intros.
elim H.
elim minus_n_n; simpl in |- *; elim le_plus_minus; auto with arith.
intros.
elim minus_Sn_m; simpl in |- *.
apply eq_S; auto with arith.
assumption.
Qed.
Hint Resolve le_le_assoc_plus_minus.

Lemma le_lt_plus : forall n m p q : nat, n <= p -> m < q -> n + m < p + q.
intros.