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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v2//EN" "http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="4">
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 <prover
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  id="0"
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  name="Alt-Ergo"
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  version="0.95.1"/>
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 <prover
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  id="1"
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  name="CVC3"
  version="2.2"/>
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 <prover
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  id="2"
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  name="CVC3"
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  version="2.4.1"/>
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 <prover
  id="3"
  name="CVC4"
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  version="1.2"/>
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 <prover
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  id="4"
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  name="Coq"
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  version="8.4pl2"/>
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 <prover
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  id="5"
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  name="Eprover"
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  version="1.6"/>
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 <prover
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  id="6"
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  name="Gappa"
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  version="1.0.0"/>
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 <prover
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  id="7"
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  name="Spass"
  version="3.7"/>
 <prover
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  id="8"
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  name="Vampire"
  version="0.6"/>
 <prover
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  id="9"
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  name="Yices"
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  version="1.0.38"/>
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 <prover
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  id="10"
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  name="Z3"
  version="2.19"/>
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 <prover
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  id="11"
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  name="Z3"
  version="3.2"/>
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 <prover
  id="12"
  name="Z3"
  version="4.3.1"/>
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 <file
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  name="../heapsort.mlw"
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  verified="true"
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  expanded="false">
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  <theory
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   name="HeapSort"
   locfile="../heapsort.mlw"
   loclnum="2" loccnumb="7" loccnume="15"
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   verified="true"
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   expanded="false">
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   <goal
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    name="Min_of_sorted"
    locfile="../heapsort.mlw"
    loclnum="15" loccnumb="6" loccnume="19"
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    sum="c7b6ff0d7d7a8503fcad8e4a6f0b639f"
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    proved="true"
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    expanded="false"
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    shape="ainfix =amin_bagaelementsV0V1V2agetV0V1Iasorted_subV0c0V2Iainfix &lt;V1V2Aainfix &lt;=c0V1F">
    <proof
     prover="4"
     timelimit="3"
     memlimit="0"
     edited="heapsort_WP_HeapSort_Min_of_sorted_1.v"
     obsolete="false"
     archived="false">
     <result status="valid" time="1.52"/>
    </proof>
   </goal>
   <goal
    name="WP_parameter heapSort"
    locfile="../heapsort.mlw"
    loclnum="22" loccnumb="4" loccnume="12"
    expl="VC for heapSort"
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    sum="35adc47d4457244aba40acc792b9ba5e"
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    proved="true"
    expanded="false"
