<?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="Coq" version="8.11.2" timelimit="10" steplimit="0" memlimit="0"/>
<prover id="3" name="Z3" version="4.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="Alt-Ergo" version="2.2.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="11" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="edit_distance.mlw"/>
<theory name="Word" proved="true">
 <goal name="first_last_explicit" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="first_last_explicit.0" proved="true">
  <proof prover="11"><result status="valid" time="0.04" steps="7628"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="first_last" proved="true">
 <proof prover="11"><result status="valid" time="0.12" steps="25647"/></proof>
 </goal>
 <goal name="key_lemma_right" proved="true">
 <proof prover="0"><path name="edit_distance_Word_key_lemma_right_1.v"/><result status="valid" time="0.32"/></proof>
 </goal>
 <goal name="dist_symetry" proved="true">
 <transf name="induction_pr" proved="true" >
  <goal name="dist_symetry.0" proved="true">
  <proof prover="11"><result status="valid" time="0.01" steps="6165"/></proof>
  </goal>
  <goal name="dist_symetry.1" proved="true">
  <proof prover="11"><result status="valid" time="0.02" steps="7648"/></proof>
  </goal>
  <goal name="dist_symetry.2" proved="true">
  <proof prover="11"><result status="valid" time="0.02" steps="7648"/></proof>
  </goal>
  <goal name="dist_symetry.3" proved="true">
  <proof prover="11"><result status="valid" time="0.02" steps="6639"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="key_lemma_left" proved="true">
 <proof prover="3"><result status="valid" time="0.02" steps="32750"/></proof>
 </goal>
 <goal name="dist_concat_left" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="dist_concat_left.0" proved="true">
  <proof prover="4"><result status="valid" time="0.03" steps="192"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="dist_concat_right" proved="true">
 <proof prover="11"><result status="valid" time="0.03" steps="10138"/></proof>
 </goal>
 <goal name="min_dist_equal" proved="true">
 <transf name="inline_goal" proved="true" >
  <goal name="min_dist_equal.0" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="min_dist_equal.0.0" proved="true">
   <proof prover="11"><result status="valid" time="0.02" steps="6932"/></proof>
   </goal>
   <goal name="min_dist_equal.0.1" proved="true">
   <transf name="inversion_pr" proved="true" >
    <goal name="min_dist_equal.0.1.0" proved="true">
    <proof prover="11"><result status="valid" time="0.03" steps="7369"/></proof>
    </goal>
    <goal name="min_dist_equal.0.1.1" proved="true">
    <proof prover="3"><result status="valid" time="0.25" steps="428560"/></proof>
    </goal>
    <goal name="min_dist_equal.0.1.2" proved="true">
    <proof prover="3"><result status="valid" time="0.22" steps="403892"/></proof>
    </goal>
    <goal name="min_dist_equal.0.1.3" proved="true">
    <proof prover="4"><result status="valid" time="0.02" steps="111"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="min_dist_diff" proved="true">
 <proof prover="0"><path name="edit_distance_Word_min_dist_diff_1.v"/><result status="valid" time="0.31"/></proof>
 </goal>
 <goal name="min_dist_eps" proved="true">
 <transf name="inline_goal" proved="true" >
  <goal name="min_dist_eps.0" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="min_dist_eps.0.0" proved="true">
   <proof prover="11"><result status="valid" time="0.02" steps="8352"/></proof>
   </goal>
   <goal name="min_dist_eps.0.1" proved="true">
   <transf name="inversion_pr" proved="true" >
    <goal name="min_dist_eps.0.1.0" proved="true">
    <proof prover="11"><result status="valid" time="0.02" steps="7547"/></proof>
    </goal>
    <goal name="min_dist_eps.0.1.1" proved="true">
    <proof prover="11"><result status="valid" time="0.05" steps="17300"/></proof>
    </goal>
    <goal name="min_dist_eps.0.1.2" proved="true">
    <proof prover="11"><result status="valid" time="0.03" steps="7856"/></proof>
    </goal>
    <goal name="min_dist_eps.0.1.3" proved="true">
    <proof prover="11"><result status="valid" time="0.04" steps="7769"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="min_dist_eps_length" proved="true">
 <transf name="induction_ty_lex" proved="true" >
  <goal name="min_dist_eps_length.0" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="min_dist_eps_length.0.0" proved="true">
   <proof prover="11"><result status="valid" time="0.04" steps="8860"/></proof>
   </goal>
   <goal name="min_dist_eps_length.0.1" proved="true">
   <proof prover="5"><result status="valid" time="0.57" steps="82484"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="EditDistance" proved="true">
 <goal name="suffix_length" proved="true">
