proposition: Lemma ZF_eq_prep T s x y : ZFeq' <<= T -> T ⊢ x ≡ y -> T ⊢ prep_string s x ≡ prep_string s y.
proof: Proof. intros HT H. induction s; cbn; try tauto. apply ZF_eq_opair; trivial. now apply ZF_refl'. Qed.
imports: Undecidability.FOL.ZF Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Sets.ZF Undecidability.FOL.Reductions.PCPb_to_ZF Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation)