proposition: Lemma ZF_eq_union T x y : ZFeq' <<= T -> T ⊢ x ≡ y -> T ⊢ ⋃ x ≡ ⋃ y.
proof: Proof. intros HT H. apply ZF_ext'; try apply ZF_sub_union; trivial. now apply ZF_sym'. 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)