 <proof prover="0" timelimit="5" memlimit="1000"><path name="edit_distance_WP_EditDistance_suffix_length_1.v"/><result status="valid" time="0.34"/></proof>
 </goal>
 <goal name="distance&#39;vc" expl="VC for distance" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="distance&#39;vc.0" expl="array creation size" proved="true">
  <proof prover="11"><result status="valid" time="0.03" steps="9239"/></proof>
  </goal>
  <goal name="distance&#39;vc.1" expl="loop invariant init" proved="true">
  <proof prover="11"><result status="valid" time="0.01" steps="9486"/></proof>
  </goal>
  <goal name="distance&#39;vc.2" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.04" steps="10529"/></proof>
  </goal>
  <goal name="distance&#39;vc.3" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="58"/></proof>
  </goal>
  <goal name="distance&#39;vc.4" expl="loop invariant init" proved="true">
  <proof prover="3"><result status="valid" time="0.04" steps="58659"/></proof>
  </goal>
  <goal name="distance&#39;vc.5" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.02" steps="11389"/></proof>
  </goal>
  <goal name="distance&#39;vc.6" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.03" steps="11389"/></proof>
  </goal>
  <goal name="distance&#39;vc.7" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.03" steps="11389"/></proof>
  </goal>
  <goal name="distance&#39;vc.8" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.20" steps="1920"/></proof>
  </goal>
  <goal name="distance&#39;vc.9" expl="loop invariant init" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="234"/></proof>
  </goal>
  <goal name="distance&#39;vc.10" expl="loop invariant init" proved="true">
  <proof prover="11"><result status="valid" time="0.03" steps="12393"/></proof>
  </goal>
  <goal name="distance&#39;vc.11" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.02" steps="12819"/></proof>
  </goal>
  <goal name="distance&#39;vc.12" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.02" steps="12737"/></proof>
  </goal>
  <goal name="distance&#39;vc.13" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.02" steps="12751"/></proof>
  </goal>
  <goal name="distance&#39;vc.14" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.04" steps="13088"/></proof>
  </goal>
  <goal name="distance&#39;vc.15" expl="loop invariant preservation" proved="true">
  <proof prover="5"><result status="valid" time="0.13" steps="25682"/></proof>
  </goal>
  <goal name="distance&#39;vc.16" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="338"/></proof>
  </goal>
  <goal name="distance&#39;vc.17" expl="loop invariant preservation" proved="true">
  <proof prover="11"><result status="valid" time="0.04" steps="15450"/></proof>
  </goal>
  <goal name="distance&#39;vc.18" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.03" steps="13101"/></proof>
  </goal>
  <goal name="distance&#39;vc.19" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.04" steps="13076"/></proof>
  </goal>
  <goal name="distance&#39;vc.20" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.02" steps="13076"/></proof>
  </goal>
  <goal name="distance&#39;vc.21" expl="loop invariant preservation" proved="true">
  <transf name="unfold" proved="true" arg1="min_suffix">
   <goal name="distance&#39;vc.21.0" expl="loop invariant preservation" proved="true">
   <proof prover="4" timelimit="5"><result status="valid" time="0.11" steps="528"/></proof>
   <proof prover="5"><result status="valid" time="0.18" steps="28463"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="distance&#39;vc.22" expl="loop invariant preservation" proved="true">
  <proof prover="4"><result status="valid" time="0.01" steps="438"/></proof>
  </goal>
  <goal name="distance&#39;vc.23" expl="loop invariant preservation" proved="true">
  <proof prover="11"><result status="valid" time="0.04" steps="15857"/></proof>
  </goal>
  <goal name="distance&#39;vc.24" expl="loop invariant preservation" proved="true">
  <proof prover="11"><result status="valid" time="0.04" steps="13087"/></proof>
  </goal>
  <goal name="distance&#39;vc.25" expl="loop invariant preservation" proved="true">
  <proof prover="11"><result status="valid" time="0.03" steps="11495"/></proof>
  </goal>
  <goal name="distance&#39;vc.26" expl="index in array bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.04" steps="11113"/></proof>
  </goal>
  <goal name="distance&#39;vc.27" expl="postcondition" proved="true">
  <proof prover="11"><result status="valid" time="0.05" steps="11512"/></proof>
  </goal>
  <goal name="distance&#39;vc.28" expl="out of loop bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.05" steps="11241"/></proof>
  </goal>
  <goal name="distance&#39;vc.29" expl="out of loop bounds" proved="true">
  <proof prover="11"><result status="valid" time="0.06" steps="21070"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
