intros n; elim n; simpl in |- *; auto.
intros m H1; Contradict H1; auto with arith.
intros n1 Rec m; case m; simpl in |- *; auto.
intros m1 H1; apply Rec; apply lt_S_n; auto.
Qed.

Theorem le_minus : forall a b : nat, a - b <= a.
Proof using.