proposition: Lemma HF_union_el' T x y z : HFeq <<= T -> T ⊢ y ∈ x ∧ z ∈ y -> T ⊢ z ∈ ⋃ x.
proof: Proof. intros HT H. assert (HU : T ⊢ ax_union) by (apply Ctx; firstorder). apply (AllE x), (AllE z) in HU; cbn in HU. subsimpl_in HU. apply CE2 in HU. eapply IE; try apply HU. apply ExI with y. cbn. subsimpl. apply H. 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)