) @ ((c/__caret__ @ V1) @ V2))) @ ((c/__caret__ @ ((c/__caret__ @ V0) @ V1)) @ V2)))))))))
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(TMONO_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c==> @ V0) @ V1)) @ ((c==> @ ((c/__caret__ @ ((c==> @ V2) @ V0)) @ ((c==> @ V1) @ V3))) @ ((c==> @ V2) @ V3))))))))))))
(TMONO_AND_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c==> @ V1) @ V3)) @ ((c==> @ V2) @ V0))) @ ((c==> @ ((c/__caret__ @ V1) @ V2)) @ V3)))))))))))
(TMONO_AND_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c==> @ V1) @ V0)) @ ((c==> @ V2) @ V3))) @ ((c==> @ ((c/__caret__ @ V1) @ V2)) @ V3)))))))))))
(TEQ_EQ_IMP_DISJ_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((c= @ V0) @ V2)) @ ((c= @ V1) @ V3))) @ ((c= @ ((c__caret__/ @ V0) @ V1)) @ ((c__caret__/ @ V2) @ V3))))))))))))
(TCOND_OR,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c__caret__/ @ (((cCOND @ V1) @ V0) @ V2)) @ V3)) @ ((c/__caret__ @ ((c__caret__/ @ (c~ @ V1)) @ ((c__caret__/ @ V0) @ V3))) @ ((c__caret__/ @ V1) @ ((c__caret__/ @ V2) @ V3)))))))))))))
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(TCOND_ID,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cCOND @ V0) @ V1) @ V1)) @ V1))))))
(TCOND_RAND,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (V2 @ (((cCOND @ V0) @ V1) @ V3))) @ (((cCOND @ V0) @ (V2 @ V1)) @ (V2 @ V3))))))))))))
(TSETSPEC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cSETSPEC @ V1) @ V0) @ V2)) @ ((c/__caret__ @ V0) @ ((c= @ V1) @ V2))))))))))
(TELEMENT_IN_LEVEL,(c! @ (^[V0]: ((cIN @ (celement @ V0)) @ (csetlevel @ (clevel @ V0))))))
(TSET_SUBSET_SETLEVEL,(c! @ (^[V0]: ((c==> @ (cisaset @ V0)) @ ((cSUBSET @ (cset @ V0)) @ (csetlevel @ (cdroplevel @ (clevel @ V0))))))))
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(TPOWERSET_conjunct0,(c! @ (^[V0]: ((c= @ (clevel @ (cpowerset @ V0))) @ (cPowerset @ (clevel @ V0))))))
(Tlevel,(c! @ (^[V0]: ((c= @ (clevel @ V0)) @ (cFST @ (cdest_V @ V0))))))
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(TSET,(c! @ (^[V0]: ((c= @ (cmk_V @ ((c__comma__ @ (clevel @ V0)) @ (celement @ V0)))) @ V0))))
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(TCOMPREHENSION_EXISTS,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c= @ (clevel @ V2)) @ (clevel @ V0))) @ (c! @ (^[V3]: ((c= @ ((c<__colon__ @ V3) @ V2)) @ ((c/__caret__ @ ((c<__colon__ @ V3) @ V0)) @ (V1 @ V3)))))))))))))
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(Tone,(c! @ (^[V0]: ((c= @ V0) @ cone))))
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(TDEGREE_DELETE_EDGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cgraph @ V1)) @ ((c/__caret__ @ (clocally_finite @ V1)) @ ((cIN @ V0) @ (cedges @ V1))))) @ ((c= @ ((cdegree @ V1) @ V2)) @ (((cCOND @ ((c= @ ((ctermini @ V1) @ V0)) @ ((cINSERT @ V2) @ cEMPTY))) @ ((c+ @ ((cdegree @ ((cdelete_edge @ V0) @ V1)) @ V2)) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ (((cCOND @ ((cIN @ V2) @ ((ctermini @ V1) @ V0))) @ ((c+ @ ((cdegree @ ((cdelete_edge @ V0) @ V1)) @ V2)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ ((cdegree @ ((cdelete_edge @ V0) @ V1)) @ V2))))))))))))
(TCASEWISE_WORKS,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ ((c/__caret__ @ ((cMEM @ ((c__comma__ @ V2) @ V3)) @ V1)) @ ((c/__caret__ @ ((cMEM @ ((c__comma__ @ V4) @ V5)) @ V1)) @ ((c= @ (V2 @ V6)) @ (V4 @ V7))))) @ ((c= @ ((V3 @ V0) @ V6)) @ ((V5 @ V0) @ V7)))))))))))))))) @ ((cALL @ (cGABS @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((cGEQ @ (V2 @ ((c__comma__ @ V3) @ V4))) @ (c! @ (^[V5]: ((c= @ (((cCASEWISE @ V1) @ V0) @ (V3 @ V5))) @ ((V4 @ V0) @ V5)))))))))))) @ V1)))))))
(TOUTR,(c! @ (^[V0]: ((c= @ (cOUTR @ (cINR @ V0))) @ V0))))
(TFINREC_FUN,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c~ @ ((c= @ V2) @ V3))) @ ((c= @ ((V1 @ V2) @ ((V1 @ V3) @ V4))) @ ((V1 @ V3) @ ((V1 @ V2) @ V4))))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ (V2 @ cEMPTY)) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cFINITE @ V3)) @ ((cIN @ V4) @ V3))) @ ((c= @ (V2 @ V3)) @ ((V1 @ V4) @ (V2 @ ((cDELETE @ V3) @ V4))))))))))))))))))
(TSET_RECURSION_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c~ @ ((c= @ V2) @ V3))) @ ((c= @ ((V1 @ V2) @ ((V1 @ V3) @ V4))) @ ((V1 @ V3) @ ((V1 @ V2) @ V4))))))))))) @ (c? @ (^[V2]: ((c/__caret__ @ ((c= @ (V2 @ cEMPTY)) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (cFINITE @ V4)) @ ((c= @ (V2 @ ((cINSERT @ V3) @ V4))) @ (((cCOND @ ((cIN @ V3) @ V4)) @ (V2 @ V4)) @ ((V1 @ V3) @ (V2 @ V4))))))))))))))))))
(TFINREC_SUC_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c! @ (^[V5]: (c! @ (^[V6]: (c! @ (^[V7]: ((c==> @ (c~ @ ((c= @ V5) @ V6))) @ ((c= @ ((V4 @ V5) @ ((V4 @ V6) @ V7))) @ ((V4 @ V6) @ ((V4 @ V5) @ V7))))))))))) @ ((c==> @ (((((cFINREC @ V4) @ V0) @ V1) @ V3) @ (cSUC @ V2))) @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V1)) @ (c? @ (^[V6]: ((c/__caret__ @ (((((cFINREC @ V4) @ V0) @ ((cDELETE @ V1) @ V5)) @ V6) @ V2)) @ ((c= @ V3) @ ((V4 @ V5) @ V6)))))))))))))))))))))
