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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="CVC3"
  version="2.2"/>
 <prover
  id="2"
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  name="CVC3"
  version="2.4.1"/>
 <prover
  id="3"
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  name="Coq"
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  version="8.3pl4"/>
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 <prover
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  id="4"
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  name="Z3"
  version="2.19"/>
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 <prover
  id="5"
  name="Z3"
  version="3.2"/>
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 <prover
  id="6"
  name="Z3"
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  version="4.2"/>
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 <file
  name="../counting_sort.mlw"
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  verified="true"
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  expanded="true">
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  <theory
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   name="Spec"
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   locfile="../counting_sort.mlw"
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   loclnum="18" loccnumb="7" loccnume="11"
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   verified="true"
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   expanded="false">
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   <goal
    name="eqlt"
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    locfile="../counting_sort.mlw"
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    loclnum="45" loccnumb="8" loccnume="12"
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    sum="8e07c2ef989e5e270178f5519d793cbc"
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    proved="true"
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    expanded="false"
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    shape="ainfix =ainfix +anumltV0V1V2V3anumeqV0V1V2V3anumltV0ainfix +V1c1V2V3Iainfix &lt;=V3alengthV0Aainfix &lt;V2V3Aainfix &lt;=c0V2FIainfix &lt;V1akAainfix &lt;=c0V1FIak_valuesV0F">
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    <proof
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     prover="3"
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     timelimit="11"
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     memlimit="1000"
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     edited="counting_sort_WP_Spec_eqlt_2.v"
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     obsolete="false"
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     archived="false">
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     <result status="valid" time="1.64"/>
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    </proof>
   </goal>
  </theory>
  <theory
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   name="CountingSort"
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   locfile="../counting_sort.mlw"
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   loclnum="59" loccnumb="7" loccnume="19"
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   verified="true"
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   expanded="true">
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   <goal
    name="WP_parameter counting_sort"
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    locfile="../counting_sort.mlw"
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    loclnum="65" loccnumb="6" loccnume="19"
