intros H'; inversion H'.
simpl in |- *; intros n H'; case t; auto with arith.
intros H'0; inversion H'0.
intros n H'; inversion H'.
intros n n0 H'; case t.
intros H'0; inversion H'0.
intros n1 H'0; apply lt_trans with (m := S n0 * S n1).
apply mult_S_lt_compat_l; auto.
rewrite (mult_comm (S n0)); rewrite (mult_comm (S n)); auto.
apply mult_S_lt_compat_l; auto.
Qed.

Theorem le_mult_right : forall x y : nat, 0 < y -> x <= x * y.
intros x y; case y.