proposition: Lemma use_ex_eq { p : peirce } A x phi psi : binZF <<= 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.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)