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

Theorem Nmult_lt_compat_rev_l2: forall n m p, p * n < p * m -> n < m.
intros n m p H1; apply Nlt_lt; apply mult_lt_compat_rev_l2 with (nat_of_N p).