proposition: Lemma binunion_el x y z : x ∈' y ∪ z <-> x ∈' y \/ x ∈' z.
proof: Proof. Proof using 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.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