From 83c7941f909ebe5150868b1242669c7f4502b528 Mon Sep 17 00:00:00 2001
From: barras <barras@85f007b7-540e-0410-9357-904b9bb8a0f7>
Date: Mon, 2 Oct 2006 15:55:52 +0000
Subject: nouveau ring/field

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@9197 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 test-suite/success/Field.v              | 41 +++++++++++------
 test-suite/success/LegacyField.v        | 78 +++++++++++++++++++++++++++++++++
 test-suite/success/NatRing.v            |  4 +-
 test-suite/success/setoid_ring_module.v |  6 +--
 4 files changed, 110 insertions(+), 19 deletions(-)
 create mode 100644 test-suite/success/LegacyField.v

diff --git a/test-suite/success/Field.v b/test-suite/success/Field.v
index 310dfb620..6fb922b0f 100644
--- a/test-suite/success/Field.v
+++ b/test-suite/success/Field.v
@@ -10,58 +10,71 @@
 
 (**** Tests of Field with real numbers ****)
 
-Require Import Reals.
+Require Import Reals RealField.
+Open Scope R_scope.
 
 (* Example 1 *)
 Goal
 forall eps : R,
-(eps * (1 / (2 + 2)) + eps * (1 / (2 + 2)))%R = (eps * (1 / 2))%R.
+eps * (1 / (2 + 2)) + eps * (1 / (2 + 2)) = eps * (1 / 2).
 Proof.
   intros.
    field.
-Abort.
+Qed.
 
 (* Example 2 *)
 Goal
 forall (f g : R -> R) (x0 x1 : R),
-((f x1 - f x0) * (1 / (x1 - x0)) + (g x1 - g x0) * (1 / (x1 - x0)))%R =
-((f x1 + g x1 - (f x0 + g x0)) * (1 / (x1 - x0)))%R.
+(f x1 - f x0) * (1 / (x1 - x0)) + (g x1 - g x0) * (1 / (x1 - x0)) =
+(f x1 + g x1 - (f x0 + g x0)) * (1 / (x1 - x0)).
 Proof.
   intros.
    field.
 Abort.
  
 (* Example 3 *)
-Goal forall a b : R, (1 / (a * b) * (1 / 1 / b))%R = (1 / a)%R.
+Goal forall a b : R, 1 / (a * b) * (1 / (1 / b)) = 1 / a.
 Proof.
   intros.
    field.
 Abort.
+
+Goal forall a b : R, 1 / (a * b) * (1 / 1 / b) = 1 / a.
+Proof.
+  intros.
+   field_simplify_eq.
+Abort.
  
+Goal forall a b : R, 1 / (a * b) * (1 / 1 / b) = 1 / a.
+Proof.
+  intros.
+   field_simplify (1 / (a * b) * (1 / 1 / b)).
+Abort.
+
 (* Example 4 *)
 Goal
-forall a b : R, a <> 0%R -> b <> 0%R -> (1 / (a * b) / 1 / b)%R = (1 / a)%R.
+forall a b : R, a <> 0 -> b <> 0 -> 1 / (a * b) / (1 / b) = 1 / a.
 Proof.
   intros.
-   field.
-Abort.
+   field; auto.
+Qed.
  
 (* Example 5 *)
-Goal forall a : R, 1%R = (1 * (1 / a) * a)%R.
+Goal forall a : R, 1 = 1 * (1 / a) * a.
 Proof.
   intros.
    field.
 Abort.
  
 (* Example 6 *)
-Goal forall a b : R, b = (b * / a * a)%R.
+Goal forall a b : R, b = b * / a * a.
 Proof.
   intros.
    field.
 Abort.
  
