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Diffstat (limited to 'test-suite/success/LegacyField.v')
-rw-r--r-- | test-suite/success/LegacyField.v | 78 |
1 files changed, 78 insertions, 0 deletions
diff --git a/test-suite/success/LegacyField.v b/test-suite/success/LegacyField.v new file mode 100644 index 00000000..d53e4010 --- /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 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. |