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-rw-r--r--test-suite/success/Field.v41
-rw-r--r--test-suite/success/LegacyField.v78
-rw-r--r--test-suite/success/NatRing.v4
-rw-r--r--test-suite/success/setoid_ring_module.v6
4 files changed, 110 insertions, 19 deletions
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.