<?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="CVC4" version="1.8" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.4.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.8.10" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="kleene_algebra.mlw"/>
<theory name="SemiRing" proved="true">
 <goal name="infix ^&#39;vc" expl="VC for infix ^" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="967"/></proof>
 </goal>
 <goal name="Exponentiation.Assoc" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="938"/></proof>
 </goal>
 <goal name="Exponentiation.Unit_def_l" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="984"/></proof>
 </goal>
 <goal name="Exponentiation.Unit_def_r" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="1028"/></proof>
 </goal>
 <goal name="Exponentiation.Power_0" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="1270"/></proof>
 </goal>
 <goal name="Exponentiation.Power_s" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="1584"/></proof>
 </goal>
</theory>
<theory name="Dioid" proved="true">
 <goal name="le_refl" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="1991"/></proof>
 </goal>
 <goal name="le_antisym" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="2177"/></proof>
 </goal>
 <goal name="le_trans" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="2288"/></proof>
 </goal>
 <goal name="zero_le" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="2237"/></proof>
 </goal>
 <goal name="le_compat_add" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="4350"/></proof>
 </goal>
 <goal name="le_add" proved="true">
 <proof prover="0"><result status="valid" time="0.03" steps="2793"/></proof>
 </goal>
 <goal name="le_add_le" proved="true">
 <proof prover="0"><result status="valid" time="0.01" steps="2591"/></proof>
 </goal>
 <goal name="add_le" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="3142"/></proof>
 </goal>
 <goal name="le_compat_add_left" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="2767"/></proof>
 </goal>
 <goal name="le_compat_add_right" proved="true">
 <proof prover="0"><result status="valid" time="0.03" steps="2859"/></proof>
 </goal>
</theory>
<theory name="KleeneAlgebra" proved="true">
 <goal name="one_le_star" proved="true">
 <proof prover="0"><result status="valid" time="0.03" steps="3429"/></proof>
 </goal>
 <goal name="mul_var_le_star" proved="true">
 <proof prover="0"><result status="valid" time="0.05" steps="4559"/></proof>
 </goal>
 <goal name="var_mul_le_star" proved="true">
 <proof prover="0"><result status="valid" time="0.04" steps="4885"/></proof>
 </goal>
 <goal name="power_le_star" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="power_le_star.0" proved="true">
  <transf name="induction" proved="true" arg1="i">
   <goal name="power_le_star.0.0" expl="base case" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="3695"/></proof>
   </goal>
   <goal name="power_le_star.0.1" expl="recursive case" proved="true">
   <proof prover="0"><result status="valid" time="0.04" steps="10567"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="star_mul_star" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="star_mul_star.0" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="3868"/></proof>
  </goal>
  <goal name="star_mul_star.1" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="12025"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="star_star" proved="true">
 <proof prover="0"><result status="valid" time="0.09" steps="21192"/></proof>
 </goal>
 <goal name="star_unfold_left" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="star_unfold_left.0" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="9147"/></proof>
  </goal>
  <goal name="star_unfold_left.1" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="5207"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="star_unfold_right" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="star_unfold_right.0" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="9038"/></proof>
  </goal>
  <goal name="star_unfold_right.1" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="5511"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="star_le" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="star_le.0" proved="true">
  <proof prover="0"><result status="valid" time="0.05" steps="7511"/></proof>
  </goal>
  <goal name="star_le.1" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="6513"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="le_star_left_right" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="le_star_left_right.0" proved="true">
