Theory Generator_Aux

section ‹Shared Utilities for all Generator›

text ‹In this theory we mainly provide some Isabelle/ML infrastructure
  that is used by several generators. It consists of a uniform interface
  to access all the theorems, terms, etc.\ from the BNF package, and 
  some auxiliary functions which provide recursors on datatypes, common tactics, etc.›

theory Generator_Aux
imports 
  Main
begin

ML_file "bnf_access.ML"
ML_file "generator_aux.ML"

lemma in_set_simps: 
  "x ∈ set (y # z # ys) = (x = y ∨ x ∈ set (z # ys))"
  "x ∈ set ([y]) = (x = y)"
  "x ∈ set [] = False" 
  "Ball (set []) P = True" 
  "Ball (set [x]) P = P x" 
  "Ball (set (x # y # zs)) P = (P x ∧ Ball (set (y # zs)) P)" 
  by auto
  
lemma conj_weak_cong: "a = b ⟹ c = d ⟹ (a ∧ c) = (b ∧ d)" by auto

lemma refl_True: "(x = x) = True" by simp

end