proposition: Theorem Nlt_in : forall n m, (nat_of_N n < nat_of_N m)%nat -> n < m.
proof: Proof. unfold N.lt; intros. rewrite nat_of_Ncompare. apply (proj1 (nat_compare_lt _ _)); assumption. Qed.
imports: Coq.Bool.Bool Coq.Classes.Morphisms Coq.Arith.Arith Coq.micromega.Lia Coq.NArith.NArith Coq.ZArith.ZArith