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

(* Specifications: *)
Theorem Nge_ge_rev: forall n  m, n >= m -> (N.to_nat n >= N.to_nat m)%nat.
intros; apply ge_Nge; repeat rewrite N2Nat.id; auto.