proposition: Lemma bunion_use T x y z phi : ZFeq' <<= T -> (x ∈ y :: T) ⊢ phi -> (x ≡ z :: T) ⊢ phi -> T ⊢ x ∈ y ∪ sing z → phi.
proof: Proof. intros HT H1 H2. apply II. eapply DE. - eapply ZF_bunion_inv; auto. - apply (Weak H1). auto. - eapply IE. + eapply Weak. apply II, H2. auto. + apply ZF_sing_iff; auto. Qed.
imports: Undecidability.FOL.ZF Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Sets.ZF Undecidability.FOL.Reductions.PCPb_to_ZF Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation)