proposition: Theorem Nneq_out : forall n m, n <> m -> nat_of_N n <> nat_of_N m.
proof: Proof. intuition; zify; intuition. Qed.
imports: Coq.Bool.Bool Coq.Classes.Morphisms Coq.Arith.Arith Coq.micromega.Lia Coq.NArith.NArith Coq.ZArith.ZArith