(TFINREC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((((cFINREC @ V4) @ V0) @ V1) @ V3) @ (cSUC @ V2))) @ (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ (((((cFINREC @ V4) @ V0) @ ((cDELETE @ V1) @ V5)) @ V6) @ V2)) @ ((c= @ V3) @ ((V4 @ V5) @ V6))))))))))))))))))))
(TVSUM_NONZERO_IMAGE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((c/__caret__ @ ((c= @ (V2 @ V0)) @ (cvec @ (cNUMERAL @ c_0)))) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ ((c/__caret__ @ ((cIN @ V4) @ V1)) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ ((c/__caret__ @ ((c= @ (V3 @ V4)) @ (V3 @ V5))) @ (c~ @ ((c= @ V4) @ V5)))))) @ ((c= @ (V2 @ (V3 @ V4))) @ (cvec @ (cNUMERAL @ c_0))))))))))) @ ((c= @ ((cvsum @ (cGSPEC @ (^[V4]: (c? @ (^[V5]: (((cSETSPEC @ V4) @ ((c/__caret__ @ ((cIN @ V5) @ V1)) @ (c~ @ ((c= @ (V3 @ V5)) @ V0)))) @ (V3 @ V5))))))) @ V2)) @ ((cvsum @ V1) @ ((co @ V2) @ V3)))))))))))))
(TIN_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ V0) @ ((cIMAGE @ V1) @ V2))) @ (c? @ (^[V3]: ((c/__caret__ @ ((c= @ V0) @ (V1 @ V3))) @ ((cIN @ V3) @ V2))))))))))))
(Tsum_INJECTIVE_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cINR @ V0)) @ (cINR @ V1))) @ ((c= @ V0) @ V1)))))))
(TABS_SIMP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((^[V2]: V1) @ V0)) @ V1))))))
(TFST,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cFST @ ((c__comma__ @ V1) @ V0))) @ V1))))))
(TIN_UNIV,(c! @ (^[V0]: ((cIN @ V0) @ cUNIV))))
(TCARD_SING,(c! @ (^[V0]: ((c= @ (cCARD @ ((cINSERT @ V0) @ cEMPTY))) @ (cNUMERAL @ (cBIT1 @ c_0))))))
(TINJA,(c! @ (^[V0]: ((c= @ (cINJA @ V0)) @ (^[V1]: (^[V2]: ((c= @ V2) @ V0)))))))
(TINSERT_UNIV,(c! @ (^[V0]: ((c= @ ((cINSERT @ V0) @ cUNIV)) @ cUNIV))))
(TEMPTY_DELETE,(c! @ (^[V0]: ((c= @ ((cDELETE @ cEMPTY) @ V0)) @ cEMPTY))))
(TREFL_CLAUSE,(c! @ (^[V0]: ((c= @ ((c= @ V0) @ V0)) @ cT))))
(TNOT_EQ_F,(c! @ (^[V0]: ((c= @ (c~ @ ((c= @ V0) @ V0))) @ cF))))
(TVECTOR_1,(c! @ (^[V0]: ((c= @ ((c$ @ (cvector @ ((cCONS @ V0) @ cNIL))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V0))))
(TOUTL,(c! @ (^[V0]: ((c= @ (cOUTL @ (cINL @ V0))) @ V0))))
(TLET_END_DEF,(c! @ (^[V0]: ((c= @ (cLET_END @ V0)) @ V0))))
(TLAST_CLAUSES_conjunct0,(c! @ (^[V0]: ((c= @ (cLAST @ ((cCONS @ V0) @ cNIL))) @ V0))))
(TI_THM,(c! @ (^[V0]: ((c= @ (cI @ V0)) @ V0))))
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(TEQ_REFL,(c! @ (^[V0]: ((c= @ V0) @ V0))))
(TNOT_IN_EMPTY,(c! @ (^[V0]: (c~ @ ((cIN @ V0) @ cEMPTY)))))
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(TEXISTS_UNIQUE_REFL,(c! @ (^[V0]: (c?! @ (^[V1]: ((c= @ V1) @ V0))))))
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(TEXISTS_REFL,(c! @ (^[V0]: (c? @ (^[V1]: ((c= @ V1) @ V0))))))
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(TDELETE1_LIST_UNIQ,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (c~ @ ((cMEM @ V0) @ ((cDELETE1 @ V0) @ V1)))) @ (cLIST_UNIQ @ ((cDELETE1 @ V0) @ V1)))) @ (cLIST_UNIQ @ V1)))))))
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(TTL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cTL @ ((cCONS @ V0) @ V1))) @ V1))))))
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(TDEPENDENT_CHOICE_FIXED,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((V1 @ (cNUMERAL @ c_0)) @ V0)) @ (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((V1 @ V3) @ V4)) @ (c? @ (^[V5]: ((c/__caret__ @ ((V1 @ (cSUC @ V3)) @ V5)) @ (((V2 @ V3) @ V4) @ V5))))))))))) @ (c? @ (^[V3]: ((c/__caret__ @ ((c= @ (V3 @ (cNUMERAL @ c_0))) @ V0)) @ ((c/__caret__ @ (c! @ (^[V4]: ((V1 @ V4) @ (V3 @ V4))))) @ (c! @ (^[V4]: (((V2 @ V4) @ (V3 @ V4)) @ (V3 @ (cSUC @ V4)))))))))))))))))
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(TITERATE_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (cmonoidal @ V1)) @ ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ ((cIN @ V0) @ V2))) @ ((c= @ ((V1 @ (V3 @ V0)) @ (((citerate @ V1) @ ((cDELETE @ V2) @ V0)) @ V3))) @ (((citerate @ V1) @ V2) @ V3)))))))))))))
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(Tnum_RECURSION,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c= @ (V2 @ (cNUMERAL @ c_0))) @ V0)) @ (c! @ (^[V3]: ((c= @ (V2 @ (cSUC @ V3))) @ ((V1 @ (V2 @ V3)) @ V3))))))))))))
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(TTC_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cTC @ V1) @ V0) @ V2)) @ ((c__caret__/ @ ((V1 @ V0) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (((cTC @ V1) @ V0) @ V3)) @ (((cTC @ V1) @ V3) @ V2)))))))))))))
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(TSTC_CASES_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cSTC @ V1) @ V0) @ V2)) @ ((c__caret__/ @ ((V1 @ V0) @ V2)) @ ((c__caret__/ @ (((cSTC @ V1) @ V2) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ (((cSTC @ V1) @ V0) @ V3)) @ ((V1 @ V3) @ V2))))))))))))))
(TSTC_CASES_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cSTC @ V1) @ V0) @ V2)) @ ((c__caret__/ @ ((V1 @ V0) @ V2)) @ ((c__caret__/ @ (((cSTC @ V1) @ V2) @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ ((V1 @ V0) @ V3)) @ (((cSTC @ V1) @ V3) @ V2))))))))))))))
(TRTC_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cRTC @ V1) @ V0) @ V2)) @ ((c__caret__/ @ ((c= @ V0) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (((cRTC @ V1) @ V0) @ V3)) @ (((cRTC @ V1) @ V3) @ V2)))))))))))))