    shape="ainfix =aelementsV7c0V0aelementsV1c0V0Aasorted_subV7c0V0Aainfix &lt;=c0V0Iainfix &lt;=agetV7V8amin_bagamodelV6Iainfix &lt;V8ainfix +V5c1Aainfix &lt;=c0V8FAasorted_subV7c0ainfix +V5c1Aainfix =aelementsV1c0V0aunionamodelV6aelementsV7c0ainfix +V5c1Aainfix =acardamodelV6ainfix -V0ainfix +V5c1Aainfix &lt;=ainfix +V5c1V0Aainfix &lt;=c0ainfix +V5c1Aainfix &lt;=agetV12V13amin_bagamodelV10Iainfix &lt;V13ainfix +V9c1Aainfix &lt;=c0V13FAasorted_subV12c0ainfix +V9c1Aainfix =aelementsV1c0V0aunionamodelV10aelementsV12c0ainfix +V9c1Aainfix =acardamodelV10ainfix -V0ainfix +V9c1Aainfix &lt;=ainfix +V9c1V0Aainfix &lt;=c0ainfix +V9c1Aainfix &lt;=agetV12V9amin_bagamodelV10Iainfix =V12asetV7V9V11Aainfix &lt;=c0V0FAainfix &lt;V9V0Aainfix &lt;=c0V9Aainfix &lt;=c0V0Iainfix =acardamodelV6ainfix +acardamodelV10c1Aainfix =amodelV6aaddV11amodelV10Lamin_bagamodelV6FANainfix =amodelV6aempty_bagIainfix &lt;=agetV7V14amin_bagamodelV6Iainfix &lt;V14V9Aainfix &lt;=c0V14FAasorted_subV7c0V9Aainfix =aelementsV1c0V0aunionamodelV6aelementsV7c0V9Aainfix =acardamodelV6ainfix -V0V9Aainfix &lt;=V9V0Aainfix &lt;=c0V9Iainfix &lt;=V9V5Aainfix &lt;=c0V9FFAainfix &lt;=agetV1V15amin_bagamodelV4Iainfix &lt;V15c0Aainfix &lt;=c0V15FAasorted_subV1c0c0Aainfix =aelementsV1c0V0aunionamodelV4aelementsV1c0c0Aainfix =acardamodelV4ainfix -V0c0Aainfix &lt;=c0V0Aainfix &lt;=c0c0Iainfix &lt;=c0V5Aasorted_subV1c0V0Iainfix &gt;c0V5Lainfix -V0c1Iainfix =amodelV4aelementsV1c0ainfix +V3c1Aainfix =acardamodelV4ainfix +V3c1Aainfix &lt;=ainfix +V3c1V0Aainfix &lt;=c0ainfix +V3c1Aainfix =amodelV17aelementsV1c0ainfix +V16c1Aainfix =acardamodelV17ainfix +V16c1Aainfix &lt;=ainfix +V16c1V0Aainfix &lt;=c0ainfix +V16c1Iainfix =amodelV17aaddagetV1V16amodelV4FAainfix &lt;V16V0Aainfix &lt;=c0V16Iainfix =amodelV4aelementsV1c0V16Aainfix =acardamodelV4V16Aainfix &lt;=V16V0Aainfix &lt;=c0V16Iainfix &lt;=V16V3Aainfix &lt;=c0V16FFAainfix =amodelV2aelementsV1c0c0Aainfix =acardamodelV2c0Aainfix &lt;=c0V0Aainfix &lt;=c0c0Iainfix &lt;=c0V3Aainfix =aelementsV20c0V0aelementsV1c0V0Aasorted_subV20c0V0Aainfix &lt;=c0V0Iainfix &lt;=agetV20V21amin_bagamodelV19Iainfix &lt;V21ainfix +V18c1Aainfix &lt;=c0V21FAasorted_subV20c0ainfix +V18c1Aainfix =aelementsV1c0V0aunionamodelV19aelementsV20c0ainfix +V18c1Aainfix =acardamodelV19ainfix -V0ainfix +V18c1Aainfix &lt;=ainfix +V18c1V0Aainfix &lt;=c0ainfix +V18c1Aainfix &lt;=agetV25V26amin_bagamodelV23Iainfix &lt;V26ainfix +V22c1Aainfix &lt;=c0V26FAasorted_subV25c0ainfix +V22c1Aainfix =aelementsV1c0V0aunionamodelV23aelementsV25c0ainfix +V22c1Aainfix =acardamodelV23ainfix -V0ainfix +V22c1Aainfix &lt;=ainfix +V22c1V0Aainfix &lt;=c0ainfix +V22c1Aainfix &lt;=agetV25V22amin_bagamodelV23Iainfix =V25asetV20V22V24Aainfix &lt;=c0V0FAainfix &lt;V22V0Aainfix &lt;=c0V22Aainfix &lt;=c0V0Iainfix =acardamodelV19ainfix +acardamodelV23c1Aainfix =amodelV19aaddV24amodelV23Lamin_bagamodelV19FANainfix =amodelV19aempty_bagIainfix &lt;=agetV20V27amin_bagamodelV19Iainfix &lt;V27V22Aainfix &lt;=c0V27FAasorted_subV20c0V22Aainfix =aelementsV1c0V0aunionamodelV19aelementsV20c0V22Aainfix =acardamodelV19ainfix -V0V22Aainfix &lt;=V22V0Aainfix &lt;=c0V22Iainfix &lt;=V22V18Aainfix &lt;=c0V22FFAainfix &lt;=agetV1V28amin_bagamodelV2Iainfix &lt;V28c0Aainfix &lt;=c0V28FAasorted_subV1c0c0Aainfix =aelementsV1c0V0aunionamodelV2aelementsV1c0c0Aainfix =acardamodelV2ainfix -V0c0Aainfix &lt;=c0V0Aainfix &lt;=c0c0Iainfix &lt;=c0V18Aasorted_subV1c0V0Iainfix &gt;c0V18Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFAainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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    <label
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     name="expl:VC for heapSort"/>
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    <transf
     name="split_goal"
     proved="true"
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     expanded="false">
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     <goal
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      name="WP_parameter heapSort.1"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
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      expl="1. precondition"
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      sum="fae15bcf8e8771fcdd82778329621100"
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      proved="true"
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      expanded="false"
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      shape="preconditionainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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      <label
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       name="expl:VC for heapSort"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="9"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.03"/>
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      </proof>
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      <proof
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       prover="10"
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       timelimit="3"
       memlimit="0"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
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     </goal>
     <goal
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      name="WP_parameter heapSort.2"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
      expl="2. postcondition"
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      sum="5c7038ea8d904e3b3b9fb7aa958a52b1"
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      proved="true"
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      expanded="false"
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      shape="postconditionasorted_subV1c0V0Iainfix &gt;c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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      <label
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       name="expl:VC for heapSort"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.00"/>
