proposition: Lemma binunion_el x y z : x ∈ y ∪ z <-> x ∈ y \/ x ∈ z.
proof: Proof. Proof using VIEQ M_ZF. split. - intros [u [H1 H2]] % M_union. apply M_pair in H1 as [->| ->]; auto. - intros [H|H]. + apply M_union. exists y. rewrite M_pair. auto. + apply M_union. exists z. rewrite M_pair. auto. Qed.
imports: Undecidability.FOL(Syntax.Facts Semantics.Tarski.FullFacts ZF) Undecidability.FOL.Sets(ZF binZF) Undecidability.FOL.Sets.Models(Aczel Aczel_CE Aczel_TD) Coq(Lia)