(* -*- coding: utf-8 -*- *)
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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
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(* <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.
(***************************)
(** * 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 *)
(** * Relating [x ?= y] to [=], [<=], [<], [>=] or [>] *)

Lemma Zcompare_elim :
forall (c1 c2 c3:Prop) (n m:Z),
(n = m -> c1) ->
(n < m -> c2) ->
(n > m -> c3) -> match n ?= m with
| Eq => c1
| Lt => c2
| Gt => c3
end.