(TRTC_CASES_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cRTC @ V1) @ V0) @ V2)) @ ((c__caret__/ @ ((c= @ V0) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (((cRTC @ V1) @ V0) @ V3)) @ ((V1 @ V3) @ V2)))))))))))))
(TRTC_CASES_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cRTC @ V1) @ V0) @ V2)) @ ((c__caret__/ @ ((c= @ V0) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((V1 @ V0) @ V3)) @ (((cRTC @ V1) @ V3) @ V2)))))))))))))
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(TSTC_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cSTC @ V1) @ V2) @ V0)) @ (((cSTC @ V1) @ V0) @ V3))) @ (((cSTC @ V1) @ V2) @ V3)))))))))))
(TSTC_TRANS_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cSTC @ V1) @ V2) @ V0)) @ ((V1 @ V0) @ V3))) @ (((cSTC @ V1) @ V2) @ V3)))))))))))
(TRTC_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cRTC @ V1) @ V2) @ V0)) @ (((cRTC @ V1) @ V0) @ V3))) @ (((cRTC @ V1) @ V2) @ V3)))))))))))
(TRTC_TRANS_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cRTC @ V1) @ V2) @ V0)) @ ((V1 @ V0) @ V3))) @ (((cRTC @ V1) @ V2) @ V3)))))))))))
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(TRSTC_TRANS_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (((cRSTC @ V1) @ V2) @ V0)) @ ((V1 @ V0) @ V3))) @ (((cRSTC @ V1) @ V2) @ V3)))))))))))
(TTC_TRANS_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V1 @ V2) @ V0)) @ (((cTC @ V1) @ V0) @ V3))) @ (((cTC @ V1) @ V2) @ V3)))))))))))
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(TRTC_TRANS_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V1 @ V2) @ V0)) @ (((cRTC @ V1) @ V0) @ V3))) @ (((cRTC @ V1) @ V2) @ V3)))))))))))
(TRSTC_TRANS_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V1 @ V2) @ V0)) @ (((cRSTC @ V1) @ V0) @ V3))) @ (((cRSTC @ V1) @ V2) @ V3)))))))))))
(TRC_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ (c! @ (^[V4]: (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((V1 @ V4) @ V5)) @ ((V1 @ V5) @ V6))) @ ((V1 @ V4) @ V6))))))))) @ ((c==> @ ((c/__caret__ @ (((cRC @ V1) @ V2) @ V0)) @ (((cRC @ V1) @ V0) @ V3))) @ (((cRC @ V1) @ V2) @ V3))))))))))))
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(TDELETE_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((cSUBSET @ ((cDELETE @ V1) @ V0)) @ V1))))))
(TCOMPONENT,(c! @ (^[V0]: (c! @ (^[V1]: ((cIN @ V0) @ ((cINSERT @ V0) @ V1)))))))
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(TCARD_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ ((c= @ (cCARD @ ((cDELETE @ V1) @ V0))) @ (((cCOND @ ((cIN @ V0) @ V1)) @ ((c- @ (cCARD @ V1)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cCARD @ V1)))))))))
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(TFINITE_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cFINITE @ V1)) @ (cFINITE @ ((cINSERT @ V0) @ V1))))))))
(TSELECT_AX,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (V1 @ V0)) @ (V1 @ (c__at__ @ V1))))))))
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(TINSERT_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINSERT @ V0) @ ((cINSERT @ V0) @ V1))) @ ((cINSERT @ V0) @ V1)))))))
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(TABSORPTION,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ V1)) @ ((c= @ ((cINSERT @ V0) @ V1)) @ V1)))))))
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(TFINITE_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cFINITE @ ((cINSERT @ V0) @ V1))) @ (cFINITE @ V1)))))))
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(TCOUNTABLE_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cCOUNTABLE @ ((cDELETE @ V1) @ V0))) @ (cCOUNTABLE @ V1)))))))
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(TNOT_EMPTY_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c~ @ ((c= @ cEMPTY) @ ((cINSERT @ V0) @ V1))))))))
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(TSUBSET_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((cIN @ V0) @ V1))) @ ((c= @ ((cSUBSET @ V1) @ ((cINSERT @ V0) @ V2))) @ ((cSUBSET @ V1) @ V2))))))))))
(TINSERT_UNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cUNION @ ((cINSERT @ V0) @ V1)) @ V2)) @ (((cCOND @ ((cIN @ V0) @ V2)) @ ((cUNION @ V1) @ V2)) @ ((cINSERT @ V0) @ ((cUNION @ V1) @ V2)))))))))))
(TINSERT_UNION_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cUNION @ ((cINSERT @ V0) @ V1)) @ V2)) @ ((cINSERT @ V0) @ ((cUNION @ V1) @ V2))))))))))
(TINSERT_INTER,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cINTER @ ((cINSERT @ V0) @ V1)) @ V2)) @ (((cCOND @ ((cIN @ V0) @ V2)) @ ((cINSERT @ V0) @ ((cINTER @ V1) @ V2))) @ ((cINTER @ V1) @ V2))))))))))
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(TINSERT_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cSUBSET @ ((cINSERT @ V0) @ V1)) @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((cSUBSET @ V1) @ V2))))))))))
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(TCOND_ELIM_THM,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (V2 @ (((cCOND @ V1) @ V0) @ V3))) @ ((c/__caret__ @ ((c==> @ V1) @ (V2 @ V0))) @ ((c==> @ (c~ @ V1)) @ (V2 @ V3)))))))))))))
