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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)           *)
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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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(** Binary Integers : results about Z.compare *)
(** 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. *)
Require Export BinPos BinInt.
Local Open Scope Z_scope.
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(** * Comparison on integers *)
Proof Z.gt_lt_iff.
Proof eq_sym (Z.compare_antisym n m).
(** * Transitivity of comparison *)
Proof Z.lt_trans.
(** * Comparison and opposite *)
(** * Comparison first-order specification *)
(** * Comparison and addition *)
(** * Successor and comparison *)
(** * Multiplication and comparison *)

Lemma Zmult_compare_compat_r n m p :
p > 0 -> (n ?= m) = (n * p ?= m * p).