proposition: Lemma is_eset_sub { p : peirce } A x y : binZF <<= A -> A ⊢ is_eset x -> A ⊢ sub' x y.
proof: Proof. intros HA HE. prv_all' z. apply II, Exp, IE with (($0 ∈' x`[↑])[z..]). - change ((z ∈' x :: A) ⊢ (¬ $0 ∈' x`[↑])[z..]). apply AllE, (Weak HE). auto. - cbn. subsimpl. auto. 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)