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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="2">
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 <prover
  id="0"
  name="Alt-Ergo"
  version="0.94"/>
 <prover
  id="1"
  name="Z3"
  version="3.2"/>
 <file
  name="../algo64.mlw"
  verified="true"
  expanded="true">
  <theory
   name="Algo64"
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   locfile="../algo64.mlw"
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   loclnum="14" loccnumb="7" loccnume="13"
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   verified="true"
   expanded="true">
   <goal
    name="WP_parameter quicksort"
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    locfile="../algo64.mlw"
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    loclnum="37" loccnumb="10" loccnume="19"
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    expl="VC for quicksort"
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    sum="3414d2e4642fa780732c72dd37a022a7"
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    proved="true"
    expanded="true"
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    shape="iainfix &lt;V1V2asorted_subV8V1ainfix +V2c1Aapermut_subV3V8V1ainfix +V2c1Aapermut_subV7V8V1ainfix +V2c1Iasorted_subV8V5ainfix +V2c1Aapermut_subV7V8V5ainfix +V2c1FAainfix &lt;V2V0Aainfix &lt;=V5V2Aainfix &lt;=c0V5Aainfix &lt;ainfix -V2V5ainfix -V2V1Aainfix &lt;=c0ainfix -V2V1Aapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FAainfix &lt;V4V0Aainfix &lt;=V1V4Aainfix &lt;=c0V1Aainfix &lt;ainfix -V4V1ainfix -V2V1Aainfix &lt;=c0ainfix -V2V1Iainfix &gt;=agetV6V10V9Iainfix &lt;=V10V2Aainfix &lt;=V5V10FAainfix =agetV6V11V9Iainfix &lt;V11V5Aainfix &lt;V4V11FAainfix &lt;=agetV6V12V9Iainfix &lt;=V12V4Aainfix &lt;=V1V12FEAapermut_subV3V6V1ainfix +V2c1Aainfix &lt;=V5V2Aainfix &lt;V4V5Aainfix &lt;=V1V4FAainfix &lt;V2V0Aainfix &lt;V1V2Aainfix &lt;=c0V1asorted_subV3V1ainfix +V2c1Aapermut_subV3V3V1ainfix +V2c1Iainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
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    <label
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     name="expl:VC for quicksort"/>
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    <transf
     name="split_goal"
     proved="true"
     expanded="true">
     <goal
      name="WP_parameter quicksort.1"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="1. precondition"
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      sum="4de9aa82739070bbf8bf3bcbb4288d7e"
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      proved="true"
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      expanded="true"
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      shape="ainfix &lt;V2V0Aainfix &lt;V1V2Aainfix &lt;=c0V1Iainfix &lt;V1V2Iainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
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      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter quicksort.2"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="2. variant decrease"
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      sum="fe9acb54daf59c069016af2650eb7b8c"
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      proved="true"
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      expanded="true"
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      shape="ainfix &lt;ainfix -V4V1ainfix -V2V1Aainfix &lt;=c0ainfix -V2V1Iainfix &gt;=agetV6V8V7Iainfix &lt;=V8V2Aainfix &lt;=V5V8FAainfix =agetV6V9V7Iainfix &lt;V9V5Aainfix &lt;V4V9FAainfix &lt;=agetV6V10V7Iainfix &lt;=V10V4Aainfix &lt;=V1V10FEAapermut_subV3V6V1ainfix +V2c1Aainfix &lt;=V5V2Aainfix &lt;V4V5Aainfix &lt;=V1V4FIainfix &lt;V2V0Aainfix &lt;V1V2Aainfix &lt;=c0V1Iainfix &lt;V1V2Iainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
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      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter quicksort.3"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="3. precondition"
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      sum="f7e560c1345b399daf76c46f99ad9c76"
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      proved="true"
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      expanded="true"
