intros; elim minus_S.
change (n0 - n1 - p = S n0 - S (n1 + p)) in |- *.
elim minus_S; apply H.
Qed.
Hint Resolve minus_minus_plus.

Lemma lt_O_minus : forall n m : nat, n < m -> 0 < m - n.
simple induction n; simple induction m; simpl in |- *; auto with arith.