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(TSND,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cSND @ ((c__comma__ @ V0) @ V1))) @ V1))))))
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(TINJA_INJ,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ (cINJA @ V0)) @ (cINJA @ V1))) @ ((c= @ V0) @ V1)))))))
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(TCOND_T,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cCOND @ cT) @ V1) @ V0)) @ V1))))))
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(Tbool_RECURSION,(c! @ (^[V0]: (c! @ (^[V1]: (c? @ (^[V2]: ((c/__caret__ @ ((c= @ (V2 @ cF)) @ V0)) @ ((c= @ (V2 @ cT)) @ V1)))))))))
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(TMEM_DELETE1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cMEM @ V0) @ V2)) @ (c~ @ ((c= @ V0) @ V1)))) @ ((cMEM @ V0) @ ((cDELETE1 @ V1) @ V2))))))))))
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(TEQ_TRANS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((c= @ V1) @ V0)) @ ((c= @ V0) @ V2))) @ ((c= @ V1) @ V2)))))))))
(TSWAP_COMMON',(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V2))) @ (c~ @ ((c= @ V1) @ V0)))) @ ((c= @ ((co @ (cswap @ ((c__comma__ @ V1) @ V0))) @ (cswap @ ((c__comma__ @ V2) @ V0)))) @ ((co @ (cswap @ ((c__comma__ @ V2) @ V0))) @ (cswap @ ((c__comma__ @ V1) @ V2))))))))))))
(TSWAP_COMMON,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V1) @ V0))) @ (c~ @ ((c= @ V2) @ V0)))) @ ((c= @ ((co @ (cswap @ ((c__comma__ @ V1) @ V2))) @ (cswap @ ((c__comma__ @ V1) @ V0)))) @ ((co @ (cswap @ ((c__comma__ @ V2) @ V0))) @ (cswap @ ((c__comma__ @ V1) @ V2))))))))))))
(TVECTOR_3_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c$ @ (cvector @ ((cCONS @ V2) @ ((cCONS @ V0) @ ((cCONS @ V1) @ cNIL))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2))))))))
(TVECTOR_3_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c$ @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V2) @ ((cCONS @ V1) @ cNIL))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V2))))))))
(TVECTOR_3_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c$ @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ V2))))))))
(TSWAP_GENERAL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V0))) @ (c~ @ ((c= @ V1) @ V2)))) @ ((c__caret__/ @ ((c= @ ((co @ (cswap @ ((c__comma__ @ V3) @ V0))) @ (cswap @ ((c__comma__ @ V1) @ V2)))) @ cI)) @ (c? @ (^[V4]: (c? @ (^[V5]: (c? @ (^[V6]: ((c/__caret__ @ (c~ @ ((c= @ V4) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V5) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V6) @ V3))) @ ((c/__caret__ @ (c~ @ ((c= @ V4) @ V5))) @ ((c= @ ((co @ (cswap @ ((c__comma__ @ V3) @ V0))) @ (cswap @ ((c__comma__ @ V1) @ V2)))) @ ((co @ (cswap @ ((c__comma__ @ V4) @ V5))) @ (cswap @ ((c__comma__ @ V3) @ V6)))))))))))))))))))))))))
(TSWAP_INDEPENDENT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V0))) @ ((c/__caret__ @ (c~ @ ((c= @ V2) @ V1))) @ ((c/__caret__ @ (c~ @ ((c= @ V3) @ V0))) @ (c~ @ ((c= @ V3) @ V1)))))) @ ((c= @ ((co @ (cswap @ ((c__comma__ @ V2) @ V3))) @ (cswap @ ((c__comma__ @ V0) @ V1)))) @ ((co @ (cswap @ ((c__comma__ @ V0) @ V1))) @ (cswap @ ((c__comma__ @ V2) @ V3))))))))))))))
(TVECTOR_4_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c$ @ (cvector @ ((cCONS @ V3) @ ((cCONS @ V0) @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL)))))) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V3))))))))))
(TVECTOR_4_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c$ @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V3) @ ((cCONS @ V1) @ ((cCONS @ V2) @ cNIL)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT1 @ c_0))))) @ V3))))))))))
(TVECTOR_4_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c$ @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V1) @ ((cCONS @ V3) @ ((cCONS @ V2) @ cNIL)))))) @ (cNUMERAL @ (cBIT1 @ (cBIT1 @ c_0))))) @ V3))))))))))
(TVECTOR_4_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c$ @ (cvector @ ((cCONS @ V0) @ ((cCONS @ V1) @ ((cCONS @ V2) @ ((cCONS @ V3) @ cNIL)))))) @ (cNUMERAL @ (cBIT0 @ (cBIT0 @ (cBIT1 @ c_0)))))) @ V3))))))))))
(TPERMUTES_SWAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cIN @ V0) @ V2)) @ ((cIN @ V1) @ V2))) @ ((cpermutes @ (cswap @ ((c__comma__ @ V0) @ V1))) @ V2)))))))))
(TPERMUTES_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cpermutes @ V1) @ ((cINSERT @ V0) @ cEMPTY))) @ ((c= @ V1) @ cI)))))))
(TSWAP_GALOIS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((c= @ V3) @ ((cswap @ ((c__comma__ @ V1) @ V2)) @ V0))) @ ((c= @ V0) @ ((cswap @ ((c__comma__ @ V1) @ V2)) @ V3))))))))))))
(TINVERSE_SWAP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cinverse @ (cswap @ ((c__comma__ @ V0) @ V1)))) @ (cswap @ ((c__comma__ @ V0) @ V1))))))))
(TSWAP_IDEMPOTENT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((co @ (cswap @ ((c__comma__ @ V0) @ V1))) @ (cswap @ ((c__comma__ @ V0) @ V1)))) @ cI))))))
(TSWAP_SYM,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cswap @ ((c__comma__ @ V1) @ V0))) @ (cswap @ ((c__comma__ @ V0) @ V1))))))))
(TSWAP_REFL,(c! @ (^[V0]: ((c= @ (cswap @ ((c__comma__ @ V0) @ V0))) @ cI))))
