proposition: Lemma opair_inj1 x x' y y' : M_opair x y ≡' M_opair x' y' -> x ≡' x'.
proof: Proof. Proof using M_ZF. intros He. assert (H : {x; x} ∈' M_opair x y) by apply M_pair1. rewrite He in H. apply M_pair in H as [H|H]; apply (sing_pair H). Qed.
imports: Undecidability.FOL.ZF Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Sets(ZF) Undecidability.FOL.Sets.ZF Undecidability.FOL.Reductions.PCPb_to_ZF Lia Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation) Morphisms