apply mult_ge_compat_l; apply ge_Nge; repeat rewrite N2Nat.id; auto.
Qed.

Theorem Nmult_gt_compat_l: forall n m p, n > m -> p > 0 -> p * n > p * m.
intros n m p H1 H2; apply Ngt_gt; repeat rewrite N2Nat.inj_mul.