      </proof>
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      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
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      <proof
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       prover="10"
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       timelimit="3"
       memlimit="0"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
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     </goal>
     <goal
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      name="WP_parameter heapSort.3"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
      expl="3. loop invariant init"
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      sum="9886d076707605ed43fec56b31378e67"
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      proved="true"
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      expanded="false"
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      shape="loop invariant initainfix &lt;=agetV1V5amin_bagamodelV2Iainfix &lt;V5c0Aainfix &lt;=c0V5FAasorted_subV1c0c0Aainfix =aelementsV1c0V0aunionamodelV2aelementsV1c0c0Aainfix =acardamodelV2ainfix -V0c0Aainfix &lt;=c0V0Aainfix &lt;=c0c0Iainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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      <label
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       name="expl:VC for heapSort"/>
      <transf
       name="split_goal"
       proved="true"
       expanded="false">
       <goal
        name="WP_parameter heapSort.3.1"
        locfile="../heapsort.mlw"
        loclnum="22" loccnumb="4" loccnume="12"
        expl="1."
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        sum="e99ad6810d10ce8601859c1986bf9786"
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        proved="true"
        expanded="false"
        shape="ainfix &lt;=c0c0Iainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
        <label
         name="expl:VC for heapSort"/>
        <proof
         prover="0"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
        <proof
         prover="1"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.01"/>
        </proof>
        <proof
         prover="9"
         timelimit="10"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.03"/>
        </proof>
        <proof
         prover="10"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.00"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter heapSort.3.2"
        locfile="../heapsort.mlw"
        loclnum="22" loccnumb="4" loccnume="12"
        expl="2."
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        sum="c4b0b4e8ba8f4e00765733cd5c7f13c6"
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        proved="true"
        expanded="false"
        shape="ainfix &lt;=c0V0Iainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
        <label
         name="expl:VC for heapSort"/>
        <proof
         prover="0"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.01"/>
        </proof>
        <proof
         prover="10"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.00"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter heapSort.3.3"
        locfile="../heapsort.mlw"
        loclnum="22" loccnumb="4" loccnume="12"
        expl="3."
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        sum="381c76578f3e03036efe37e13faddc38"
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        proved="true"
        expanded="false"
        shape="ainfix =acardamodelV2ainfix -V0c0Iainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
        <label
         name="expl:VC for heapSort"/>
        <proof
         prover="0"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.01"/>
        </proof>
        <proof
         prover="1"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
        <proof
         prover="8"
         timelimit="30"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.15"/>
        </proof>
        <proof
         prover="9"
         timelimit="10"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.01"/>
        </proof>
        <proof
         prover="10"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.00"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter heapSort.3.4"
        locfile="../heapsort.mlw"
        loclnum="22" loccnumb="4" loccnume="12"
        expl="4."
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        sum="06e53da4596c41e6144f24d169e06436"
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        proved="true"
        expanded="false"
        shape="ainfix =aelementsV1c0V0aunionamodelV2aelementsV1c0c0Iainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
        <label
         name="expl:VC for heapSort"/>
        <proof
         prover="0"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.01"/>
        </proof>
        <proof
         prover="1"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.03"/>
        </proof>
        <proof
         prover="9"
         timelimit="10"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
        <proof
         prover="10"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.00"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter heapSort.3.5"
        locfile="../heapsort.mlw"
        loclnum="22" loccnumb="4" loccnume="12"
        expl="5."
