proposition: Lemma sing_pair x y z : {x; x} ≡' {y; z} -> x ≡' y /\ x ≡' z.
proof: Proof. Proof using M_ZF. intros He. split. - assert (H : y ∈' {y; z}) by apply M_pair1. rewrite <- He in H. apply M_pair in H. intuition (auto with crelations). - assert (H : z ∈' {y; z}) by apply M_pair2. rewrite <- He in H. apply M_pair in H. intuition (auto with crelations). 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