induction n2; destruct n3; intuition; simpl in *; try omega.
exfalso.
remember (n2 * n1)%nat as x.
omega.
eapply le_n_S.
eapply IHn2; eauto.
omega.
Qed.

(* Specifications: *)
Lemma mult_le_compat_r_iff : forall n1 n2 n3,
n1 > O ->
(n2 * n1 <= n3 * n1)%nat ->
(n2 <= n3)%nat.