update proof

examples/programs/my_cosine.mlw

@@ -40,6 +40,6 @@ end
 
 (*
 Local Variables:
-compile-command: "../../bin/whyide.byte my_cosine.mlw"
+compile-command: "../../bin/why3ide.byte my_cosine.mlw"
 End:
 *)

examples/programs/my_cosine/my_cosine_M_WP_parameter_my_cosine_1.v

@@ -8,13 +8,9 @@ Require Import Rtrigo.
 Require Import AltSeries. (* for def of pi *)
 Definition unit  := unit.
 
-Parameter ignore: forall (a:Type), a  -> unit.
+Parameter mark : Type.
 
-Implicit Arguments ignore.
-
-Parameter label_ : Type.
-
-Parameter at1: forall (a:Type), a -> label_  -> a.
+Parameter at1: forall (a:Type), a -> mark  -> a.
 
 Implicit Arguments at1.
 
@@ -22,6 +18,15 @@ Parameter old: forall (a:Type), a  -> a.
 
 Implicit Arguments old.
 
+Axiom assoc_mul_div : forall (x:R) (y:R) (z:R), (~ (z = (0)%R)) ->
+  ((Rdiv (x * y)%R z)%R = (x * (Rdiv y z)%R)%R).
+
+Axiom assoc_div_mul : forall (x:R) (y:R) (z:R), ((~ (y = (0)%R)) /\
+  ~ (z = (0)%R)) -> ((Rdiv (Rdiv x y)%R z)%R = (Rdiv x (y * z)%R)%R).
+
+Axiom assoc_div_div : forall (x:R) (y:R) (z:R), ((~ (y = (0)%R)) /\
+  ~ (z = (0)%R)) -> ((Rdiv x (Rdiv y z)%R)%R = (Rdiv (x * z)%R y)%R).
+
 Axiom Abs_le : forall (x:R) (y:R), ((Rabs x) <= y)%R <-> (((-y)%R <= x)%R /\
   (x <= y)%R).
 
@@ -82,10 +87,10 @@ Parameter atan: R  -> R.
 Axiom Tan_atan : forall (x:R), ((Rtrigo.tan (atan x)) = x).
 
 Inductive mode  :=
-  | NearestTiesToEven : mode
-  | ToZero : mode
-  | Up : mode
-  | Down : mode
+  | NearestTiesToEven : mode 
+  | ToZero : mode 
+  | Up : mode 
+  | Down : mode 
   | NearTiesToAway : mode .
 
 Parameter single : Type.
@@ -145,12 +150,17 @@ Axiom Round_down_neg : forall (x:R), ((round (Down ) (-x)%R) = (-(round (Up )
 Axiom Round_up_neg : forall (x:R), ((round (Up ) (-x)%R) = (-(round (Down )
   x))%R).
 
+(* YOU MAY EDIT THE CONTEXT BELOW *)
+
+Require Import Interval_tactic.
+
+(* DO NOT EDIT BELOW *)
+
 Theorem WP_parameter_my_cosine : forall (x:single),
   ((Rabs (value x)) <= (1 / 32)%R)%R ->
   ((Rabs (((1)%R - (((value x) * (value x))%R * (05 / 10)%R)%R)%R - (Rtrigo_def.cos (value x)))%R) <= (1 / 16777216)%R)%R.
 (* YOU MAY EDIT THE PROOF BELOW *)
 intros x H.
-Require Import Interval_tactic.
 interval with (i_bisect_diff (value x)).
 Qed.
 (* DO NOT EDIT BELOW *)