(Tswap,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cswap @ ((c__comma__ @ V1) @ V0)) @ V2)) @ (((cCOND @ ((c= @ V2) @ V1)) @ V0) @ (((cCOND @ ((c= @ V2) @ V0)) @ V1) @ V2))))))))))
(TSEM_ABORT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((csem @ cABORT) @ V0) @ V1)) @ cF))))))
(TSEM_SKIP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((csem @ cSKIP) @ V1) @ V0)) @ ((c= @ V0) @ V1)))))))
(TSEM_ASSIGN,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((csem @ (cAssign @ V1)) @ V2) @ V0)) @ ((c= @ V0) @ (V1 @ V2))))))))))
(TWFP_CASES,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cWFP @ V1) @ V0)) @ (c! @ (^[V2]: ((c==> @ ((V1 @ V2) @ V0)) @ ((cWFP @ V1) @ V2))))))))))
(TMUNION_INUNION,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ ((cmmember @ V1) @ ((cmunion @ V2) @ (cmsing @ V0)))) @ (c~ @ ((c= @ V0) @ V1)))) @ ((cmmember @ V1) @ V2)))))))))
(TMMEMBER_MSING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cmmember @ V0) @ (cmsing @ V1))) @ ((c= @ V0) @ V1)))))))
(TMEMPTY,(c! @ (^[V0]: ((c= @ ((cmultiplicity @ cmempty) @ V0)) @ (cNUMERAL @ c_0)))))
(Tmsing,(c! @ (^[V0]: ((c= @ (cmsing @ V0)) @ (cmultiset @ (^[V1]: (((cCOND @ ((c= @ V1) @ V0)) @ (cNUMERAL @ (cBIT1 @ c_0))) @ (cNUMERAL @ c_0))))))))
(TSING_IS_FINITE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c= @ V1) @ ((cINSERT @ V0) @ cEMPTY))) @ (cFINITE @ V1)))))))
(TJOINABLE_TRANS_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((V1 @ V2) @ V0)) @ (((cJOINABLE @ V1) @ V0) @ V3))) @ (((cJOINABLE @ V1) @ V2) @ V3)))))))))))
(TJOINABLE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cJOINABLE @ V1) @ V0) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (((cRTC @ V1) @ V0) @ V3)) @ (((cRTC @ V1) @ V2) @ V3))))))))))))
(TCASEWISE_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cCASEWISE @ cNIL) @ V0) @ V1)) @ (c__at__ @ (^[V2]: cT))))))))
(TCASEWISE_DEF_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cCASEWISE @ cNIL) @ V0) @ V1)) @ (c__at__ @ (^[V2]: cT))))))))
(TGRAPH_DELETE_EDGE,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cgraph @ V1)) @ (cgraph @ ((cdelete_edge @ V0) @ V1))))))))
(TDELETE_EDGE_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cvertices @ ((cdelete_edge @ V0) @ V1))) @ (cvertices @ V1)))))))
(TDELETE_EDGE_CLAUSES_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (ctermini @ ((cdelete_edge @ V0) @ V1))) @ (ctermini @ V1)))))))
(TDELETE_EDGE_CLAUSES_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cedges @ ((cdelete_edge @ V0) @ V1))) @ ((cDELETE @ (cedges @ V1)) @ V0)))))))
(TTERMINI_IN_VERTICES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cgraph @ V2)) @ ((c/__caret__ @ ((cIN @ V0) @ (cedges @ V2))) @ ((cIN @ V1) @ ((ctermini @ V2) @ V0))))) @ ((cIN @ V1) @ (cvertices @ V2))))))))))
(TNPRODUCT_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V2)) @ ((c= @ ((cnproduct @ ((cINSERT @ V0) @ V2)) @ V1)) @ (((cCOND @ ((cIN @ V0) @ V2)) @ ((cnproduct @ V2) @ V1)) @ ((c* @ (V1 @ V0)) @ ((cnproduct @ V2) @ V1))))))))))))
(TITER_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cITER @ (cNUMERAL @ c_0)) @ V1) @ V0)) @ V0))))))
(TITER_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cITER @ (cSUC @ V2)) @ V1) @ V0)) @ (V1 @ (((cITER @ V2) @ V1) @ V0))))))))))
(TSUM_DELETE_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V1)) @ ((c= @ ((csum @ ((cDELETE @ V1) @ V0)) @ V2)) @ (((cCOND @ ((cIN @ V0) @ V1)) @ ((creal_sub @ ((csum @ V1) @ V2)) @ (V2 @ V0))) @ ((csum @ V1) @ V2)))))))))))
(TVALMOD_SWAP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ (c~ @ ((c= @ V2) @ V0))) @ ((c= @ (((c|-> @ V2) @ V3) @ (((c|-> @ V0) @ V1) @ V4))) @ (((c|-> @ V0) @ V1) @ (((c|-> @ V2) @ V3) @ V4)))))))))))))))
(TFORALL_VALMOD,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (c! @ (^[V2]: (c! @ (^[V3]: (V1 @ (((c|-> @ V0) @ V3) @ V2))))))) @ (c! @ (^[V2]: (V1 @ V2)))))))))
(TVALMOD_REPEAT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((c|-> @ V0) @ (V1 @ V0)) @ V1)) @ V1))))))
(TVALMOD_VALMOD_BASIC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((c|-> @ V1) @ V2) @ (((c|-> @ V1) @ V0) @ V3))) @ (((c|-> @ V1) @ V2) @ V3)))))))))))
(TVALMOD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((((c|-> @ V0) @ V1) @ V2) @ V3)) @ (((cCOND @ ((c= @ V3) @ V0)) @ V1) @ (V2 @ V3))))))))))))
(TREV_ASSOCD_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (((cREV_ASSOCD @ V0) @ cNIL) @ V1)) @ V1))))))
(TREV_ASSOCD_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((cREV_ASSOCD @ V2) @ ((cCONS @ ((c__comma__ @ V1) @ V0)) @ V3)) @ V4)) @ (((cCOND @ ((c= @ V0) @ V2)) @ V1) @ (((cREV_ASSOCD @ V2) @ V3) @ V4))))))))))))))
(TSUM_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V2)) @ ((c= @ ((csum @ ((cINSERT @ V0) @ V2)) @ V1)) @ (((cCOND @ ((cIN @ V0) @ V2)) @ ((csum @ V2) @ V1)) @ ((creal_add @ (V1 @ V0)) @ ((csum @ V2) @ V1))))))))))))
(TCOUNTABLE_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cCOUNTABLE @ ((cINSERT @ V0) @ V1))) @ (cCOUNTABLE @ V1)))))))
(TCOUNTABLE_SING,(c! @ (^[V0]: (cCOUNTABLE @ ((cINSERT @ V0) @ cEMPTY)))))
