proposition: Lemma minZF_trans { p : peirce } A x y z : binZF <<= A -> A ⊢ x ≡' y -> A ⊢ y ≡' z -> A ⊢ x ≡' z.
proof: Proof. intros HA H1 H2. prv_all' a. apply (AllE a) in H1. cbn in H1. subsimpl_in H1. apply (AllE a) in H2. cbn in H2. subsimpl_in H2. apply CE in H1 as [H1 H1']. apply CE in H2 as [H2 H2']. apply CI; apply II; eapply IE. - apply (Weak H2); auto. - now apply imps. - apply (Weak H1'); auto. - now apply imps. Qed.
imports: Undecidability.FOL.Syntax.Facts Undecidability.FOL.Syntax.Asimpl Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Deduction.FullNDFacts Undecidability.FOL.Sets(binZF ZF) Undecidability.FOL.Reductions.PCPb_to_ZF Undecidability(Shared.ListAutomation) Morphisms Undecidability.FOL(Reductions.PCPb_to_ZFeq)