induction n2; destruct n4; simpl in *; intuition.
rewrite <- mult_1_l at 1.
eapply mult_le_compat.
omega.
eapply expnat_ge_1; trivial.
destruct (eq_nat_dec n 0); subst.
simpl; intuition.
eapply mult_le_compat; intuition.
Qed.

Lemma mult_lt_compat :
forall a b c d,
a < b ->
c < d ->
a * c < b * d.