Tests pour Field avec les nombres reels

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@1644 85f007b7-540e-0410-9357-904b9bb8a0f7

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+(***********************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team    *)
+(* <O___,, *        INRIA-Rocquencourt  &  LRI-CNRS-Orsay              *)
+(*   \VV/  *************************************************************)
+(*    //   *      This file is distributed under the terms of the      *)
+(*         *       GNU Lesser General Public License Version 2.1       *)
+(***********************************************************************)
+
+(* $Id$ *)
+
+(**** Tests of Field with real numbers ****)
+
+Require Reals.
+
+(* Example 1 *)
+Goal (eps:R)``eps*1/(2+2)+eps*1/(2+2) == eps*1/2``.
+Proof.
+  Intros.
+  Field.
+Abort.
+
+(* Example 2 *)
+Goal  (f,g:(R->R); x0,x1: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 (a,b:R)``1/(a*b)*1/1/b == 1/a``.
+Proof.
+  Intros.
+  Field.
+Abort.
+ 
+(* Example 4 *)
+Goal (a,b:R)``a <> 0``->``b <> 0``->``1/(a*b)/1/b == 1/a``.
+Proof.
+  Intros.
+  Field.
+Abort.
+ 
+(* Example 5 *)
+Goal (a:R)``1 == 1*1/a*a``.
+Proof.
+  Intros.
+  Field.
+Abort.
+ 
+(* Example 6 *)
+Goal (a,b:R)``b == b*/a*a``.
+Proof.
+  Intros.
+  Field.
+Abort.
+ 
+(* Example 7 *)
+Goal (a,b:R)``b == b*1/a*a``.
+Proof.
+  Intros.
+  Field.
+Abort.
+
+(* Example 8 *)
+Goal (x,y:R)``x*((1/x)+x/(x+y)) == -(1/y)*y*(-(x*x/(x+y))-1)``.
+Proof.
+  Intros.
+  Field.
+Abort.