proposition: Lemma ZF_sym' T x y : ZFeq' <<= T -> T ⊢ x ≡ y -> T ⊢ y ≡ x.
proof: Proof. intros H1 H2. eapply IE; try apply H2. assert (H : T ⊢ ax_sym) by (apply Ctx; firstorder). apply (AllE x), (AllE y) in H; cbn in H. now subsimpl_in H. 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)