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        sum="b5d42e9104172194f816dc83aa5f3543"
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        proved="true"
        expanded="false"
        shape="asorted_subV1c0c0Iainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
        <label
         name="expl:VC for heapSort"/>
        <proof
         prover="0"
         timelimit="10"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.01"/>
        </proof>
       </goal>
       <goal
        name="WP_parameter heapSort.3.6"
        locfile="../heapsort.mlw"
        loclnum="22" loccnumb="4" loccnume="12"
        expl="6."
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        sum="e5255b96328ffbb4a5cf89a32afd68ec"
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        proved="true"
        expanded="false"
        shape="ainfix &lt;=agetV1V5amin_bagamodelV2Iainfix &lt;V5c0Aainfix &lt;=c0V5FIainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
        <label
         name="expl:VC for heapSort"/>
        <proof
         prover="0"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.01"/>
        </proof>
        <proof
         prover="1"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
        <proof
         prover="9"
         timelimit="10"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.03"/>
        </proof>
        <proof
         prover="10"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.00"/>
        </proof>
       </goal>
      </transf>
     </goal>
     <goal
      name="WP_parameter heapSort.4"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
      expl="4. precondition"
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      sum="20626f08e2633a81bed44575d2d011f0"
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      proved="true"
      expanded="false"
      shape="preconditionNainfix =amodelV5aempty_bagIainfix &lt;=agetV6V8amin_bagamodelV5Iainfix &lt;V8V7Aainfix &lt;=c0V8FAasorted_subV6c0V7Aainfix =aelementsV1c0V0aunionamodelV5aelementsV6c0V7Aainfix =acardamodelV5ainfix -V0V7Aainfix &lt;=V7V0Aainfix &lt;=c0V7Iainfix &lt;=V7V4Aainfix &lt;=c0V7FFIainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
      <label
       name="expl:VC for heapSort"/>
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      <proof
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       prover="0"
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       timelimit="5"
       memlimit="1000"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
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     </goal>
     <goal
      name="WP_parameter heapSort.5"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
      expl="5. type invariant"
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      sum="0300b3efe9ef4d3f331684095a1a1858"
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      proved="true"
      expanded="false"
      shape="type invariantainfix &lt;=c0V0Iainfix =acardamodelV5ainfix +acardamodelV8c1Aainfix =amodelV5aaddV9amodelV8Lamin_bagamodelV5FINainfix =amodelV5aempty_bagIainfix &lt;=agetV6V10amin_bagamodelV5Iainfix &lt;V10V7Aainfix &lt;=c0V10FAasorted_subV6c0V7Aainfix =aelementsV1c0V0aunionamodelV5aelementsV6c0V7Aainfix =acardamodelV5ainfix -V0V7Aainfix &lt;=V7V0Aainfix &lt;=c0V7Iainfix &lt;=V7V4Aainfix &lt;=c0V7FFIainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
      <label
       name="expl:VC for heapSort"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter heapSort.6"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
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      expl="6. index in array bounds"
      sum="faa4893c3dad42a28a3d2dfd6b3ac335"
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      proved="true"
      expanded="false"
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      shape="index in array boundsainfix &lt;V7V0Aainfix &lt;=c0V7Iainfix &lt;=c0V0Iainfix =acardamodelV5ainfix +acardamodelV8c1Aainfix =amodelV5aaddV9amodelV8Lamin_bagamodelV5FINainfix =amodelV5aempty_bagIainfix &lt;=agetV6V10amin_bagamodelV5Iainfix &lt;V10V7Aainfix &lt;=c0V10FAasorted_subV6c0V7Aainfix =aelementsV1c0V0aunionamodelV5aelementsV6c0V7Aainfix =acardamodelV5ainfix -V0V7Aainfix &lt;=V7V0Aainfix &lt;=c0V7Iainfix &lt;=V7V4Aainfix &lt;=c0V7FFIainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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      <label
       name="expl:VC for heapSort"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter heapSort.7"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
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      expl="7. assertion"
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      sum="7c837b0c28ba8c4ac825322bbce32d89"
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      proved="true"
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      expanded="false"
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      shape="assertionainfix &lt;=agetV10V7amin_bagamodelV8Iainfix =V10asetV6V7V9Aainfix &lt;=c0V0FIainfix &lt;V7V0Aainfix &lt;=c0V7Aainfix &lt;=c0V0Iainfix =acardamodelV5ainfix +acardamodelV8c1Aainfix =amodelV5aaddV9amodelV8Lamin_bagamodelV5FINainfix =amodelV5aempty_bagIainfix &lt;=agetV6V11amin_bagamodelV5Iainfix &lt;V11V7Aainfix &lt;=c0V11FAasorted_subV6c0V7Aainfix =aelementsV1c0V0aunionamodelV5aelementsV6c0V7Aainfix =acardamodelV5ainfix -V0V7Aainfix &lt;=V7V0Aainfix &lt;=c0V7Iainfix &lt;=V7V4Aainfix &lt;=c0V7FFIainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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      <label
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       name="expl:VC for heapSort"/>
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      <proof
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       prover="0"
       timelimit="5"
       memlimit="1000"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter heapSort.8"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
      expl="8. loop invariant preservation"
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      sum="577dc760d8ab32b421985ca26989143d"
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      proved="true"
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      expanded="false"
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      shape="loop invariant preservationainfix &lt;=agetV10V11amin_bagamodelV8Iainfix &lt;V11ainfix +V7c1Aainfix &lt;=c0V11FAasorted_subV10c0ainfix +V7c1Aainfix =aelementsV1c0V0aunionamodelV8aelementsV10c0ainfix +V7c1Aainfix =acardamodelV8ainfix -V0ainfix +V7c1Aainfix &lt;=ainfix +V7c1V0Aainfix &lt;=c0ainfix +V7c1Iainfix &lt;=agetV10V7amin_bagamodelV8Iainfix =V10asetV6V7V9Aainfix &lt;=c0V0FIainfix &lt;V7V0Aainfix &lt;=c0V7Aainfix &lt;=c0V0Iainfix =acardamodelV5ainfix +acardamodelV8c1Aainfix =amodelV5aaddV9amodelV8Lamin_bagamodelV5FINainfix =amodelV5aempty_bagIainfix &lt;=agetV6V12amin_bagamodelV5Iainfix &lt;V12V7Aainfix &lt;=c0V12FAasorted_subV6c0V7Aainfix =aelementsV1c0V0aunionamodelV5aelementsV6c0V7Aainfix =acardamodelV5ainfix -V0V7Aainfix &lt;=V7V0Aainfix &lt;=c0V7Iainfix &lt;=V7V4Aainfix &lt;=c0V7FFIainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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      <label
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       name="expl:VC for heapSort"/>
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      <proof
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       prover="0"
       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.03"/>
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      </proof>
      <proof
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       prover="5"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.04"/>
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      </proof>
      <proof
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       prover="9"
       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.03"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter heapSort.9"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
      expl="9. type invariant"
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      sum="cfd3f421d9b5b9e4c04521d631cceb60"
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      proved="true"
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      expanded="false"
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      shape="type invariantainfix &lt;=c0V0Iainfix &lt;=agetV6V7amin_bagamodelV5Iainfix &lt;V7ainfix +V4c1Aainfix &lt;=c0V7FAasorted_subV6c0ainfix +V4c1Aainfix =aelementsV1c0V0aunionamodelV5aelementsV6c0ainfix +V4c1Aainfix =acardamodelV5ainfix -V0ainfix +V4c1Aainfix &lt;=ainfix +V4c1V0Aainfix &lt;=c0ainfix +V4c1FIainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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      <label
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       name="expl:VC for heapSort"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter heapSort.10"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
      expl="10. postcondition"
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      sum="d33b959a6eac6ffefbbf197cf093f45a"
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      proved="true"
      expanded="false"
      shape="postconditionainfix =aelementsV6c0V0aelementsV1c0V0Aasorted_subV6c0V0Iainfix &lt;=c0V0Iainfix &lt;=agetV6V7amin_bagamodelV5Iainfix &lt;V7ainfix +V4c1Aainfix &lt;=c0V7FAasorted_subV6c0ainfix +V4c1Aainfix =aelementsV1c0V0aunionamodelV5aelementsV6c0ainfix +V4c1Aainfix =acardamodelV5ainfix -V0ainfix +V4c1Aainfix &lt;=ainfix +V4c1V0Aainfix &lt;=c0ainfix +V4c1FIainfix &lt;=c0V4Lainfix -V0c1Iainfix &gt;c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
      <label
       name="expl:VC for heapSort"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
      </proof>
      <proof
       prover="6"
       timelimit="10"
       memlimit="0"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
       prover="9"
       timelimit="10"
       memlimit="0"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
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      </proof>
      <proof
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       prover="10"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.00"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter heapSort.11"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
      expl="11. loop invariant init"
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      sum="e88365bdc53bd43d50731210d1b94839"
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      proved="true"
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      expanded="false"
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      shape="loop invariant initainfix =amodelV2aelementsV1c0c0Aainfix =acardamodelV2c0Aainfix &lt;=c0V0Aainfix &lt;=c0c0Iainfix &lt;=c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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      <label
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       name="expl:VC for heapSort"/>
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      <proof
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       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
      <proof
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       prover="9"
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       timelimit="10"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.03"/>
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      </proof>
      <proof
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       prover="10"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.04"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter heapSort.12"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
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      expl="12. index in array bounds"
      sum="b7b7289b05e99c8aa37b77fb6f40b0f5"
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      proved="true"
