proposition: Lemma FST_eq_prep T s x y : FSTeq <<= T -> T ⊢ x ≡ y -> T ⊢ prep_string s x ≡ prep_string s y.
proof: Proof. intros HT H. induction s; cbn; try tauto. apply FST_eq_opair; trivial. now apply FST_refl'. Qed.
imports: Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Deduction.FullNDFacts Undecidability.FOL.Sets.FST Undecidability.FOL.FST Undecidability.FOL.Reductions.PCPb_to_FST Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation)