apply mult_gt_compat_l; apply gt_Ngt; repeat rewrite N2Nat.id; auto.
Qed.

Theorem Nmult_lt_compat_rev_l1: forall n m p, p * n < p * m -> 0 < p.
intros n m p H1; apply Nlt_lt; apply mult_lt_compat_rev_l1 with (nat_of_N n) (nat_of_N m).