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      expanded="false"
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      shape="index in array boundsainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix =amodelV4aelementsV1c0V5Aainfix =acardamodelV4V5Aainfix &lt;=V5V0Aainfix &lt;=c0V5Iainfix &lt;=V5V3Aainfix &lt;=c0V5FFIainfix &lt;=c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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      <label
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       name="expl:VC for heapSort"/>
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      <proof
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       prover="0"
       timelimit="5"
       memlimit="1000"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter heapSort.13"
      locfile="../heapsort.mlw"
      loclnum="22" loccnumb="4" loccnume="12"
      expl="13. loop invariant preservation"
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      sum="8808cb918c7c227780b638a2d5641181"
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      proved="true"
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      expanded="false"
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      shape="loop invariant preservationainfix =amodelV6aelementsV1c0ainfix +V5c1Aainfix =acardamodelV6ainfix +V5c1Aainfix &lt;=ainfix +V5c1V0Aainfix &lt;=c0ainfix +V5c1Iainfix =amodelV6aaddagetV1V5amodelV4FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix =amodelV4aelementsV1c0V5Aainfix =acardamodelV4V5Aainfix &lt;=V5V0Aainfix &lt;=c0V5Iainfix &lt;=V5V3Aainfix &lt;=c0V5FFIainfix &lt;=c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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      <label
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       name="expl:VC for heapSort"/>
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      <transf
       name="split_goal"
       proved="true"
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       expanded="false">
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       <goal
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        name="WP_parameter heapSort.13.1"
        locfile="../heapsort.mlw"
        loclnum="22" loccnumb="4" loccnume="12"
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        expl="1."
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        sum="27020a6fde8ac5b16ad89235c1918bbf"
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        proved="true"
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        expanded="false"
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        shape="ainfix &lt;=c0ainfix +V5c1Iainfix =amodelV6aaddagetV1V5amodelV4FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix =amodelV4aelementsV1c0V5Aainfix =acardamodelV4V5Aainfix &lt;=V5V0Aainfix &lt;=c0V5Iainfix &lt;=V5V3Aainfix &lt;=c0V5FFIainfix &lt;=c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
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        <label
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         name="expl:VC for heapSort"/>
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        <proof
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         prover="0"
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         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.02"/>
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        </proof>
        <proof
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         prover="1"
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         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
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Andrei Paskevich committed
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         <result status="valid" time="0.02"/>
Andrei Paskevich's avatar
Andrei Paskevich committed
729 730
        </proof>
        <proof
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         prover="5"
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Andrei Paskevich committed
732 733 734 735
         timelimit="10"
         memlimit="0"
         obsolete="false"
         archived="false">
MARCHE Claude's avatar
MARCHE Claude committed
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         <result status="valid" time="0.03"/>
Andrei Paskevich's avatar
Andrei Paskevich committed
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        </proof>
        <proof
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         prover="8"
         timelimit="5"
Andrei Paskevich's avatar
Andrei Paskevich committed
741 742 743
         memlimit="0"
         obsolete="false"
         archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
744
         <result status="valid" time="0.11"/>
Andrei Paskevich's avatar
Andrei Paskevich committed
745 746
        </proof>
        <proof
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         prover="9"
         timelimit="10"
Andrei Paskevich's avatar
Andrei Paskevich committed
749 750 751
         memlimit="0"
         obsolete="false"
         archived="false">
752
         <result status="valid" time="0.03"/>
Andrei Paskevich's avatar
Andrei Paskevich committed
753 754
        </proof>
        <proof
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Andrei Paskevich committed
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         prover="10"
         timelimit="3"
Andrei Paskevich's avatar
Andrei Paskevich committed
757 758 759
         memlimit="0"
         obsolete="false"
         archived="false">
760
         <result status="valid" time="0.04"/>
Andrei Paskevich's avatar
Andrei Paskevich committed
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        </proof>
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Andrei Paskevich committed
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       </goal>
       <goal
        name="WP_parameter heapSort.13.2"
        locfile="../heapsort.mlw"
        loclnum="22" loccnumb="4" loccnume="12"
        expl="2."
