intros; simpl in |- *; elim (plus_comm m (y * m + (y + m))).
rewrite (plus_assoc m (y * m) (y + m)); auto with arith.
Qed.

(**************)
Lemma lt_minus2 : forall n m : nat, n < m -> 0 < m - n.
simple induction 1; intros; elim minus_Sn_m; auto with arith.