proposition: Lemma ZF_trans' T x y z : ZFeq' <<= T -> T ⊢ x ≡ y -> T ⊢ y ≡ z -> T ⊢ x ≡ z.
proof: Proof. intros H1 H2 H3. eapply IE; try apply H3. eapply IE; try apply H2. assert (H : T ⊢ ax_trans) by (apply Ctx; firstorder). now apply (AllE x), (AllE y), (AllE z) in H; cbn in H; 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)