MARCHE Claude's avatar
MARCHE Claude committed
768
        sum="10fb9996df2b6982d0f34febdf0fdfa7"
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Andrei Paskevich committed
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        proved="true"
        expanded="false"
        shape="ainfix &lt;=ainfix +V5c1V0Iainfix =amodelV6aaddagetV1V5amodelV4FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix =amodelV4aelementsV1c0V5Aainfix =acardamodelV4V5Aainfix &lt;=V5V0Aainfix &lt;=c0V5Iainfix &lt;=V5V3Aainfix &lt;=c0V5FFIainfix &lt;=c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
        <label
         name="expl:VC for heapSort"/>
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Andrei Paskevich committed
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        <proof
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         prover="1"
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         timelimit="3"
Andrei Paskevich's avatar
Andrei Paskevich committed
777 778 779
         memlimit="0"
         obsolete="false"
         archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
780
         <result status="valid" time="0.02"/>
Andrei Paskevich's avatar
Andrei Paskevich committed
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        </proof>
       </goal>
       <goal
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        name="WP_parameter heapSort.13.3"
        locfile="../heapsort.mlw"
        loclnum="22" loccnumb="4" loccnume="12"
787
        expl="3."
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MARCHE Claude committed
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        sum="841cf897229d3a07d06dd48c383fa19d"
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Andrei Paskevich committed
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        proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
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        expanded="false"
Andrei Paskevich's avatar
Andrei Paskevich committed
791
        shape="ainfix =acardamodelV6ainfix +V5c1Iainfix =amodelV6aaddagetV1V5amodelV4FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix =amodelV4aelementsV1c0V5Aainfix =acardamodelV4V5Aainfix &lt;=V5V0Aainfix &lt;=c0V5Iainfix &lt;=V5V3Aainfix &lt;=c0V5FFIainfix &lt;=c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
Andrei Paskevich's avatar
Andrei Paskevich committed
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        <label
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         name="expl:VC for heapSort"/>
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        <proof
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         prover="0"
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         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
800
         <result status="valid" time="0.01"/>
Andrei Paskevich's avatar
Andrei Paskevich committed
801 802
        </proof>
        <proof
803
         prover="1"
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Andrei Paskevich committed
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         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
808
         <result status="valid" time="0.02"/>
Andrei Paskevich's avatar
Andrei Paskevich committed
809 810
        </proof>
        <proof
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         prover="9"
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         timelimit="16"
Andrei Paskevich's avatar
Andrei Paskevich committed
813 814 815
         memlimit="0"
         obsolete="false"
         archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
816
         <result status="valid" time="0.03"/>
Andrei Paskevich's avatar
Andrei Paskevich committed
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        </proof>
        <proof
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         prover="10"
820
         timelimit="3"
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Andrei Paskevich committed
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         memlimit="0"
         obsolete="false"
         archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
824
         <result status="valid" time="0.04"/>
Andrei Paskevich's avatar
Andrei Paskevich committed
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        </proof>
       </goal>
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Andrei Paskevich committed
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       <goal
        name="WP_parameter heapSort.13.4"
        locfile="../heapsort.mlw"
        loclnum="22" loccnumb="4" loccnume="12"
        expl="4."
