apply mult_lt_compat_l; apply lt_Nlt; repeat rewrite N2Nat.id; auto.
Qed.

(* Specifications: *)
Theorem Nmult_le_compat_l: forall n m p, n <= m -> p * n <= p * m.
intros n m p H1; apply Nle_le; repeat rewrite N2Nat.inj_mul.