(************************************************************************)
(*         *      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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(** THIS FILE IS DEPRECATED. *)
Require Export BinInt Zcompare Zorder.
Local Open Scope Z_scope.
(** Definition [Z.max] is now [BinInt.Z.max]. *)
(** Exact compatibility *)
Notation Zmax_right := Z.max_r (only parsing).
Notation Zle_max_compat_r := Z.max_le_compat_r (only parsing).
Notation Zle_max_compat_l := Z.max_le_compat_l (only parsing).
Notation Zmax_idempotent := Z.max_id (only parsing).
Notation Zmax_n_n := Z.max_id (only parsing).
Notation Zmax_irreducible_dec := Z.max_dec (only parsing).
Notation Zmax_le_prime := Z.max_le (only parsing).
Notation Zmax_SS := Z.succ_max_distr (only parsing).
Notation Zplus_max_distr_l := Z.add_max_distr_l (only parsing).
Notation Zplus_max_distr_r := Z.add_max_distr_r (only parsing).
Notation Zmax_plus := Z.add_max_distr_r (only parsing).
Notation Zmax1 := Z.le_max_l (only parsing).
Notation Zmax2 := Z.le_max_r (only parsing).
Notation Zmax_irreducible_inf := Z.max_dec (only parsing).
Notation Zmax_le_prime_inf := Z.max_le (only parsing).
Notation Zpos_max := Pos2Z.inj_max (only parsing).
Notation Zpos_minus := Pos2Z.inj_sub_max (only parsing).
(** Slightly different lemmas *)

Lemma Zmax_spec x y :
x >= y /\ Z.max x y = x  \/ x < y /\ Z.max x y = y.