proposition: Theorem Nge_in : forall n m, (nat_of_N n >= nat_of_N m)%nat -> n >= m.
proof: Proof. unfold N.ge; intros. rewrite nat_of_Ncompare. apply nat_compare_ge; assumption. Qed.
imports: Coq.Bool.Bool Coq.Classes.Morphisms Coq.Arith.Arith Coq.micromega.Lia Coq.NArith.NArith Coq.ZArith.ZArith