proposition: Lemma minZF_ext { p : peirce } A x y : binZF <<= A -> A ⊢ sub' x y -> A ⊢ sub' y x -> A ⊢ x ≡' y.
proof: Proof. intros HA H1 H2. assert (HS : A ⊢ ax_ext'). apply Ctx. firstorder. apply (AllE x) in HS. unfold eq' in HS. cbn in HS. apply (AllE y) in HS. cbn in HS. subsimpl_in HS. eapply IE. now apply (IE HS). assumption. 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)