<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="Eprover" version="1.9.1-001" timelimit="5" steplimit="0" memlimit="2000"/>
<prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="CVC5" version="1.0.5" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="Z3" version="4.11.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="6" name="Alt-Ergo" version="2.1.0" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="lemmas.mlw"/>
<theory name="Lemmas" proved="true">
 <goal name="map_eq_shift&#39;vc" expl="VC for map_eq_shift" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="map_eq_shift&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="10"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="map_eq_shift_zero&#39;vc" expl="VC for map_eq_shift_zero" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="map_eq_shift_zero&#39;vc.0" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="10"/></proof>
  </goal>
  <goal name="map_eq_shift_zero&#39;vc.1" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="12"/></proof>
  </goal>
  <goal name="map_eq_shift_zero&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="4"/></proof>
  </goal>
  <goal name="map_eq_shift_zero&#39;vc.3" expl="precondition" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="map_eq_shift_zero&#39;vc.3.0" expl="precondition" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="map_eq_shift_zero&#39;vc.3.0.0" expl="precondition" proved="true">
    <proof prover="6" timelimit="1"><result status="valid" time="0.000000" steps="13"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="map_eq_shift_zero&#39;vc.4" expl="postcondition" proved="true">
  <transf name="inline_all" proved="true" >
   <goal name="map_eq_shift_zero&#39;vc.4.0" expl="postcondition" proved="true">
   <proof prover="6" memlimit="2000"><result status="valid" time="0.000000" steps="14"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="limb_max_bound" proved="true">
 <proof prover="6"><result status="valid" time="0.020000" steps="12"/></proof>
 </goal>
 <goal name="prod_compat_strict_r&#39;vc" expl="VC for prod_compat_strict_r" proved="true">
 <proof prover="1"><result status="valid" time="0.050000"/></proof>
 </goal>
 <goal name="prod_compat_r&#39;vc" expl="VC for prod_compat_r" proved="true">
 <proof prover="6" memlimit="2000"><result status="valid" time="0.020000" steps="79"/></proof>
 </goal>
 <goal name="prod_compat_strict_lr&#39;vc" expl="VC for prod_compat_strict_lr" proved="true">
 <proof prover="3"><result status="valid" time="0.587866" steps="63177"/></proof>
 </goal>
 <goal name="prod_compat_lr&#39;vc" expl="VC for prod_compat_lr" proved="true">
 <proof prover="3"><result status="valid" time="0.663247" steps="69809"/></proof>
 </goal>
 <goal name="simp_compat_strict_l&#39;vc" expl="VC for simp_compat_strict_l" proved="true">
 <proof prover="3"><result status="valid" time="0.462592" steps="46271"/></proof>
 </goal>
 <goal name="value_sub&#39;vc" expl="VC for value_sub" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="15"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_frame&#39;vc" expl="VC for value_sub_frame" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_frame&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="17"/></proof>
  </goal>
  <goal name="value_sub_frame&#39;vc.1" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="69"/></proof>
  </goal>
  <goal name="value_sub_frame&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.070000" steps="86"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_frame_shift&#39;vc" expl="VC for value_sub_frame_shift" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_frame_shift&#39;vc.0" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="17"/></proof>
  </goal>
  <goal name="value_sub_frame_shift&#39;vc.1" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="17"/></proof>
  </goal>
  <goal name="value_sub_frame_shift&#39;vc.2" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="25"/></proof>
  </goal>
  <goal name="value_sub_frame_shift&#39;vc.3" expl="variant decrease" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="19"/></proof>
  </goal>
  <goal name="value_sub_frame_shift&#39;vc.4" expl="precondition" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="value_sub_frame_shift&#39;vc.4.0" expl="precondition" proved="true">
   <transf name="inline_goal" proved="true" >
    <goal name="value_sub_frame_shift&#39;vc.4.0.0" expl="precondition" proved="true">
    <proof prover="0"><result status="valid" time="0.040000"/></proof>
    <proof prover="5"><result status="valid" time="0.010000" steps="3233"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="value_sub_frame_shift&#39;vc.5" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="17"/></proof>
  </goal>
  <goal name="value_sub_frame_shift&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="67"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_tail&#39;vc" expl="VC for value_sub_tail" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_tail&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="17"/></proof>
  </goal>
  <goal name="value_sub_tail&#39;vc.1" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="17"/></proof>
  </goal>
  <goal name="value_sub_tail&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.070000" steps="263"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_concat&#39;vc" expl="VC for value_sub_concat" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_concat&#39;vc.0" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="13"/></proof>
  </goal>
  <goal name="value_sub_concat&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="19"/></proof>
  </goal>
  <goal name="value_sub_concat&#39;vc.2" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="19"/></proof>
