proposition: Lemma mon_ack_in_b : forall n a, 2 <= a -> mon (fun b => ack n a b).
proof: Proof. induction n; intros. - simpl; intros b m; lia. - simpl. intros b m le. case n as [|n]; [lia|]. induction le; auto. rewrite unfold_iter. transitivity (S (iter (ack (S n) a) m)). + lia. + apply geS_ack; auto. Qed.
imports: Arith Lia