examples/programs/my_cosine/why3session.xml

 <?xml version="1.0" encoding="UTF-8"?>
 <!DOCTYPE why3session SYSTEM "why3session.dtd">
-<why3session name="examples/programs/my_cosine/why3session.xml">
+<why3session name="my_cosine/why3session.xml">
+ <prover id="alt-ergo" name="Alt-Ergo" version="0.93"/>
+ <prover id="coq" name="Coq" version="8.2pl1"/>
+ <prover id="cvc3" name="CVC3" version="2.2"/>
+ <prover id="eprover" name="Eprover" version="1.0-004 Temi"/>
+ <prover id="gappa" name="Gappa" version="0.13.0"/>
+ <prover id="simplify" name="Simplify" version="1.5.4"/>
+ <prover id="vampire" name="Vampire" version="0.6"/>
+ <prover id="verit" name="veriT" version="200907"/>
+ <prover id="yices" name="Yices" version="1.0.11"/>
+ <prover id="z3" name="Z3" version="2.19"/>
  <file name="../my_cosine.mlw" verified="true" expanded="true">
   <theory name="WP M" verified="true" expanded="true">
-   <goal name="WP_parameter my_cosine" expl="correctness of parameter my_cosine" sum="8917f8b8fafa070df7c50f12f5f2ffdc" proved="true" expanded="true">
+   <goal name="WP_parameter my_cosine" expl="correctness of parameter my_cosine" sum="8917f8b8fafa070df7c50f12f5f2ffdc" proved="true" expanded="true" shape="ainfix <=.aabsainfix -.avalueV5acosavalueV0c0x1.p-23Iainfix =avalueV5aroundaNearestTiesToEvenainfix -.avalueV1avalueV4FAainfix <=aabsaroundaNearestTiesToEvenainfix -.avalueV1avalueV4amax_singleIainfix =avalueV4aroundaNearestTiesToEvenainfix *.avalueV2avalueV3FAainfix <=aabsaroundaNearestTiesToEvenainfix *.avalueV2avalueV3amax_singleIainfix =avalueV3c0.5FIainfix =avalueV2aroundaNearestTiesToEvenainfix *.avalueV0avalueV0FAainfix <=aabsaroundaNearestTiesToEvenainfix *.avalueV0avalueV0amax_singleIainfix =avalueV1c1.0FAainfix <=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix <=.aabsavalueV0c0x1.p-5F">
     <transf name="split_goal" proved="true" expanded="true">
-     <goal name="WP_parameter my_cosine.1" expl="assertion" sum="6f92398fe46b35b067b387d190c5416a" proved="true" expanded="true">
+     <goal name="WP_parameter my_cosine.1" expl="assertion" sum="6f92398fe46b35b067b387d190c5416a" proved="true" expanded="true" shape="ainfix <=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix <=.aabsavalueV0c0x1.p-5F">
       <proof prover="coq" timelimit="2" edited="my_cosine_M_WP_parameter_my_cosine_1.v" obsolete="false">
-       <result status="valid" time="3.59"/>
+       <result status="valid" time="3.86"/>
       </proof>
      </goal>
-     <goal name="WP_parameter my_cosine.2" expl="precondition" sum="f19dc2becd59bbba14c5ca96b76e2290" proved="true" expanded="true">
+     <goal name="WP_parameter my_cosine.2" expl="precondition" sum="f19dc2becd59bbba14c5ca96b76e2290" proved="true" expanded="true" shape="ainfix <=aabsaroundaNearestTiesToEvenainfix *.avalueV0avalueV0amax_singleIainfix =avalueV1c1.0FIainfix <=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix <=.aabsavalueV0c0x1.p-5F">
       <proof prover="gappa" timelimit="2" edited="" obsolete="false">
-       <result status="valid" time="0.00"/>
+       <result status="valid" time="0.01"/>
       </proof>
      </goal>
-     <goal name="WP_parameter my_cosine.3" expl="precondition" sum="e5aa3eded8b53ca61fd7ab1e2266e079" proved="true" expanded="true">
+     <goal name="WP_parameter my_cosine.3" expl="precondition" sum="e5aa3eded8b53ca61fd7ab1e2266e079" proved="true" expanded="true" shape="ainfix <=aabsaroundaNearestTiesToEvenainfix *.avalueV2avalueV3amax_singleIainfix =avalueV3c0.5FIainfix =avalueV2aroundaNearestTiesToEvenainfix *.avalueV0avalueV0FIainfix <=aabsaroundaNearestTiesToEvenainfix *.avalueV0avalueV0amax_singleIainfix =avalueV1c1.0FIainfix <=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix <=.aabsavalueV0c0x1.p-5F">
       <proof prover="gappa" timelimit="2" edited="" obsolete="false">
-       <result status="valid" time="0.00"/>
+       <result status="valid" time="0.01"/>
       </proof>
      </goal>
-     <goal name="WP_parameter my_cosine.4" expl="precondition" sum="c3d55a84a06c89ca74c45f43116d5a34" proved="true" expanded="true">
+     <goal name="WP_parameter my_cosine.4" expl="precondition" sum="c3d55a84a06c89ca74c45f43116d5a34" proved="true" expanded="true" shape="ainfix <=aabsaroundaNearestTiesToEvenainfix -.avalueV1avalueV4amax_singleIainfix =avalueV4aroundaNearestTiesToEvenainfix *.avalueV2avalueV3FIainfix <=aabsaroundaNearestTiesToEvenainfix *.avalueV2avalueV3amax_singleIainfix =avalueV3c0.5FIainfix =avalueV2aroundaNearestTiesToEvenainfix *.avalueV0avalueV0FIainfix <=aabsaroundaNearestTiesToEvenainfix *.avalueV0avalueV0amax_singleIainfix =avalueV1c1.0FIainfix <=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix <=.aabsavalueV0c0x1.p-5F">
       <proof prover="gappa" timelimit="2" edited="" obsolete="false">
-       <result status="valid" time="0.00"/>
+       <result status="valid" time="0.01"/>
       </proof>
      </goal>
-     <goal name="WP_parameter my_cosine.5" expl="normal postcondition" sum="1e1226c0230f4a9f70f9f653fc8b090a" proved="true" expanded="true">
+     <goal name="WP_parameter my_cosine.5" expl="normal postcondition" sum="1e1226c0230f4a9f70f9f653fc8b090a" proved="true" expanded="true" shape="ainfix <=.aabsainfix -.avalueV5acosavalueV0c0x1.p-23Iainfix =avalueV5aroundaNearestTiesToEvenainfix -.avalueV1avalueV4FIainfix <=aabsaroundaNearestTiesToEvenainfix -.avalueV1avalueV4amax_singleIainfix =avalueV4aroundaNearestTiesToEvenainfix *.avalueV2avalueV3FIainfix <=aabsaroundaNearestTiesToEvenainfix *.avalueV2avalueV3amax_singleIainfix =avalueV3c0.5FIainfix =avalueV2aroundaNearestTiesToEvenainfix *.avalueV0avalueV0FIainfix <=aabsaroundaNearestTiesToEvenainfix *.avalueV0avalueV0amax_singleIainfix =avalueV1c1.0FIainfix <=.aabsainfix -.ainfix -.c1.0ainfix *.ainfix *.avalueV0avalueV0c0.5acosavalueV0c0x1.p-24Iainfix <=.aabsavalueV0c0x1.p-5F">
       <proof prover="gappa" timelimit="2" edited="" obsolete="false">
-       <result status="valid" time="0.01"/>
+       <result status="valid" time="0.02"/>
       </proof>
      </goal>
     </transf>