auto with arith.
intros n Hrec m; case m; clear m.
simpl in |- *; intros Heq; discriminate Heq.
simpl in |- *; intros; apply le_n_S; apply Hrec; auto.
Qed.

Theorem le_minus_O : forall n m : nat, n <= m -> n - m = 0.
intros n; elim n; clear n.