repeat rewrite <- N2Nat.inj_mul; apply gt_Ngt; repeat rewrite N2Nat.id; auto.
Qed.

(* Specifications: *)
Theorem Nmult_gt_compat_rev_l2: forall n m p, p * n > p * m -> n > m.
intros n m p H1; apply Ngt_gt; apply mult_gt_compat_rev_l2 with (nat_of_N p).
Theorem Nmult_le_compat_rev_l: forall n m p, p * n <= p * m -> 0 < p -> n <= m.
intros n m p H1 H2; apply Nle_le; apply mult_le_compat_rev_l with (nat_of_N p).