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

(* Specifications: *)
Theorem Ngt_mult_rev_0_r: forall a b, a * b > 0  ->  b > 0 .
intros a b H1; apply Ngt_gt; apply gt_mult_rev_0_r with (nat_of_N a).
Theorem Nle_0_eq_0: forall n, n <= 0 -> n = 0.
intros n H1; rewrite <- (N2Nat.id n).