(* -*- coding: utf-8 -*- *)
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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \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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(** Binary Integers : results about order predicates *)
(** Initial author : Pierre Crégut (CNET, Lannion, France) *)
(** THIS FILE IS DEPRECATED. It is now almost entirely made of compatibility formulations for results already present in BinInt.Z. *)
Local Open Scope Z_scope.
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(** Properties of the order relations on binary integers *)
(** * Trichotomy *)
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(** * Decidability of equality and order on Z *)
Notation dec_eq := Z.eq_decidable (only parsing).
Notation dec_Zle := Z.le_decidable (only parsing).
Notation dec_Zlt := Z.lt_decidable (only parsing).
Register dec_Zne as plugins.omega.dec_Zne.
Register dec_Zgt as plugins.omega.dec_Zgt.
Register dec_Zge as plugins.omega.dec_Zge.
Register not_Zeq as plugins.omega.not_Zeq.
(** * Relating strict and large orders *)
Notation Zgt_iff_lt := Z.gt_lt_iff (only parsing).
Notation Zge_iff_le := Z.ge_le_iff (only parsing).

Lemma Zle_not_lt n m : n <= m -> ~ m < n.