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

Theorem Nlt_mult_rev_0_r: forall a b, 0 < a * b ->  0 < b .
intros a b H1; apply Nlt_lt; apply lt_mult_rev_0_r with (nat_of_N a).