<?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="Alt-Ergo" version="2.3.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="CVC4" version="1.7" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml">
<path name=".."/><path name="380_doc_trans.mlw"/>
<theory name="Apply">
 <goal name="G">
 <transf name="apply" arg1="zero_is_even">
  <goal name="G.0" expl="apply premises">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Transitivity">
 <goal name="transitivity">
 </goal>
 <goal name="G" proved="true">
 <transf name="apply" proved="true" arg1="transitivity" arg2="with" arg3="c">
  <goal name="G.0" expl="apply premises" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="4"/></proof>
  </goal>
  <goal name="G.1" expl="apply premises" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="4"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Transitivity2">
 <goal name="t">
 </goal>
 <goal name="G" proved="true">
 <transf name="apply" proved="true" arg1="t" arg2="with" arg3="c,0">
  <goal name="G.0" expl="apply premises" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="4"/></proof>
  </goal>
  <goal name="G.1" expl="apply premises" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="4"/></proof>
  </goal>
  <goal name="G.2" expl="apply premises" proved="true">
  <proof prover="0"><result status="valid" time="0.000000" steps="4"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Assert">
 <goal name="G">
 <transf name="assert" arg1="(n = 0)" arg2="as" arg3="n0">
  <goal name="G.0" expl="asserted formula">
  <transf name="assert" arg1="(n = 0)">
   <goal name="G.0.0" expl="asserted formula">
   </goal>
   <goal name="G.0.1" expl="asserted formula">
   <transf name="case" arg1="(n = 0)">
    <goal name="G.0.1.0" expl="true case (asserted formula)">
    </goal>
    <goal name="G.0.1.1" expl="false case (asserted formula)">
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="G.1">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Case">
 <goal name="G">
 <transf name="case" arg1="(x = 0)">
  <goal name="G.0" expl="true case">
  </goal>
  <goal name="G.1" expl="false case">
  <transf name="clear_but" arg1="G">
   <goal name="G.1.0" expl="false case">
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Destruct">
 <goal name="G">
 <transf name="destruct" arg1="h">
  <goal name="G.0">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Destruct_rec">
 <goal name="G">
 <transf name="destruct_rec" arg1="H">
  <goal name="G.0">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Destruct_term">
 <goal name="G">
 <transf name="destruct_term" arg1="a">
  <goal name="G.0">
  </goal>
  <goal name="G.1">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Exists" proved="true">
 <goal name="G" proved="true">
 <transf name="exists" proved="true" arg1="0">
  <goal name="G.0" proved="true">
  <proof prover="1"><result status="valid" time="0.030000" steps="21"/></proof>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Hide">
 <goal name="h">
 </goal>
 <goal name="G">
 <transf name="hide" arg1="t" arg2="(1 + 1)">
  <goal name="G.0">
  </goal>
 </transf>
 <transf name="hide_and_clear" arg1="t" arg2="(1 + 1)">
  <goal name="G.0">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Induction">
 <goal name="G">
 <transf name="induction" arg1="n">
  <goal name="G.0" expl="base case">
  </goal>
  <goal name="G.1" expl="recursive case">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Instantiate">
 <goal name="G">
 <transf name="instantiate" arg1="h" arg2="0, 1">
  <goal name="G.0">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Intros">
 <goal name="G">
 <transf name="intros" arg1="n,m">
  <goal name="G.0">
  </goal>
 </transf>
 <transf name="intros_n" arg1="2">
  <goal name="G.0">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Left">
 <goal name="G">
 <transf name="left" >
  <goal name="G.0" expl="left case">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Pose">
 <goal name="G">
 <transf name="pose" arg1="t" arg2="(x + 2)">
  <goal name="G.0">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Remove">
 <goal name="h">
 </goal>
 <goal name="G">
 <transf name="remove" arg1="h">
  <goal name="G.0">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Replace">
 <goal name="G">
 <transf name="replace" arg1="(y + 1)" arg2="(x + 2)" arg3="in" arg4="h">
  <goal name="G.0">
  </goal>
  <goal name="G.1" expl="equality hypothesis">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Revert">
 <goal name="G">
 <transf name="revert" arg1="x">
  <goal name="G.0">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Rewrite">
 <goal name="G">
 <transf name="rewrite" arg1="eq">
  <goal name="G.0">
  </goal>
  <goal name="G.1" expl="rewrite premises">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Rewrite2">
 <goal name="G">
 <transf name="rewrite" arg1="eq" arg2="with" arg3="0">
  <goal name="G.0">
  </goal>
  <goal name="G.1" expl="rewrite premises">
  </goal>
  <goal name="G.2" expl="rewrite premises">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Right">
 <goal name="G">
 <transf name="right" >
  <goal name="G.0" expl="right case">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Subst">
 <goal name="G">
 <transf name="subst" arg1="x">
  <goal name="G.0">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Subst_all">
 <goal name="G">
 <transf name="subst_all" >
  <goal name="G.0">
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Unfold">
 <goal name="h">
 </goal>
 <goal name="G">
 <transf name="unfold" arg1="p">
  <goal name="G.0">
  <transf name="unfold" arg1="p" arg2="in" arg3="h">
   <goal name="G.0.0">
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
<theory name="Use_th">
 <goal name="G">
 <transf name="use_th" arg1="int.Int">
  <goal name="G.0">
  <transf name="replace" arg1="5" arg2="(2 + 3)">
   <goal name="G.0.0">
   </goal>
   <goal name="G.0.1" expl="equality hypothesis">
   </goal>
  </transf>
  </goal>
 </transf>
 </goal>
</theory>
</file>
</why3session>
