proposition: Lemma sing_pair2 T x y z : HFeq <<= T -> T ⊢ sing x ≡ {y; z} -> T ⊢ x ≡ z.
proof: Proof. intros HT H. apply HF_sym'; trivial. apply HF_sing_iff; trivial. eapply HF_eq_elem; trivial. apply HF_refl'; trivial. apply HF_sym'; eauto. apply HF_pair_el'; trivial. apply DI2. now apply HF_refl'. 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)