(TIN_CARD_MUL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cIN @ ((c__comma__ @ V0) @ V2)) @ ((c*_c @ V1) @ V3))) @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ ((cIN @ V2) @ V3))))))))))))
(TPERMUTED_TAIL,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cPERMUTED @ ((cCONS @ V0) @ V1)) @ ((cCONS @ V0) @ V2))) @ ((cPERMUTED @ V1) @ V2)))))))))
(TPERMUTED_SWAP_HEAD,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((cPERMUTED @ ((cCONS @ V1) @ ((cCONS @ V0) @ V2))) @ ((cCONS @ V0) @ ((cCONS @ V1) @ V2))))))))))
(TPERMUTED_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cPERMUTED @ V1) @ V2)) @ ((cPERMUTED @ ((cCONS @ V0) @ V1)) @ ((cCONS @ V0) @ V2))))))))))
(TPERMUTED_RULES_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((cPERMUTED @ ((cCONS @ V0) @ ((cCONS @ V1) @ V2))) @ ((cCONS @ V1) @ ((cCONS @ V0) @ V2))))))))))
(TLIST_UNIQ_DELETE1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (cLIST_UNIQ @ V1)) @ (cLIST_UNIQ @ ((cDELETE1 @ V0) @ V1))))))))
(TLIST_UNIQ_conjunct2,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cLIST_UNIQ @ ((cCONS @ V0) @ V1))) @ ((c/__caret__ @ (c~ @ ((cMEM @ V0) @ V1))) @ (cLIST_UNIQ @ V1))))))))
(TLIST_UNIQ_conjunct1,(c! @ (^[V0]: (cLIST_UNIQ @ ((cCONS @ V0) @ cNIL)))))
(TLIST_UNIQ_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ ((c/__caret__ @ (cLIST_UNIQ @ V1)) @ (c~ @ ((cMEM @ V0) @ V1)))) @ (cLIST_UNIQ @ ((cCONS @ V0) @ V1))))))))
(TMEM_COUNT,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cMEM @ V0) @ V1)) @ (c~ @ ((c= @ ((cCOUNT @ V0) @ V1)) @ (cNUMERAL @ c_0)))))))))
(TCOUNT_ZERO,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((c= @ ((cCOUNT @ V0) @ V1)) @ (cNUMERAL @ c_0))) @ (c~ @ ((cMEM @ V0) @ V1))))))))
(TCOUNT_LE_LENGTH,(c! @ (^[V0]: (c! @ (^[V1]: ((c<= @ ((cCOUNT @ V0) @ V1)) @ (cLENGTH @ V1)))))))
(TCOUNT_LENGTH_FILTER,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cCOUNT @ V0) @ V1)) @ (cLENGTH @ ((cFILTER @ (c= @ V0)) @ V1))))))))
(TCOUNT_conjunct0,(c! @ (^[V0]: ((c= @ ((cCOUNT @ V0) @ cNIL)) @ (cNUMERAL @ c_0)))))
(TCOUNT_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cCOUNT @ V0) @ ((cCONS @ V1) @ V2))) @ (((cCOND @ ((c= @ V0) @ V1)) @ (cSUC @ ((cCOUNT @ V0) @ V2))) @ ((cCOUNT @ V0) @ V2))))))))))
(TALL_DELETE1_ALL_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (V1 @ V0)) @ ((cALL @ V1) @ ((cDELETE1 @ V0) @ V2)))) @ ((cALL @ V1) @ V2)))))))))
(TNOT_MEM_DELETE1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (c~ @ ((cMEM @ V0) @ V2))) @ (c~ @ ((cMEM @ V0) @ ((cDELETE1 @ V1) @ V2)))))))))))
(TMEM_DELETE1_MEM_IMP,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cMEM @ V1) @ ((cDELETE1 @ V0) @ V2))) @ ((cMEM @ V1) @ V2)))))))))
(TFILTER_DELETE1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cFILTER @ V1) @ ((cDELETE1 @ V0) @ V2))) @ (((cCOND @ (V1 @ V0)) @ ((cDELETE1 @ V0) @ ((cFILTER @ V1) @ V2))) @ ((cFILTER @ V1) @ V2))))))))))
(TDELETE1_ID,(c! @ (^[V0]: (c! @ (^[V1]: ((c==> @ (c~ @ ((cMEM @ V0) @ V1))) @ ((c= @ ((cDELETE1 @ V0) @ V1)) @ V1)))))))
(TDELETE1_conjunct0,(c! @ (^[V0]: ((c= @ ((cDELETE1 @ V0) @ cNIL)) @ cNIL))))
(TDELETE1_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cDELETE1 @ V0) @ ((cCONS @ V1) @ V2))) @ (((cCOND @ ((c= @ V0) @ V1)) @ V2) @ ((cCONS @ V1) @ ((cDELETE1 @ V0) @ V2)))))))))))
(TTC_RTC_TC_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cTC @ V1) @ V0) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (((cRTC @ V1) @ V0) @ V3)) @ (((cTC @ V1) @ V3) @ V2))))))))))))
(TTC_TC_RTC_CASES,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cTC @ V1) @ V0) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (((cTC @ V1) @ V0) @ V3)) @ (((cRTC @ V1) @ V3) @ V2))))))))))))
(TTC_RTC_CASES_R,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cTC @ V1) @ V0) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ ((V1 @ V0) @ V3)) @ (((cRTC @ V1) @ V3) @ V2))))))))))))
(TTC_RTC_CASES_L,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cTC @ V1) @ V0) @ V2)) @ (c? @ (^[V3]: ((c/__caret__ @ (((cRTC @ V1) @ V0) @ V3)) @ ((V1 @ V3) @ V2))))))))))))
(TNSUM_DELETE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V1)) @ ((cIN @ V0) @ V1))) @ ((c= @ ((c+ @ (V2 @ V0)) @ ((cnsum @ ((cDELETE @ V1) @ V0)) @ V2))) @ ((cnsum @ V1) @ V2))))))))))
(TNSUM_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V2)) @ ((c= @ ((cnsum @ ((cINSERT @ V0) @ V2)) @ V1)) @ (((cCOND @ ((cIN @ V0) @ V2)) @ ((cnsum @ V2) @ V1)) @ ((c+ @ (V1 @ V0)) @ ((cnsum @ V2) @ V1))))))))))))
(TFINITE_SUPPORT_DELTA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (cFINITE @ (((csupport @ V2) @ (^[V4]: (((cCOND @ ((c= @ V4) @ V0)) @ (V1 @ V4)) @ (cneutral @ V2)))) @ V3)))))))))))
(TPAIRWISE_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cpairwise @ V1) @ ((cINSERT @ V0) @ V2))) @ ((c/__caret__ @ (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cIN @ V3) @ V2)) @ (c~ @ ((c= @ V3) @ V0)))) @ ((c/__caret__ @ ((V1 @ V0) @ V3)) @ ((V1 @ V3) @ V0)))))) @ ((cpairwise @ V1) @ V2))))))))))
(TLIST_OF_SET_SING,(c! @ (^[V0]: ((c= @ (clist_of_set @ ((cINSERT @ V0) @ cEMPTY))) @ ((cCONS @ V0) @ cNIL)))))
(TIN_SET_OF_LIST,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cIN @ V0) @ (cset_of_list @ V1))) @ ((cMEM @ V0) @ V1)))))))
