proposition: Theorem Nlt_out : forall n m, n < m -> (nat_of_N n < nat_of_N m)%nat.
proof: Proof. unfold N.lt; intros ?? H. rewrite nat_of_Ncompare in H. apply nat_compare_Lt_lt; assumption. Qed.
imports: Coq.Bool.Bool Coq.Classes.Morphisms Coq.Arith.Arith Coq.micromega.Lia Coq.NArith.NArith Coq.ZArith.ZArith