  <proof prover="0"><result status="valid" time="0.27" steps="39530"/></proof>
  </goal>
  <goal name="le_star_left_right.1" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="3755"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="le_star_right_left" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="le_star_right_left.0" proved="true">
  <proof prover="0"><result status="valid" time="0.33" steps="39976"/></proof>
  </goal>
  <goal name="le_star_right_left.1" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="3869"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="slide_left" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="slide_left.0" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="4464"/></proof>
  </goal>
  <goal name="slide_left.1" proved="true">
  <proof prover="0"><result status="valid" time="0.15" steps="39962"/></proof>
  </goal>
  <goal name="slide_left.2" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="3956"/></proof>
  </goal>
  <goal name="slide_left.3" proved="true">
  <proof prover="0"><result status="valid" time="0.06" steps="4002"/></proof>
  </goal>
  <goal name="slide_left.4" proved="true">
  <proof prover="0"><result status="valid" time="0.08" steps="15041"/></proof>
  </goal>
  <goal name="slide_left.5" proved="true">
  <proof prover="0"><result status="valid" time="0.43" steps="82939"/></proof>
  </goal>
  <goal name="slide_left.6" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="12193"/></proof>
  </goal>
  <goal name="slide_left.7" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="4081"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="slide_right" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="slide_right.0" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="4569"/></proof>
  </goal>
  <goal name="slide_right.1" proved="true">
  <proof prover="0"><result status="valid" time="0.42" steps="56607"/></proof>
  </goal>
  <goal name="slide_right.2" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="4015"/></proof>
  </goal>
  <goal name="slide_right.3" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="4061"/></proof>
  </goal>
  <goal name="slide_right.4" proved="true">
  <proof prover="0"><result status="valid" time="0.07" steps="18874"/></proof>
  </goal>
  <goal name="slide_right.5" proved="true">
  <proof prover="0"><result status="valid" time="0.86" steps="112414"/></proof>
  </goal>
  <goal name="slide_right.6" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="14066"/></proof>
  </goal>
  <goal name="slide_right.7" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="4140"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sum_pow&#39;vc" expl="VC for sum_pow" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="4308"/></proof>
 </goal>
 <goal name="sum_pow_left" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="sum_pow_left.0" proved="true">
  <transf name="induction" proved="true" arg1="b" arg2="from" arg3="a">
   <goal name="sum_pow_left.0.0" expl="base case" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="4126"/></proof>
   </goal>
   <goal name="sum_pow_left.0.1" expl="recursive case" proved="true">
   <proof prover="0"><result status="valid" time="0.03" steps="8244"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="mul_sum_pow" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="mul_sum_pow.0" proved="true">
  <transf name="induction" proved="true" arg1="b" arg2="from" arg3="a">
   <goal name="mul_sum_pow.0.0" expl="base case" proved="true">
   <proof prover="0"><result status="valid" time="0.03" steps="4963"/></proof>
   </goal>
   <goal name="mul_sum_pow.0.1" expl="recursive case" proved="true">
   <proof prover="0"><result status="valid" time="0.03" steps="18505"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="sum_pow_le_star" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="sum_pow_le_star.0" proved="true">
  <transf name="induction" proved="true" arg1="b" arg2="from" arg3="a">
   <goal name="sum_pow_le_star.0.0" expl="base case" proved="true">
   <proof prover="0"><result status="valid" time="0.02" steps="5119"/></proof>
   </goal>
   <goal name="sum_pow_le_star.0.1" expl="recursive case" proved="true">
   <proof prover="0"><result status="valid" time="0.04" steps="9085"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="Conway_equality" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="Conway_equality.0" proved="true">