  </goal>
  <goal name="value_sub_concat&#39;vc.3" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="0.120000"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_head&#39;vc" expl="VC for value_sub_head" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_head&#39;vc.0" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="15"/></proof>
  </goal>
  <goal name="value_sub_head&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.060000" steps="19"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_update&#39;vc" expl="VC for value_sub_update" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_update&#39;vc.0" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="66"/></proof>
  </goal>
  <goal name="value_sub_update&#39;vc.1" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="72"/></proof>
  </goal>
  <goal name="value_sub_update&#39;vc.2" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="21"/></proof>
  </goal>
  <goal name="value_sub_update&#39;vc.3" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="23"/></proof>
  </goal>
  <goal name="value_sub_update&#39;vc.4" expl="precondition" proved="true">
  <proof prover="6" timelimit="20" memlimit="2000"><result status="valid" time="0.020000" steps="25"/></proof>
  </goal>
  <goal name="value_sub_update&#39;vc.5" expl="precondition" proved="true">
  <proof prover="6" timelimit="20" memlimit="2000"><result status="valid" time="0.020000" steps="27"/></proof>
  </goal>
  <goal name="value_sub_update&#39;vc.6" expl="postcondition" proved="true">
  <proof prover="1" memlimit="2000"><result status="valid" time="0.060000"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_zero&#39;vc" expl="VC for value_zero" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_zero&#39;vc.0" expl="variant decrease" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="17"/></proof>
  </goal>
  <goal name="value_zero&#39;vc.1" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="71"/></proof>
  </goal>
  <goal name="value_zero&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="5"><result status="valid" time="0.020000" steps="55810"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_update_no_change&#39;vc" expl="VC for value_sub_update_no_change" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_update_no_change&#39;vc.0" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="70"/></proof>
  </goal>
  <goal name="value_sub_update_no_change&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="13"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_shift_no_change&#39;vc" expl="VC for value_sub_shift_no_change" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_shift_no_change&#39;vc.0" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="68"/></proof>
  </goal>
  <goal name="value_sub_shift_no_change&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.020000" steps="13"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_lower_bound&#39;vc" expl="VC for value_sub_lower_bound" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_lower_bound&#39;vc.0" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="15"/></proof>
  </goal>
  <goal name="value_sub_lower_bound&#39;vc.1" expl="variant decrease" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="17"/></proof>
  </goal>
  <goal name="value_sub_lower_bound&#39;vc.2" expl="postcondition" proved="true">
  <proof prover="3" timelimit="5"><result status="valid" time="0.060000" steps="13199"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_upper_bound&#39;vc" expl="VC for value_sub_upper_bound" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_upper_bound&#39;vc.0" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="17"/></proof>
  </goal>
  <goal name="value_sub_upper_bound&#39;vc.1" expl="assertion" proved="true">
  <proof prover="1"><result status="valid" time="0.060000"/></proof>
  </goal>
  <goal name="value_sub_upper_bound&#39;vc.2" expl="variant decrease" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="21"/></proof>
  </goal>
  <goal name="value_sub_upper_bound&#39;vc.3" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="21"/></proof>
  </goal>
  <goal name="value_sub_upper_bound&#39;vc.4" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.080000" steps="127"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_lower_bound_tight&#39;vc" expl="VC for value_sub_lower_bound_tight" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_lower_bound_tight&#39;vc.0" expl="assertion" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="17"/></proof>
  </goal>
  <goal name="value_sub_lower_bound_tight&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="6"><result status="valid" time="0.030000" steps="19"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_sub_upper_bound_tight&#39;vc" expl="VC for value_sub_upper_bound_tight" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="value_sub_upper_bound_tight&#39;vc.0" expl="precondition" proved="true">
  <proof prover="6"><result status="valid" time="0.040000" steps="15"/></proof>
  </goal>
  <goal name="value_sub_upper_bound_tight&#39;vc.1" expl="postcondition" proved="true">
  <proof prover="5"><result status="valid" time="0.020000" steps="52624"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="value_tail&#39;vc" expl="VC for value_tail" proved="true">
 <proof prover="6" timelimit="1"><result status="valid" time="0.010000" steps="19"/></proof>
 </goal>
 <goal name="value_concat&#39;vc" expl="VC for value_concat" proved="true">
 <proof prover="6" timelimit="1"><result status="valid" time="0.040000" steps="21"/></proof>
 </goal>
 <goal name="value_sub_eq&#39;vc" expl="VC for value_sub_eq" proved="true">
 <proof prover="3"><result status="valid" time="0.030000" steps="7145"/></proof>
 </goal>
</theory>
</file>
</why3session>
