proposition: Lemma minZF_trans { p : peirce } A x y z : minZFeq' <<= A -> A ⊢ x ≡' y -> A ⊢ y ≡' z -> A ⊢ x ≡' z.
proof: Proof. intros HA H1 H2. assert (HS : A ⊢ ax_trans'). apply Ctx. firstorder. apply (AllE x) in HS. cbn in HS. apply (AllE y) in HS. cbn in HS. apply (AllE z) in HS. cbn in HS. subsimpl_in HS. eapply IE. now apply (IE HS). assumption. Qed.
imports: Undecidability.FOL.ZF Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Sets(minZF ZF) Undecidability.FOL.Sets.ZF Undecidability.FOL.Reductions.PCPb_to_ZF Undecidability(Shared.ListAutomation)