(TCARD_FUNSPACE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (cFINITE @ V2)) @ (cFINITE @ V1))) @ ((c= @ (cCARD @ (cGSPEC @ (^[V3]: (c? @ (^[V4]: (((cSETSPEC @ V3) @ ((c/__caret__ @ (c! @ (^[V5]: ((c==> @ ((cIN @ V5) @ V2)) @ ((cIN @ (V4 @ V5)) @ V1))))) @ (c! @ (^[V5]: ((c==> @ (c~ @ ((cIN @ V5) @ V2))) @ ((c= @ (V4 @ V5)) @ V0)))))) @ V4))))))) @ ((cEXP @ (cCARD @ V1)) @ (cCARD @ V2)))))))))))
(TIN_CROSS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cIN @ ((c__comma__ @ V0) @ V2)) @ ((cCROSS @ V1) @ V3))) @ ((c/__caret__ @ ((cIN @ V0) @ V1)) @ ((cIN @ V2) @ V3))))))))))))
(TITERATE_NONZERO_IMAGE_LEMMA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c==> @ ((c/__caret__ @ (cmonoidal @ V1)) @ ((c/__caret__ @ (cFINITE @ V2)) @ ((c/__caret__ @ ((c= @ (V3 @ V0)) @ (cneutral @ V1))) @ (c! @ (^[V5]: (c! @ (^[V6]: ((c==> @ ((c/__caret__ @ ((cIN @ V5) @ V2)) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ ((c/__caret__ @ ((c= @ (V4 @ V5)) @ (V4 @ V6))) @ (c~ @ ((c= @ V5) @ V6)))))) @ ((c= @ (V3 @ (V4 @ V5))) @ (cneutral @ V1))))))))))) @ ((c= @ (((citerate @ V1) @ (cGSPEC @ (^[V5]: (c? @ (^[V6]: (((cSETSPEC @ V5) @ ((c/__caret__ @ ((cIN @ V6) @ V2)) @ (c~ @ ((c= @ (V4 @ V6)) @ V0)))) @ (V4 @ V6))))))) @ V3)) @ (((citerate @ V1) @ V2) @ ((co @ V3) @ V4)))))))))))))))
(TITSET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (((cITSET @ V1) @ V2) @ V0)) @ ((c__at__ @ (^[V3]: ((c/__caret__ @ ((c= @ (V3 @ cEMPTY)) @ V0)) @ (c! @ (^[V4]: (c! @ (^[V5]: ((c==> @ (cFINITE @ V5)) @ ((c= @ (V3 @ ((cINSERT @ V4) @ V5))) @ (((cCOND @ ((cIN @ V4) @ V5)) @ (V3 @ V5)) @ ((V1 @ V4) @ (V3 @ V5)))))))))))) @ V2)))))))))
(TFINITE_SING,(c! @ (^[V0]: (cFINITE @ ((cINSERT @ V0) @ cEMPTY)))))
(TSING_GSPEC_conjunct1,(c! @ (^[V0]: ((c= @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c= @ V0) @ V2)) @ V2)))))) @ ((cINSERT @ V0) @ cEMPTY)))))
(TSING_GSPEC_conjunct0,(c! @ (^[V0]: ((c= @ (cGSPEC @ (^[V1]: (c? @ (^[V2]: (((cSETSPEC @ V1) @ ((c= @ V2) @ V0)) @ V2)))))) @ ((cINSERT @ V0) @ cEMPTY)))))
(TFUN_IN_IMAGE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V0) @ V2)) @ ((cIN @ (V1 @ V0)) @ ((cIMAGE @ V1) @ V2))))))))))
(TIMAGE_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIMAGE @ V1) @ ((cINSERT @ V0) @ V2))) @ ((cINSERT @ (V1 @ V0)) @ ((cIMAGE @ V1) @ V2))))))))))
(TINSERT_AC_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cINSERT @ V0) @ ((cINSERT @ V0) @ V1))) @ ((cINSERT @ V0) @ V1)))))))
(TINSERT_AC_conjunct0,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cINSERT @ V1) @ ((cINSERT @ V0) @ V2))) @ ((cINSERT @ V0) @ ((cINSERT @ V1) @ V2))))))))))
(TSING_SUBSET,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cSUBSET @ ((cINSERT @ V0) @ cEMPTY)) @ V1)) @ ((cIN @ V0) @ V1)))))))
(TEXISTS_IN_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ ((cINSERT @ V0) @ V1))) @ (V2 @ V3))))) @ ((c__caret__/ @ (V2 @ V0)) @ (c? @ (^[V3]: ((c/__caret__ @ ((cIN @ V3) @ V1)) @ (V2 @ V3)))))))))))))
(TFORALL_IN_INSERT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ ((cINSERT @ V0) @ V1))) @ (V2 @ V3))))) @ ((c/__caret__ @ (V2 @ V0)) @ (c! @ (^[V3]: ((c==> @ ((cIN @ V3) @ V1)) @ (V2 @ V3)))))))))))))
(TAPPEND_SING,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cAPPEND @ ((cCONS @ V0) @ cNIL)) @ V1)) @ ((cCONS @ V0) @ V1)))))))
(TEL_CONS,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cEL @ V1) @ ((cCONS @ V0) @ V2))) @ (((cCOND @ ((c= @ V1) @ (cNUMERAL @ c_0))) @ V0) @ ((cEL @ ((c- @ V1) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ V2))))))))))
(TMEM_EXISTS_EL,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cMEM @ V0) @ V1)) @ (c? @ (^[V2]: ((c/__caret__ @ ((c< @ V2) @ (cLENGTH @ V1))) @ ((c= @ V0) @ ((cEL @ V2) @ V1)))))))))))
(TMEM_ASSOC,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ ((cMEM @ ((c__comma__ @ V0) @ ((cASSOC @ V0) @ V1))) @ V1)) @ ((cMEM @ V0) @ ((cMAP @ cFST) @ V1))))))))
(TLENGTH_REPLICATE,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cLENGTH @ ((cREPLICATE @ V1) @ V0))) @ V1))))))
(TOLDNET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((c/__caret__ @ (((cnetord @ V1) @ V0) @ V0)) @ (((cnetord @ V1) @ V2) @ V2))) @ (c? @ (^[V3]: ((c/__caret__ @ (((cnetord @ V1) @ V3) @ V3)) @ (c! @ (^[V4]: ((c==> @ (((cnetord @ V1) @ V4) @ V3)) @ ((c/__caret__ @ (((cnetord @ V1) @ V4) @ V0)) @ (((cnetord @ V1) @ V4) @ V2))))))))))))))))
(TNET,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c__caret__/ @ (c! @ (^[V3]: ((c==> @ (((cnetord @ V1) @ V3) @ V2)) @ (((cnetord @ V1) @ V3) @ V0))))) @ (c! @ (^[V3]: ((c==> @ (((cnetord @ V1) @ V3) @ V0)) @ (((cnetord @ V1) @ V3) @ V2))))))))))))
(TZIP_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ ((cZIP @ ((cCONS @ V0) @ V2)) @ ((cCONS @ V1) @ V3))) @ ((cCONS @ ((c__comma__ @ V0) @ V1)) @ ((cZIP @ V2) @ V3))))))))))))
(TZIP_DEF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cZIP @ ((cCONS @ V0) @ V1)) @ V2)) @ ((cCONS @ ((c__comma__ @ V0) @ (cHD @ V2))) @ ((cZIP @ V1) @ (cTL @ V2)))))))))))
(TITLIST2_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: (c! @ (^[V5]: ((c= @ ((((cITLIST2 @ V2) @ ((cCONS @ V0) @ V3)) @ ((cCONS @ V1) @ V4)) @ V5)) @ (((V2 @ V0) @ V1) @ ((((cITLIST2 @ V2) @ V3) @ V4) @ V5))))))))))))))))
