(n m i : nat) : i < n - m -> m <= n. Proof. revert m i; simple_induction n n IHn. - intros m i l. simpl in l. contradiction (not_lt_zero_r _ _). - intros m i l. destruct m. + apply leq_zero_l. + apply leq_succ. simpl in l. apply (IHn m i l). Defined.
Require Import Basics. Require Import Spaces.Nat.Core.