intros n1 H1; case H1; auto.
intros m1 n1 H1; case (le_or_lt n1 m1); auto with arith.
intros H2; case H1.
apply nat_of_P_gt_Gt_compare_complement_morphism.
repeat rewrite  nat_of_P_o_P_of_succ_nat_eq_succ; auto with arith.
Qed.

Theorem Nle_le_rev: forall n  m, n <= m -> (N.to_nat n <= N.to_nat m)%nat.
intros; apply le_Nle; repeat rewrite N2Nat.id; auto.