 (* Example 7 *)
-Goal forall a b : R, b = (b * (1 / a) * a)%R.
+Goal forall a b : R, b = b * (1 / a) * a.
 Proof.
   intros.
    field.
@@ -70,8 +83,8 @@ Abort.
 (* Example 8 *)
 Goal
 forall x y : R,
-(x * (1 / x + x / (x + y)))%R =
-(- (1 / y) * y * (- (x * (x / (x + y))) - 1))%R.
+x * (1 / x + x / (x + y)) =
+- (1 / y) * y * (- (x * (x / (x + y))) - 1).
 Proof.
   intros.
    field.
diff --git a/test-suite/success/LegacyField.v b/test-suite/success/LegacyField.v
new file mode 100644
index 000000000..bc2cffa4d
--- /dev/null
+++ b/test-suite/success/LegacyField.v
@@ -0,0 +1,78 @@
+(************************************************************************)
+(*  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: Field.v 7693 2005-12-21 23:50:17Z herbelin $ *)
+
+(**** Tests of Field with real numbers ****)
+
+Require Import Reals.
+
+(* Example 1 *)
+Goal
+forall eps : R,
+(eps * (1 / (2 + 2)) + eps * (1 / (2 + 2)))%R = (eps * (1 / 2))%R.
+Proof.
+  intros.
+   legacy field.
+Abort.
+
+(* Example 2 *)
+Goal
+forall (f g : R -> R) (x0 x1 : R),
+((f x1 - f x0) * (1 / (x1 - x0)) + (g x1 - g x0) * (1 / (x1 - x0)))%R =
+((f x1 + g x1 - (f x0 + g x0)) * (1 / (x1 - x0)))%R.
+Proof.
+  intros.
+   legacy field.
+Abort.
+ 
+(* Example 3 *)
+Goal forall a b : R, (1 / (a * b) * (1 / 1 / b))%R = (1 / a)%R.
+Proof.
+  intros.
+   legacy field.
+Abort.
+ 
+(* Example 4 *)
+Goal
+forall a b : R, a <> 0%R -> b <> 0%R -> (1 / (a * b) / 1 / b)%R = (1 / a)%R.
+Proof.
+  intros.
+   legacy field.
+Abort.
+ 
+(* Example 5 *)
+Goal forall a : R, 1%R = (1 * (1 / a) * a)%R.
+Proof.
+  intros.
+   legacy field.
+Abort.
+ 
+(* Example 6 *)
+Goal forall a b : R, b = (b * / a * a)%R.
+Proof.
+  intros.
+   legacy field.
+Abort.
+ 
+(* Example 7 *)
+Goal forall a b : R, b = (b * (1 / a) * a)%R.
+Proof.
+  intros.
+   legacy field.
+Abort.
+
+(* Example 8 *)
+Goal
+forall x y : R,
+(x * (1 / x + x / (x + y)))%R =
+(- (1 / y) * y * (- (x * (x / (x + y))) - 1))%R.
+Proof.
+  intros.
+   legacy field.
+Abort.
diff --git a/test-suite/success/NatRing.v b/test-suite/success/NatRing.v
index 8426c7e48..22d021d54 100644
--- a/test-suite/success/NatRing.v
+++ b/test-suite/success/NatRing.v
@@ -1,10 +1,10 @@
 Require Import ArithRing.
 
 Lemma l1 : 2 = 1 + 1.
-ring_nat.
+ring.
 Qed.
 
 Lemma l2 : forall x : nat, S (S x) = 1 + S x.
 intro.
-ring_nat.
+ring.
 Qed.
diff --git a/test-suite/success/setoid_ring_module.v b/test-suite/success/setoid_ring_module.v
index 9dfedce35..e947c6d9c 100644
--- a/test-suite/success/setoid_ring_module.v
+++ b/test-suite/success/setoid_ring_module.v
@@ -1,4 +1,4 @@
-Require Import Setoid ZRing_th Ring_th.
+Require Import Setoid Ring Ring_theory.
 
 Module abs_ring.
 
@@ -28,7 +28,7 @@ Admitted.
 Definition cRth : ring_theory c0 c1 cadd cmul csub copp ceq.
 Admitted.
 
-Add New Ring CoefRing : cRth Abstract. 
+Add Ring CoefRing : cRth.
 
 End abs_ring.
 Import abs_ring.
@@ -36,5 +36,5 @@ Import abs_ring.
 Theorem check_setoid_ring_modules :
   forall a b, ceq (cadd a b) (cadd b a).
 intros.
-setoid ring.
+ring.
 Qed.
-- 
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