proposition: Lemma use_ex_eq { p : peirce } A x phi psi : minZFeq' <<= A -> A ⊢ phi[x..] → psi <-> A ⊢ (∃ $0 ≡' x`[↑] ∧ phi) → psi.
proof: Proof. intros H. apply impl_equiv; try tauto. intros B HB. apply prv_ex_eq. now rewrite H. 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)