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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 NMulOrder.
Module Type NSubProp (Import N : NAxiomsMiniSig').
Include NMulOrderProp N.

(* This could be proved by adding m to both sides. Then the proof would use add_sub_assoc and sub_0_le, which is proven below. *)
Theorem add_sub_eq_nz : forall n m p, p ~= 0 -> n - m == p -> m + p == n.