  <proof prover="0"><result status="valid" time="0.05" steps="12965"/></proof>
  </goal>
  <goal name="Conway_equality.1" proved="true">
  <proof prover="0"><result status="valid" time="0.09" steps="19218"/></proof>
  </goal>
  <goal name="Conway_equality.2" proved="true">
  <proof prover="0"><result status="valid" time="1.22" steps="188776"/></proof>
  </goal>
  <goal name="Conway_equality.3" proved="true">
  <proof prover="0"><result status="valid" time="1.42" steps="153270"/></proof>
  </goal>
  <goal name="Conway_equality.4" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="13927"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="RelAlgebra" proved="true">
 <goal name="zero_def" proved="true">
 <proof prover="0"><result status="valid" time="0.05" steps="10216"/></proof>
 </goal>
 <goal name="one_def" proved="true">
 <proof prover="0"><result status="valid" time="0.08" steps="13957"/></proof>
 </goal>
 <goal name="post&#39;vc" expl="VC for post" proved="true">
 <proof prover="0"><result status="valid" time="0.16" steps="38098"/></proof>
 </goal>
 <goal name="pre&#39;vc" expl="VC for pre" proved="true">
 <proof prover="0"><result status="valid" time="0.27" steps="55631"/></proof>
 </goal>
 <goal name="infix +&#39;vc" expl="VC for infix +" proved="true">
 <proof prover="0"><result status="valid" time="0.05" steps="13091"/></proof>
 </goal>
 <goal name="infix *&#39;vc" expl="VC for infix *" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="infix *&#39;vc.0" expl="postcondition" proved="true">
  <proof prover="1"><result status="valid" time="1.12" steps="6860"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="unit_l" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="unit_l.0" proved="true">
  <proof prover="1"><result status="valid" time="0.88" steps="5406"/></proof>
  </goal>
  <goal name="unit_l.1" proved="true">
  <proof prover="0"><result status="valid" time="0.05" steps="11495"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="unit_r" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="unit_r.0" proved="true">
  <proof prover="1"><result status="valid" time="0.86" steps="5414"/></proof>
  </goal>
  <goal name="unit_r.1" proved="true">
  <proof prover="0"><result status="valid" time="0.04" steps="11547"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="assoc_mul" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="assoc_mul.0" proved="true">
  <proof prover="1"><result status="valid" time="0.40" steps="2160"/></proof>
  </goal>
  <goal name="assoc_mul.1" proved="true">
  <proof prover="1"><result status="valid" time="0.40" steps="2160"/></proof>
  </goal>
  <goal name="assoc_mul.2" proved="true">
  <proof prover="2"><result status="valid" time="0.06" steps="93694"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="Dioid.Assoc" proved="true">
 <proof prover="0"><result status="valid" time="0.04" steps="12072"/></proof>
 </goal>
 <goal name="Dioid.Unit_def_l" proved="true">
 <proof prover="0"><result status="valid" time="0.04" steps="12471"/></proof>
 </goal>
 <goal name="Dioid.Unit_def_r" proved="true">
 <proof prover="0"><result status="valid" time="0.05" steps="12415"/></proof>
 </goal>
 <goal name="Dioid.Comm" proved="true">
 <proof prover="0"><result status="valid" time="0.06" steps="12069"/></proof>
 </goal>
 <goal name="Dioid.Monoid.Assoc" proved="true">
 <proof prover="0"><result status="valid" time="0.05" steps="11668"/></proof>
 </goal>
 <goal name="Dioid.Monoid.Unit_def_l" proved="true">
 <proof prover="0"><result status="valid" time="0.07" steps="11729"/></proof>
 </goal>
 <goal name="Dioid.Monoid.Unit_def_r" proved="true">
 <proof prover="0"><result status="valid" time="0.03" steps="11786"/></proof>
 </goal>
 <goal name="Dioid.Mul_zero_l" proved="true">
 <proof prover="1"><result status="valid" time="0.02" steps="88"/></proof>
 </goal>
 <goal name="Dioid.Mul_zero_r" proved="true">
 <proof prover="1"><result status="valid" time="0.03" steps="88"/></proof>
 </goal>
 <goal name="Dioid.Mul_distr_l" proved="true">
 <proof prover="1"><result status="valid" time="0.88" steps="8008"/></proof>
 </goal>
 <goal name="Dioid.Mul_distr_r" proved="true">
 <proof prover="1"><result status="valid" time="0.88" steps="8012"/></proof>
 </goal>
 <goal name="Dioid.Idem" proved="true">
 <proof prover="0"><result status="valid" time="0.09" steps="14041"/></proof>
 </goal>
 <goal name="le_mem" proved="true">
 <proof prover="0"><result status="valid" time="0.07" steps="19293"/></proof>
