proposition: Lemma HF_sig_iff T x y : HFeq <<= T -> T ⊢ y ∈ σ x -> T ⊢ y ∈ x ∨ y ≡ x.
proof: Proof. intros HT H % HF_bunion_inv; auto. eapply DE; try apply H; auto. apply DI2. eapply DE; try apply HF_pair_el'; auto. Qed.
imports: Undecidability.FOL.ZF Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Sets.ZF Undecidability.FOL.Reductions.PCPb_to_HF Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation)