proposition: Lemma prv_cut A B phi : A ⊢ phi -> (forall psi, psi el A -> B ⊢ psi) -> B ⊢ phi.
proof: Proof. induction A in phi |- *; intros H1 H2. - eapply Weak; eauto. - rewrite <- imps in H1. apply IHA in H1; auto. apply IE with a; trivial. now apply H2. Qed.
imports: Undecidability.Synthetic(Definitions DecidabilityFacts EnumerabilityFacts ListEnumerabilityFacts ReducibilityFacts) Undecidability.FOL(Syntax.Facts Syntax.Theories Syntax.Asimpl) Undecidability(Shared.ListAutomation) Lia EqdepFacts