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

Theorem Nlt_mult_0: forall a b, 0 < a -> 0 < b -> 0 < a * b.
intros a b H1 H2; apply Nlt_lt; rewrite N2Nat.inj_mul; apply lt_mult_0; apply lt_Nlt; repeat rewrite N2Nat.id; auto.