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(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
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Local Open Scope nat_scope.
Implicit Types m n x y : nat.
Definition zerop n : {n = 0} + {0 < n}.

(* Specifications: *)
Theorem dec_lt n m : decidable (n < m).
Theorem dec_gt n m : decidable (n > m).
Theorem dec_ge n m : decidable (n >= m).
Theorem not_eq n m : n <> m -> n < m \/ m < n.
Theorem not_le n m : ~ n <= m -> n > m.
Theorem not_gt n m : ~ n > m -> n <= m.
Theorem not_ge n m : ~ n >= m -> n < m.
Theorem not_lt n m : ~ n < m -> n >= m.
Register dec_le as num.nat.dec_le.