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

Theorem Ngt_mult_rev_0_l: forall a b, a * b > 0 ->  a > 0.
intros a b H1; apply Ngt_gt; apply gt_mult_rev_0_l with (nat_of_N b).