proposition: Lemma FST_eq_pair T x y x' y' : FSTeq <<= T -> T ⊢ x ≡ x' -> T ⊢ y ≡ y' -> T ⊢ {x; y} ≡ {x'; y'}.
proof: Proof. intros HT H1 H2. apply FST_ext'; trivial. - now apply FST_sub_pair. - apply FST_sub_pair; trivial. all: now apply FST_sym'. 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)