proposition: Lemma impl_equiv { p : peirce } (phi psi phi' psi' : form') A : (forall B, A <<= B -> B ⊢ phi <-> B ⊢ phi') -> (forall B, A <<= B -> B ⊢ psi <-> B ⊢ psi') -> (A ⊢ phi → psi) <-> (A ⊢ phi' → psi').
proof: Proof. intros H1 H2. split; intros H; apply II. - apply H2; auto. eapply IE. apply (Weak H). auto. apply H1; auto. - apply H2; auto. eapply IE. apply (Weak H). auto. 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)