proposition: Lemma minZF_elem { p : peirce } A x y u v : binZF <<= A -> A ⊢ x ≡' u -> A ⊢ y ≡' v -> A ⊢ x ∈' y -> A ⊢ u ∈' v.
proof: Proof. intros HA H1 H2 H3. eapply IE. eapply IE. eapply IE. eapply Weak. eapply minZF_elem'. auto. all: eauto. 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)