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    expl="VC for counting_sort"
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    sum="99323c9cc78cdd695e1575445117c28c"
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    proved="true"
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    expanded="true"
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    shape="apermutV5V9Aasorted_subV8c0V1Aainfix =V7V1Iainfix =anum_ofaTuple2V9V10c0V7anum_ofaTuple2V5V10c0V0Iainfix &lt;V10ainfix +ainfix -akc1c1Aainfix &lt;=c0V10FAainfix &lt;agetV8V11ainfix +ainfix -akc1c1Aainfix &lt;=c0agetV8V11Iainfix &lt;V11V7Aainfix &lt;=c0V11FAasorted_subV8c0V7Aainfix =V7anum_ofaTuple2V5ainfix +ainfix -akc1c1c0V0Aainfix =anum_ofaTuple2V16V17c0V14anum_ofaTuple2V5V17c0V0Iainfix &lt;V17ainfix +V12c1Aainfix &lt;=c0V17FAainfix &lt;agetV15V18ainfix +V12c1Aainfix &lt;=c0agetV15V18Iainfix &lt;V18V14Aainfix &lt;=c0V18FAasorted_subV15c0V14Aainfix =V14anum_ofaTuple2V5ainfix +V12c1c0V0Iainfix =anum_ofaTuple2V16V12c0V14ainfix -ainfix +V13c1c1Aainfix =anum_ofaTuple2V16V19c0V14anum_ofaTuple2V5V19c0V0Iainfix &lt;V19V12Aainfix &lt;=c0V19FAainfix &lt;=agetV15V20V12Aainfix &lt;=c0agetV15V20Iainfix &lt;V20V14Aainfix &lt;=c0V20FAasorted_subV15c0V14Aainfix =ainfix +ainfix -V14ainfix +V13c1c1anum_ofaTuple2V5V12c0V0Aainfix =anum_ofaTuple2V23V12c0V24ainfix -ainfix +V21c1c1Aainfix =anum_ofaTuple2V23V25c0V24anum_ofaTuple2V5V25c0V0Iainfix &lt;V25V12Aainfix &lt;=c0V25FAainfix &lt;=agetV22V26V12Aainfix &lt;=c0agetV22V26Iainfix &lt;V26V24Aainfix &lt;=c0V26FAasorted_subV22c0V24Aainfix =ainfix +ainfix -V24ainfix +V21c1c1anum_ofaTuple2V5V12c0V0Iainfix =V24ainfix +V14c1FIainfix =V22asetV15V14V12Lamk arrayV1V22FAainfix &lt;V14V1Aainfix &lt;=c0V14Iainfix =anum_ofaTuple2V16V12c0V14ainfix -V21c1Aainfix =anum_ofaTuple2V16V27c0V14anum_ofaTuple2V5V27c0V0Iainfix &lt;V27V12Aainfix &lt;=c0V27FAainfix &lt;=agetV15V28V12Aainfix &lt;=c0agetV15V28Iainfix &lt;V28V14Aainfix &lt;=c0V28FAasorted_subV15c0V14Aainfix =ainfix +ainfix -V14V21c1anum_ofaTuple2V5V12c0V0Iainfix &lt;=V21V13Aainfix &lt;=c1V21FLamk arrayV1V15FAainfix =anum_ofaTuple2V9V12c0V7ainfix -c1c1Aainfix =anum_ofaTuple2V9V29c0V7anum_ofaTuple2V5V29c0V0Iainfix &lt;V29V12Aainfix &lt;=c0V29FAainfix &lt;=agetV8V30V12Aainfix &lt;=c0agetV8V30Iainfix &lt;V30V7Aainfix &lt;=c0V30FAasorted_subV8c0V7Aainfix =ainfix +ainfix -V7c1c1anum_ofaTuple2V5V12c0V0Iainfix &lt;=c1V13Aainfix =anum_ofaTuple2V9V31c0V7anum_ofaTuple2V5V31c0V0Iainfix &lt;V31ainfix +V12c1Aainfix &lt;=c0V31FAainfix &lt;agetV8V32ainfix +V12c1Aainfix &lt;=c0agetV8V32Iainfix &lt;V32V7Aainfix &lt;=c0V32FAasorted_subV8c0V7Aainfix =V7anum_ofaTuple2V5ainfix +V12c1c0V0Iainfix &gt;c1V13LagetV6V12Aainfix &lt;V12akAainfix &lt;=c0V12Iainfix =anum_ofaTuple2V9V33c0V7anum_ofaTuple2V5V33c0V0Iainfix &lt;V33V12Aainfix &lt;=c0V33FAainfix &lt;agetV8V34V12Aainfix &lt;=c0agetV8V34Iainfix &lt;V34V7Aainfix &lt;=c0V34FAasorted_subV8c0V7Aainfix =V7anum_ofaTuple2V5V12c0V0Iainfix &lt;=V12ainfix -akc1Aainfix &lt;=c0V12FLamk arrayV1V8FAainfix =anum_ofaTuple2V4V35c0c0anum_ofaTuple2V5V35c0V0Iainfix &lt;V35c0Aainfix &lt;=c0V35FAainfix &lt;agetV2V36c0Aainfix &lt;=c0agetV2V36Iainfix &lt;V36c0Aainfix &lt;=c0V36FAasorted_subV2c0c0Aainfix =c0anum_ofaTuple2V5c0c0V0Iainfix &lt;=c0ainfix -akc1AapermutV5V4Aasorted_subV2c0V1Aainfix =c0V1Iainfix &gt;c0ainfix -akc1Iainfix =agetV6V37anum_ofaTuple2V5V37c0ainfix +ainfix -V0c1c1Iainfix &lt;V37akAainfix &lt;=c0V37FAainfix =agetV40V41anum_ofaTuple2V5V41c0ainfix +V38c1Iainfix &lt;V41akAainfix &lt;=c0V41FIainfix =V40asetV6V39ainfix +agetV6V39c1FAainfix &lt;V39akAainfix &lt;=c0V39Aainfix &lt;V39akAainfix &lt;=c0V39LagetV3V38Aainfix &lt;V38V0Aainfix &lt;=c0V38Iainfix =agetV6V42anum_ofaTuple2V5V42c0V38Iainfix &lt;V42akAainfix &lt;=c0V42FIainfix &lt;=V38ainfix -V0c1Aainfix &lt;=c0V38FFAainfix =agetaconstc0V43anum_ofaTuple2V5V43c0c0Iainfix &lt;V43akAainfix &lt;=c0V43FIainfix &lt;=c0ainfix -V0c1AapermutV5V46Aasorted_subV45c0V1Aainfix =V44V1Iainfix =anum_ofaTuple2V46V47c0V44anum_ofaTuple2V5V47c0V0Iainfix &lt;V47ainfix +ainfix -akc1c1Aainfix &lt;=c0V47FAainfix &lt;agetV45V48ainfix +ainfix -akc1c1Aainfix &lt;=c0agetV45V48Iainfix &lt;V48V44Aainfix &lt;=c0V48FAasorted_subV45c0V44Aainfix =V44anum_ofaTuple2V5ainfix +ainfix -akc1c1c0V0Aainfix =anum_ofaTuple2V53V54c0V51anum_ofaTuple2V5V54c0V0Iainfix &lt;V54ainfix +V49c1Aainfix &lt;=c0V54FAainfix &lt;agetV52V55ainfix +V49c1Aainfix &lt;=c0agetV52V55Iainfix &lt;V55V51Aainfix &lt;=c0V55FAasorted_subV52c0V51Aainfix =V51anum_ofaTuple2V5ainfix +V49c1c0V0Iainfix =anum_ofaTuple2V53V49c0V51ainfix -ainfix +V50c1c1Aainfix =anum_ofaTuple2V53V56c0V51anum_ofaTuple2V5V56c0V0Iainfix &lt;V56V49Aainfix &lt;=c0V56FAainfix &lt;=agetV52V57V49Aainfix &lt;=c0agetV52V57Iainfix &lt;V57V51Aainfix &lt;=c0V57FAasorted_subV52c0V51Aainfix =ainfix +ainfix -V51ainfix +V50c1c1anum_ofaTuple2V5V49c0V0Aainfix =anum_ofaTuple2V60V49c0V61ainfix -ainfix +V58c1c1Aainfix =anum_ofaTuple2V60V62c0V61anum_ofaTuple2V5V62c0V0Iainfix &lt;V62V49Aainfix &lt;=c0V62FAainfix &lt;=agetV59V63V49Aainfix &lt;=c0agetV59V63Iainfix &lt;V63V61Aainfix &lt;=c0V63FAasorted_subV59c0V61Aainfix =ainfix +ainfix -V61ainfix +V58c1c1anum_ofaTuple2V5V49c0V0Iainfix =V61ainfix +V51c1FIainfix =V59asetV52V51V49Lamk arrayV1V59FAainfix &lt;V51V1Aainfix &lt;=c0V51Iainfix =anum_ofaTuple2V53V49c0V51ainfix -V58c1Aainfix =anum_ofaTuple2V53V64c0V51anum_ofaTuple2V5V64c0V0Iainfix &lt;V64V49Aainfix &lt;=c0V64FAainfix &lt;=agetV52V65V49Aainfix &lt;=c0agetV52V65Iainfix &lt;V65V51Aainfix &lt;=c0V65FAasorted_subV52c0V51Aainfix =ainfix +ainfix -V51V58c1anum_ofaTuple2V5V49c0V0Iainfix &lt;=V58V50Aainfix &lt;=c1V58FLamk arrayV1V52FAainfix =anum_ofaTuple2V46V49c0V44ainfix -c1c1Aainfix =anum_ofaTuple2V46V66c0V44anum_ofaTuple2V5V66c0V0Iainfix &lt;V66V49Aainfix &lt;=c0V66FAainfix &lt;=agetV45V67V49Aainfix &lt;=c0agetV45V67Iainfix &lt;V67V44Aainfix &lt;=c0V67FAasorted_subV45c0V44Aainfix =ainfix +ainfix -V44c1c1anum_ofaTuple2V5V49c0V0Iainfix &lt;=c1V50Aainfix =anum_ofaTuple2V46V68c0V44anum_ofaTuple2V5V68c0V0Iainfix &lt;V68ainfix +V49c1Aainfix &lt;=c0V68FAainfix &lt;agetV45V69ainfix +V49c1Aainfix &lt;=c0agetV45V69Iainfix &lt;V69V44Aainfix &lt;=c0V69FAasorted_subV45c0V44Aainfix =V44anum_ofaTuple2V5ainfix +V49c1c0V0Iainfix &gt;c1V50Lagetaconstc0V49Aainfix &lt;V49akAainfix &lt;=c0V49Iainfix =anum_ofaTuple2V46V70c0V44anum_ofaTuple2V5V70c0V0Iainfix &lt;V70V49Aainfix &lt;=c0V70FAainfix &lt;agetV45V71V49Aainfix &lt;=c0agetV45V71Iainfix &lt;V71V44Aainfix &lt;=c0V71FAasorted_subV45c0V44Aainfix =V44anum_ofaTuple2V5V49c0V0Iainfix &lt;=V49ainfix -akc1Aainfix &lt;=c0V49FLamk arrayV1V45FAainfix =anum_ofaTuple2V4V72c0c0anum_ofaTuple2V5V72c0V0Iainfix &lt;V72c0Aainfix &lt;=c0V72FAainfix &lt;agetV2V73c0Aainfix &lt;=c0agetV2V73Iainfix &lt;V73c0Aainfix &lt;=c0V73FAasorted_subV2c0c0Aainfix =c0anum_ofaTuple2V5c0c0V0Iainfix &lt;=c0ainfix -akc1AapermutV5V4Aasorted_subV2c0V1Aainfix =c0V1Iainfix &gt;c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Aainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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    <label
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     name="expl:VC for counting_sort"/>
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    <transf
     name="split_goal"
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     proved="true"