 </goal>
 <goal name="power_in_star" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="power_in_star.0" proved="true">
  <transf name="induction" proved="true" arg1="i">
   <goal name="power_in_star.0.0" expl="base case" proved="true">
   <proof prover="1"><result status="valid" time="1.20" steps="18857"/></proof>
   </goal>
   <goal name="power_in_star.0.1" expl="recursive case" proved="true">
   <transf name="split_all_full" proved="true" >
    <goal name="power_in_star.0.1.0" proved="true">
    <proof prover="2"><result status="valid" time="0.66" steps="721231"/></proof>
    </goal>
    <goal name="power_in_star.0.1.1" proved="true">
    <proof prover="2"><result status="valid" time="0.06" steps="196278"/></proof>
    </goal>
    <goal name="power_in_star.0.1.2" proved="true">
    <proof prover="2"><result status="valid" time="0.01" steps="7180"/></proof>
    </goal>
    <goal name="power_in_star.0.1.3" proved="true">
    <proof prover="1"><result status="valid" time="1.30" steps="8994"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="star_in_power" proved="true">
 <transf name="introduce_premises" proved="true" >
  <goal name="star_in_power.0" proved="true">
  <transf name="induction_arg_pr" proved="true" arg1="H" arg2="with_gen" arg3="x,y">
   <goal name="star_in_power.0.0" proved="true">
   <transf name="split_vc" proved="true" >
    <goal name="star_in_power.0.0.0" proved="true">
    <transf name="exists" proved="true" arg1="0">
     <goal name="star_in_power.0.0.0.0" proved="true">
     <proof prover="2"><result status="valid" time="0.03" steps="93559"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="star_in_power.0.1" proved="true">
   <proof prover="0"><result status="valid" time="0.29" steps="76210"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="star_spec" proved="true">
 <proof prover="1"><result status="valid" time="0.10" steps="991"/></proof>
 </goal>
 <goal name="star_unfold_l" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="star_unfold_l.0" proved="true">
  <proof prover="0"><result status="valid" time="0.07" steps="18099"/></proof>
  </goal>
  <goal name="star_unfold_l.1" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="119114"/></proof>
  </goal>
  <goal name="star_unfold_l.2" proved="true">
  <transf name="exists" proved="true" arg1="i">
   <goal name="star_unfold_l.2.0" proved="true">
   <proof prover="1" timelimit="10"><result status="valid" time="0.05" steps="242"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="star_unfold_l.3" proved="true">
  <proof prover="1"><result status="valid" time="0.32" steps="2543"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="star_unfold_r" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="star_unfold_r.0" proved="true">
  <proof prover="0"><result status="valid" time="0.10" steps="18187"/></proof>
  </goal>
  <goal name="star_unfold_r.1" proved="true">
  <proof prover="2"><result status="valid" time="0.05" steps="120089"/></proof>
  </goal>
  <goal name="star_unfold_r.2" proved="true">
  <transf name="exists" proved="true" arg1="i">
   <goal name="star_unfold_r.2.0" proved="true">
   <proof prover="1" timelimit="10"><result status="valid" time="0.03" steps="242"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="star_unfold_r.3" proved="true">
  <proof prover="0"><result status="valid" time="0.11" steps="39266"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="star_induct_left_ind" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="star_induct_left_ind.0" proved="true">
  <transf name="induction" proved="true" arg1="i">
   <goal name="star_induct_left_ind.0.0" expl="base case" proved="true">
   <proof prover="2"><result status="valid" time="0.04" steps="84058"/></proof>
   </goal>
   <goal name="star_induct_left_ind.0.1" expl="recursive case" proved="true">
   <proof prover="0"><result status="valid" time="0.42" steps="58173"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="star_induct_left_lem" proved="true">
 <transf name="rewrite" proved="true" arg1="&lt;-" arg2="le_mem">
  <goal name="star_induct_left_lem.0" proved="true">
  <proof prover="0"><result status="valid" time="0.05" steps="15554"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="star_induct_left" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="star_induct_left.0" proved="true">
  <proof prover="0"><result status="valid" time="0.09" steps="18170"/></proof>
  </goal>
  <goal name="star_induct_left.1" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="134568"/></proof>
