proposition: Lemma ex_equiv { p : peirce } (phi psi : form') A : (forall B t, A <<= B -> B ⊢ phi[t..] <-> B ⊢ psi[t..]) -> (A ⊢ ∃ phi) <-> (A ⊢ ∃ psi).
proof: Proof. intros H1. split; intros H2. - apply (ExE H2). edestruct (nameless_equiv_ex A) as [x ->]. apply ExI with x. apply H1; auto. - apply (ExE H2). edestruct (nameless_equiv_ex A) as [x ->]. apply ExI with x. apply H1; 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)