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      shape="ainfix &lt;V4V0Aainfix &lt;=V1V4Aainfix &lt;=c0V1Iainfix &gt;=agetV6V8V7Iainfix &lt;=V8V2Aainfix &lt;=V5V8FAainfix =agetV6V9V7Iainfix &lt;V9V5Aainfix &lt;V4V9FAainfix &lt;=agetV6V10V7Iainfix &lt;=V10V4Aainfix &lt;=V1V10FEAapermut_subV3V6V1ainfix +V2c1Aainfix &lt;=V5V2Aainfix &lt;V4V5Aainfix &lt;=V1V4FIainfix &lt;V2V0Aainfix &lt;V1V2Aainfix &lt;=c0V1Iainfix &lt;V1V2Iainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
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      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter quicksort.4"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="4. assertion"
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      sum="78c6b7bf60012475b3c18c0503798128"
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      proved="true"
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      expanded="true"
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      shape="apermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix &lt;V4V0Aainfix &lt;=V1V4Aainfix &lt;=c0V1Iainfix &gt;=agetV6V9V8Iainfix &lt;=V9V2Aainfix &lt;=V5V9FAainfix =agetV6V10V8Iainfix &lt;V10V5Aainfix &lt;V4V10FAainfix &lt;=agetV6V11V8Iainfix &lt;=V11V4Aainfix &lt;=V1V11FEAapermut_subV3V6V1ainfix +V2c1Aainfix &lt;=V5V2Aainfix &lt;V4V5Aainfix &lt;=V1V4FIainfix &lt;V2V0Aainfix &lt;V1V2Aainfix &lt;=c0V1Iainfix &lt;V1V2Iainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
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      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter quicksort.5"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="5. variant decrease"
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      sum="4789ff6d40269d9aee44e92bc732ab07"
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      proved="true"
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      expanded="true"
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      shape="ainfix &lt;ainfix -V2V5ainfix -V2V1Aainfix &lt;=c0ainfix -V2V1Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix &lt;V4V0Aainfix &lt;=V1V4Aainfix &lt;=c0V1Iainfix &gt;=agetV6V9V8Iainfix &lt;=V9V2Aainfix &lt;=V5V9FAainfix =agetV6V10V8Iainfix &lt;V10V5Aainfix &lt;V4V10FAainfix &lt;=agetV6V11V8Iainfix &lt;=V11V4Aainfix &lt;=V1V11FEAapermut_subV3V6V1ainfix +V2c1Aainfix &lt;=V5V2Aainfix &lt;V4V5Aainfix &lt;=V1V4FIainfix &lt;V2V0Aainfix &lt;V1V2Aainfix &lt;=c0V1Iainfix &lt;V1V2Iainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
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      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter quicksort.6"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="6. precondition"
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      sum="031be5673d647ec9954456c5cc75b69c"
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      proved="true"
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      expanded="true"
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      shape="ainfix &lt;V2V0Aainfix &lt;=V5V2Aainfix &lt;=c0V5Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix &lt;V4V0Aainfix &lt;=V1V4Aainfix &lt;=c0V1Iainfix &gt;=agetV6V9V8Iainfix &lt;=V9V2Aainfix &lt;=V5V9FAainfix =agetV6V10V8Iainfix &lt;V10V5Aainfix &lt;V4V10FAainfix &lt;=agetV6V11V8Iainfix &lt;=V11V4Aainfix &lt;=V1V11FEAapermut_subV3V6V1ainfix +V2c1Aainfix &lt;=V5V2Aainfix &lt;V4V5Aainfix &lt;=V1V4FIainfix &lt;V2V0Aainfix &lt;V1V2Aainfix &lt;=c0V1Iainfix &lt;V1V2Iainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
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      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter quicksort.7"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="7. assertion"
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      sum="15335218c0920c2b27f53084e898652d"
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      proved="true"
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      expanded="true"
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      shape="apermut_subV7V8V1ainfix +V2c1Iasorted_subV8V5ainfix +V2c1Aapermut_subV7V8V5ainfix +V2c1FIainfix &lt;V2V0Aainfix &lt;=V5V2Aainfix &lt;=c0V5Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix &lt;V4V0Aainfix &lt;=V1V4Aainfix &lt;=c0V1Iainfix &gt;=agetV6V10V9Iainfix &lt;=V10V2Aainfix &lt;=V5V10FAainfix =agetV6V11V9Iainfix &lt;V11V5Aainfix &lt;V4V11FAainfix &lt;=agetV6V12V9Iainfix &lt;=V12V4Aainfix &lt;=V1V12FEAapermut_subV3V6V1ainfix +V2c1Aainfix &lt;=V5V2Aainfix &lt;V4V5Aainfix &lt;=V1V4FIainfix &lt;V2V0Aainfix &lt;V1V2Aainfix &lt;=c0V1Iainfix &lt;V1V2Iainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
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      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter quicksort.8"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="8. postcondition"
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      sum="0e475c7b87ff418a971cf0077f779587"
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      proved="true"
      expanded="true"
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      shape="apermut_subV3V8V1ainfix +V2c1Iapermut_subV7V8V1ainfix +V2c1Iasorted_subV8V5ainfix +V2c1Aapermut_subV7V8V5ainfix +V2c1FIainfix &lt;V2V0Aainfix &lt;=V5V2Aainfix &lt;=c0V5Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix &lt;V4V0Aainfix &lt;=V1V4Aainfix &lt;=c0V1Iainfix &gt;=agetV6V10V9Iainfix &lt;=V10V2Aainfix &lt;=V5V10FAainfix =agetV6V11V9Iainfix &lt;V11V5Aainfix &lt;V4V11FAainfix &lt;=agetV6V12V9Iainfix &lt;=V12V4Aainfix &lt;=V1V12FEAapermut_subV3V6V1ainfix +V2c1Aainfix &lt;=V5V2Aainfix &lt;V4V5Aainfix &lt;=V1V4FIainfix &lt;V2V0Aainfix &lt;V1V2Aainfix &lt;=c0V1Iainfix &lt;V1V2Iainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
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      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="0"
       timelimit="17"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.04"/>
      </proof>
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     </goal>
     <goal
      name="WP_parameter quicksort.9"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="9. postcondition"
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      sum="3933512821bb054f623f5f2b6415aa88"
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      proved="true"
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      expanded="true"
      shape="asorted_subV8V1ainfix +V2c1Iapermut_subV7V8V1ainfix +V2c1Iasorted_subV8V5ainfix +V2c1Aapermut_subV7V8V5ainfix +V2c1FIainfix &lt;V2V0Aainfix &lt;=V5V2Aainfix &lt;=c0V5Iapermut_subV6V7V1ainfix +V2c1Iasorted_subV7V1ainfix +V4c1Aapermut_subV6V7V1ainfix +V4c1FIainfix &lt;V4V0Aainfix &lt;=V1V4Aainfix &lt;=c0V1Iainfix &gt;=agetV6V10V9Iainfix &lt;=V10V2Aainfix &lt;=V5V10FAainfix =agetV6V11V9Iainfix &lt;V11V5Aainfix &lt;V4V11FAainfix &lt;=agetV6V12V9Iainfix &lt;=V12V4Aainfix &lt;=V1V12FEAapermut_subV3V6V1ainfix +V2c1Aainfix &lt;=V5V2Aainfix &lt;V4V5Aainfix &lt;=V1V4FIainfix &lt;V2V0Aainfix &lt;V1V2Aainfix &lt;=c0V1Iainfix &lt;V1V2Iainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="1"
       timelimit="17"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="1.32"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter quicksort.10"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="10. postcondition"
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      sum="57c1b8d1dad49efee4f1794fdb1d6602"
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      proved="true"
      expanded="true"
      shape="apermut_subV3V3V1ainfix +V2c1Iainfix &lt;V1V2NIainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
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      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="0"
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       timelimit="17"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter quicksort.11"
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      locfile="../algo64.mlw"
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      loclnum="37" loccnumb="10" loccnume="19"
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      expl="11. postcondition"
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      sum="87272b6861af90e3b0e54ec76afafa77"
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      proved="true"
      expanded="true"
      shape="asorted_subV3V1ainfix +V2c1Iainfix &lt;V1V2NIainfix &lt;V2V0Aainfix &lt;=V1V2Aainfix &lt;=c0V1FF">
      <label
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       name="expl:VC for quicksort"/>
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      <proof
       prover="0"
       timelimit="17"
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       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
    </transf>
   </goal>
  </theory>
 </file>
</why3session>