  </goal>
  <goal name="star_induct_left.2" proved="true">
  <transf name="exists" proved="true" arg1="i">
   <goal name="star_induct_left.2.0" proved="true">
   <proof prover="1" timelimit="10"><result status="valid" time="0.04" steps="225"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="star_induct_left.3" proved="true">
  <proof prover="0"><result status="valid" time="0.32" steps="40648"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="star_induct_right_ind" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="star_induct_right_ind.0" proved="true">
  <transf name="induction" proved="true" arg1="i">
   <goal name="star_induct_right_ind.0.0" expl="base case" proved="true">
   <proof prover="2"><result status="valid" time="0.03" steps="86296"/></proof>
   </goal>
   <goal name="star_induct_right_ind.0.1" expl="recursive case" proved="true">
   <proof prover="2" timelimit="10"><result status="valid" time="0.54" steps="331724"/></proof>
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
 <goal name="star_induct_right_lem" proved="true">
 <transf name="rewrite" proved="true" arg1="&lt;-" arg2="le_mem">
  <goal name="star_induct_right_lem.0" proved="true">
  <proof prover="0"><result status="valid" time="0.05" steps="15948"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="star_induct_right" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="star_induct_right.0" proved="true">
  <proof prover="0"><result status="valid" time="0.09" steps="18595"/></proof>
  </goal>
  <goal name="star_induct_right.1" proved="true">
  <proof prover="2"><result status="valid" time="0.03" steps="137061"/></proof>
  </goal>
  <goal name="star_induct_right.2" proved="true">
  <transf name="exists" proved="true" arg1="i">
   <goal name="star_induct_right.2.0" proved="true">
   <proof prover="1" timelimit="10"><result status="valid" time="0.04" steps="226"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="star_induct_right.3" proved="true">
  <proof prover="0"><result status="valid" time="0.17" steps="43884"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="KleeneAlgebra.Assoc" proved="true">
 <proof prover="0"><result status="valid" time="0.06" steps="16180"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Unit_def_l" proved="true">
 <proof prover="0"><result status="valid" time="0.06" steps="16226"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Unit_def_r" proved="true">
 <proof prover="0"><result status="valid" time="0.12" steps="16270"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Comm" proved="true">
 <proof prover="0"><result status="valid" time="0.07" steps="16313"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Monoid.Assoc" proved="true">
 <proof prover="0"><result status="valid" time="0.08" steps="16697"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Monoid.Unit_def_l" proved="true">
 <proof prover="0"><result status="valid" time="0.03" steps="16758"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Monoid.Unit_def_r" proved="true">
 <proof prover="0"><result status="valid" time="0.05" steps="16815"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Mul_zero_l" proved="true">
 <proof prover="1"><result status="valid" time="0.02" steps="5"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Mul_zero_r" proved="true">
 <proof prover="1"><result status="valid" time="0.02" steps="5"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Mul_distr_l" proved="true">
 <proof prover="1"><result status="valid" time="0.02" steps="9"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Mul_distr_r" proved="true">
 <proof prover="1"><result status="valid" time="0.02" steps="9"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Idem" proved="true">
 <proof prover="0"><result status="valid" time="0.08" steps="17974"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Star_unfold_left" proved="true">
 <proof prover="0"><result status="valid" time="0.09" steps="22288"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Star_unfold_right" proved="true">
 <proof prover="0"><result status="valid" time="0.06" steps="23096"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Star_induct_left" proved="true">
 <proof prover="0"><result status="valid" time="0.12" steps="19757"/></proof>
 </goal>
 <goal name="KleeneAlgebra.Star_induct_right" proved="true">
 <proof prover="0"><result status="valid" time="0.08" steps="20006"/></proof>
 </goal>
</theory>
</file>
</why3session>
