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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) *)
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(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
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(** * Properties of minimum and maximum specific to integer numbers *)
Module Type ZMaxMinProp (Import Z : ZAxiomsMiniSig').
Include ZMulOrderProp Z.
(** The following results are concrete instances of [max_monotone] and similar lemmas. *)
(** Succ *)

Lemma mul_max_distr_nonpos_l n m p : p <= 0 ->
max (p * n) (p * m) == p * min n m.