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+(************************************************************************)
+(*  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 LegacyRfield.
+
+(* 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.