From 5b7eafd0f00a16d78f99a27f5c7d5a0de77dc7e6 Mon Sep 17 00:00:00 2001
From: Stephane Glondu <steph@glondu.net>
Date: Wed, 21 Jul 2010 09:46:51 +0200
Subject: Imported Upstream snapshot 8.3~beta0+13298

---
 plugins/ring/LegacyZArithRing.v | 37 +++++++++++++++++++++++++++++++++++++
 1 file changed, 37 insertions(+)
 create mode 100644 plugins/ring/LegacyZArithRing.v

(limited to 'plugins/ring/LegacyZArithRing.v')

diff --git a/plugins/ring/LegacyZArithRing.v b/plugins/ring/LegacyZArithRing.v
new file mode 100644
index 00000000..68a0dd27
--- /dev/null
+++ b/plugins/ring/LegacyZArithRing.v
@@ -0,0 +1,37 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(* $Id$ *)
+
+(* Instantiation of the Ring tactic for the binary integers of ZArith *)
+
+Require Export LegacyArithRing.
+Require Export ZArith_base.
+Require Import Eqdep_dec.
+Require Import LegacyRing.
+
+Unboxed Definition Zeq (x y:Z) :=
+  match (x ?= y)%Z with
+  | Datatypes.Eq => true
+  | _ => false
+  end.
+
+Lemma Zeq_prop : forall x y:Z, Is_true (Zeq x y) -> x = y.
+  intros x y H; unfold Zeq in H.
+  apply Zcompare_Eq_eq.
+  destruct (x ?= y)%Z; [ reflexivity | contradiction | contradiction ].
+Qed.
+
+Definition ZTheory : Ring_Theory Zplus Zmult 1%Z 0%Z Zopp Zeq.
+  split; intros; eauto with zarith.
+  apply Zeq_prop; assumption.
+Qed.
+
+(* NatConstants and NatTheory are defined in Ring_theory.v *)
+Add Legacy Ring Z Zplus Zmult 1%Z 0%Z Zopp Zeq ZTheory
+ [ Zpos Zneg 0%Z xO xI 1%positive ].
-- 
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