intros H1; inversion H1.
intros p H1; inversion H1.
intros; apply nat_of_P_gt_Gt_compare_complement_morphism; auto.
Qed.

Theorem gt_Ngt: forall n m, N.of_nat n > N.of_nat m -> (n > m)%nat.
intros n m; case n; case m; unfold N.gt; simpl; try (intros; discriminate); auto with arith.