MARCHE Claude's avatar
MARCHE Claude committed
832
        sum="9cd8a27e15d54fc171dde47f81a9aece"
Andrei Paskevich's avatar
Andrei Paskevich committed
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        proved="true"
        expanded="false"
        shape="ainfix =amodelV6aelementsV1c0ainfix +V5c1Iainfix =amodelV6aaddagetV1V5amodelV4FIainfix &lt;V5V0Aainfix &lt;=c0V5Iainfix =amodelV4aelementsV1c0V5Aainfix =acardamodelV4V5Aainfix &lt;=V5V0Aainfix &lt;=c0V5Iainfix &lt;=V5V3Aainfix &lt;=c0V5FFIainfix &lt;=c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
        <label
         name="expl:VC for heapSort"/>
        <proof
         prover="0"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
        <proof
         prover="1"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.02"/>
        </proof>
        <proof
         prover="9"
         timelimit="10"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.03"/>
        </proof>
        <proof
         prover="10"
         timelimit="3"
         memlimit="0"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.03"/>
        </proof>
       </goal>
      </transf>
     </goal>
873
     <goal
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      name="WP_parameter heapSort.14"
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      locfile="../heapsort.mlw"
876
      loclnum="22" loccnumb="4" loccnume="12"
Andrei Paskevich's avatar
Andrei Paskevich committed
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      expl="14. postcondition"
MARCHE Claude's avatar
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      sum="fd1eca4aa375e88226d7d87e21638b88"
879
      proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
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      expanded="false"
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Andrei Paskevich committed
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      shape="postconditionasorted_subV1c0V0Iainfix &gt;c0V5Lainfix -V0c1Iainfix =amodelV4aelementsV1c0ainfix +V3c1Aainfix =acardamodelV4ainfix +V3c1Aainfix &lt;=ainfix +V3c1V0Aainfix &lt;=c0ainfix +V3c1FIainfix &lt;=c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
882
      <label
883
       name="expl:VC for heapSort"/>
884
      <proof
885
       prover="0"
886
       timelimit="3"
887
       memlimit="0"
888 889
       obsolete="false"
       archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
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       <result status="valid" time="0.02"/>
891 892
      </proof>
      <proof
893
       prover="1"
894
       timelimit="3"
895
       memlimit="0"
896 897
       obsolete="false"
       archived="false">
898
       <result status="valid" time="0.03"/>
899 900
      </proof>
      <proof
901
       prover="10"
902
       timelimit="3"
903
       memlimit="0"
904 905
       obsolete="false"
       archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
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       <result status="valid" time="0.04"/>
907
      </proof>
MARCHE Claude's avatar
MARCHE Claude committed
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     </goal>
909
     <goal
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Andrei Paskevich committed
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      name="WP_parameter heapSort.15"
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      locfile="../heapsort.mlw"
912
      loclnum="22" loccnumb="4" loccnume="12"
Andrei Paskevich's avatar
Andrei Paskevich committed
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      expl="15. loop invariant init"
MARCHE Claude's avatar
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      sum="023a3f086cb6352cee3ca0739351229b"
915
      proved="true"
MARCHE Claude's avatar
MARCHE Claude committed
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      expanded="false"
Andrei Paskevich's avatar
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      shape="loop invariant initainfix &lt;=agetV1V6amin_bagamodelV4Iainfix &lt;V6c0Aainfix &lt;=c0V6FAasorted_subV1c0c0Aainfix =aelementsV1c0V0aunionamodelV4aelementsV1c0c0Aainfix =acardamodelV4ainfix -V0c0Aainfix &lt;=c0V0Aainfix &lt;=c0c0Iainfix &lt;=c0V5Lainfix -V0c1Iainfix =amodelV4aelementsV1c0ainfix +V3c1Aainfix =acardamodelV4ainfix +V3c1Aainfix &lt;=ainfix +V3c1V0Aainfix &lt;=c0ainfix +V3c1FIainfix &lt;=c0V3Lainfix -V0c1Iainfix =amodelV2aempty_bagFIainfix &lt;=c0V0Iainfix &gt;=V0c0Aainfix &lt;=c0V0F">
918
      <label
919
       name="expl:VC for heapSort"/>
920
      <proof
921
       prover="0"
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       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
926
       <result status="valid" time="0.02"/>
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Asma Tafat-Bouzid committed
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      </proof>