proposition: Lemma sing_pair x y z : {x; x} = {y; z} -> x = y /\ x = z.
proof: Proof. Proof using M_ZF VIEQ. intros He. split. - assert (H : y ∈ {y; z}) by apply M_pair1. rewrite <- He in H. apply M_pair in H. intuition. - assert (H : z ∈ {y; z}) by apply M_pair2. rewrite <- He in H. apply M_pair in H. intuition. Qed.
imports: Undecidability.FOL(Syntax.Facts Semantics.Tarski.FullFacts) Undecidability.FOL(Sets.ZF) Undecidability.FOL(ZF) Undecidability.FOL.TRAKHTENBROT(hfs) Undecidability.Shared.Libs.DLW.Utils(finite) Undecidability(Shared.ListAutomation) Lia