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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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(*                      Evgeny Makarov, INRIA, 2007                     *)
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Require Export NOrder.
Module NAddOrderProp (Import N : NAxiomsMiniSig').
Include NOrderProp N.
(** Theorems true for natural numbers, not for integers *)

(* Specifications: *)
Theorem le_add_r : forall n m, n <= n + m.
Theorem le_add_l : forall n m, n <= m + n.
Theorem lt_lt_add_r : forall n m p, n < m -> n < m + p.
Theorem lt_lt_add_l : forall n m p, n < m -> n < p + m.
Theorem add_pos_l : forall n m, 0 < n -> 0 < n + m.
Theorem add_pos_r : forall n m, 0 < m -> 0 < n + m.
End NAddOrderProp.