proposition: Lemma ZF_sing_iff T x y : ZFeq' <<= T -> T ⊢ x ∈ sing y <-> T ⊢ x ≡ y.
proof: Proof. intros HT. unfold sing. rewrite <- ZF_pair_el'; trivial. split; intros H. - apply (DE H); auto. - now apply DI1. 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)