(TITLIST2_DEF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ ((((cITLIST2 @ V1) @ ((cCONS @ V0) @ V2)) @ V3) @ V4)) @ (((V1 @ V0) @ (cHD @ V3)) @ ((((cITLIST2 @ V1) @ V2) @ (cTL @ V3)) @ V4))))))))))))))
(TFILTER_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cFILTER @ V1) @ ((cCONS @ V0) @ V2))) @ (((cCOND @ (V1 @ V0)) @ ((cCONS @ V0) @ ((cFILTER @ V1) @ V2))) @ ((cFILTER @ V1) @ V2))))))))))
(TMAP2_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((cMAP2 @ V2) @ ((cCONS @ V0) @ V3)) @ ((cCONS @ V1) @ V4))) @ ((cCONS @ ((V2 @ V0) @ V1)) @ (((cMAP2 @ V2) @ V3) @ V4))))))))))))))
(TMAP2_DEF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((cMAP2 @ V1) @ ((cCONS @ V0) @ V2)) @ V3)) @ ((cCONS @ ((V1 @ V0) @ (cHD @ V3))) @ (((cMAP2 @ V1) @ V2) @ (cTL @ V3)))))))))))))
(TALL2_conjunct3,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: (c! @ (^[V4]: ((c= @ (((cALL2 @ V2) @ ((cCONS @ V0) @ V3)) @ ((cCONS @ V1) @ V4))) @ ((c/__caret__ @ ((V2 @ V0) @ V1)) @ (((cALL2 @ V2) @ V3) @ V4))))))))))))))
(TALL2_DEF_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((cALL2 @ V1) @ ((cCONS @ V0) @ V2)) @ V3)) @ (((cCOND @ ((c= @ V3) @ cNIL)) @ cF) @ ((c/__caret__ @ ((V1 @ V0) @ (cHD @ V3))) @ (((cALL2 @ V1) @ V2) @ (cTL @ V3))))))))))))))
(TMEM_conjunct0,(c! @ (^[V0]: ((c= @ ((cMEM @ V0) @ cNIL)) @ cF))))
(TMEM_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cMEM @ V1) @ ((cCONS @ V0) @ V2))) @ ((c__caret__/ @ ((c= @ V1) @ V0)) @ ((cMEM @ V1) @ V2))))))))))
(TITLIST_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c= @ (((cITLIST @ V1) @ ((cCONS @ V0) @ V2)) @ V3)) @ ((V1 @ V0) @ (((cITLIST @ V1) @ V2) @ V3))))))))))))
(TEX_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cEX @ V1) @ ((cCONS @ V0) @ V2))) @ ((c__caret__/ @ (V1 @ V0)) @ ((cEX @ V1) @ V2))))))))))
(TALL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cALL @ V1) @ ((cCONS @ V0) @ V2))) @ ((c/__caret__ @ (V1 @ V0)) @ ((cALL @ V1) @ V2))))))))))
(TNULL_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cNULL @ ((cCONS @ V0) @ V1))) @ cF))))))
(TREPLICATE_conjunct0,(c! @ (^[V0]: ((c= @ ((cREPLICATE @ (cNUMERAL @ c_0)) @ V0)) @ cNIL))))
(TBUTLAST_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (cBUTLAST @ ((cCONS @ V0) @ V1))) @ (((cCOND @ ((c= @ V1) @ cNIL)) @ cNIL) @ ((cCONS @ V0) @ (cBUTLAST @ V1)))))))))
(TMEASURE_LE,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ (c! @ (^[V3]: ((c==> @ (((cMEASURE @ V1) @ V3) @ V0)) @ (((cMEASURE @ V1) @ V3) @ V2))))) @ ((c<= @ (V1 @ V0)) @ (V1 @ V2))))))))))
(TVSUM_DELTA,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cvsum @ V1) @ (^[V3]: (((cCOND @ ((c= @ V3) @ V0)) @ V2) @ (cvec @ (cNUMERAL @ c_0)))))) @ (((cCOND @ ((cIN @ V0) @ V1)) @ V2) @ (cvec @ (cNUMERAL @ c_0)))))))))))
(TVSUM_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V2)) @ ((c= @ ((cvsum @ ((cINSERT @ V0) @ V2)) @ V1)) @ (((cCOND @ ((cIN @ V0) @ V2)) @ ((cvsum @ V2) @ V1)) @ ((cvector_add @ (V1 @ V0)) @ ((cvsum @ V2) @ V1))))))))))))
(THULL_INC,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V0) @ V2)) @ ((cIN @ V0) @ ((chull @ V1) @ V2))))))))))
(THULL_REDUNDANT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ ((cIN @ V0) @ ((chull @ V1) @ V2))) @ ((c= @ ((chull @ V1) @ ((cINSERT @ V0) @ V2))) @ ((chull @ V1) @ V2))))))))))
(THULL_REDUNDANT_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((cIN @ V0) @ ((chull @ V1) @ V2))) @ ((c= @ ((chull @ V1) @ ((cINSERT @ V0) @ V2))) @ ((chull @ V1) @ V2))))))))))
(TPRODUCT_CLAUSES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c==> @ (cFINITE @ V2)) @ ((c= @ ((cproduct @ ((cINSERT @ V0) @ V2)) @ V1)) @ (((cCOND @ ((cIN @ V0) @ V2)) @ ((cproduct @ V2) @ V1)) @ ((creal_mul @ (V1 @ V0)) @ ((cproduct @ V2) @ V1))))))))))))
(TSIGN_SWAP,(c! @ (^[V0]: (c! @ (^[V1]: ((c= @ (csign @ (cswap @ ((c__comma__ @ V0) @ V1)))) @ (((cCOND @ ((c= @ V0) @ V1)) @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (creal_neg @ (creal_of_num @ (cNUMERAL @ (cBIT1 @ c_0)))))))))))
(TPERMUTATION_SWAP,(c! @ (^[V0]: (c! @ (^[V1]: (cpermutation @ (cswap @ ((c__comma__ @ V0) @ V1))))))))
(TSWAPSEQ_SWAP,(c! @ (^[V0]: (c! @ (^[V1]: ((cswapseq @ (((cCOND @ ((c= @ V0) @ V1)) @ (cNUMERAL @ c_0)) @ (cNUMERAL @ (cBIT1 @ c_0)))) @ (cswap @ ((c__comma__ @ V0) @ V1))))))))
(Tswapseq_RULES_conjunct1,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c/__caret__ @ ((cswapseq @ V3) @ V2)) @ (c~ @ ((c= @ V0) @ V1)))) @ ((cswapseq @ (cSUC @ V3)) @ ((co @ (cswap @ ((c__comma__ @ V0) @ V1))) @ V2))))))))))))
(TCOND_RIGHT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c==> @ (c~ @ V1)) @ ((c= @ V0) @ V3))) @ ((c= @ (((cCOND @ V1) @ V2) @ V0)) @ (((cCOND @ V1) @ V2) @ V3))))))))))))
(TCOND_LEFT,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: (c! @ (^[V3]: ((c==> @ ((c==> @ V1) @ ((c= @ V0) @ V2))) @ ((c= @ (((cCOND @ V1) @ V0) @ V3)) @ (((cCOND @ V1) @ V2) @ V3))))))))))))
(TEQ_EQ,(c! @ (^[V0]: (c! @ (^[V1]: (c! @ (^[V2]: ((c= @ ((c= @ V2) @ ((c= @ V0) @ V1))) @ (((cCOND @ ((c= @ V0) @ V1)) @ ((c= @ V2) @ cT)) @ ((c= @ V2) @ cF))))))))))
(TTRUTH,cT)