intros; simpl in |- *.
elim plus_n_O; auto with arith.
intro.
elim mult_n_O; elim mult_n_O; auto with arith.
intros; simpl in |- *; apply lt_n_S; auto with arith.
Qed.
Hint Resolve lt_mult_n_Sn.

Lemma lt_mult_cst : forall x y a : nat, x < y -> 0 < a -> a * x < a * y.
intros.