proposition: Lemma HF_eq_union T x y : HFeq <<= T -> T ⊢ x ≡ y -> T ⊢ ⋃ x ≡ ⋃ y.
proof: Proof. intros HT H. apply HF_ext'; try apply HF_sub_union; trivial. now apply HF_sym'. 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)