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     expanded="true">
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     <goal
      name="WP_parameter counting_sort.1"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="1. precondition"
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      sum="d48c39cac9ec485884c8d1bc681b0d07"
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      proved="true"
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      expanded="false"
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      shape="ainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="20"
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       memlimit="0"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.2"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="2. assertion"
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      sum="1dfbdae5f8dc8da26ba2b4a347ee1faf"
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      proved="true"
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      expanded="false"
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      shape="ainfix =c0V1Iainfix &gt;c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="20"
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       memlimit="0"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.3"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="3. postcondition"
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      sum="32c60b8b99a05fcc6dc14da4dd79beb1"
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      proved="true"
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      expanded="false"
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      shape="apermutV5V4Aasorted_subV2c0V1Iainfix =c0V1Iainfix &gt;c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="20"
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       memlimit="0"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter counting_sort.4"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="4. loop invariant init"
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      sum="85378252ee3eb2cc33bb4f2bb32e0385"
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      proved="true"
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      expanded="false"
      shape="ainfix =c0anum_ofaTuple2V5c0c0V0Iainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
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     </goal>
     <goal
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      name="WP_parameter counting_sort.5"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="5. loop invariant init"
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      sum="a63bc053741f3dd9ba671ffb12cd4a75"
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      proved="true"
      expanded="false"
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      shape="asorted_subV2c0c0Iainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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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 counting_sort.6"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="6. loop invariant init"
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      sum="5c81daef0a9585fdeafb199e040d256b"
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      proved="true"
      expanded="false"
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      shape="ainfix &lt;agetV2V6c0Aainfix &lt;=c0agetV2V6Iainfix &lt;V6c0Aainfix &lt;=c0V6FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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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 counting_sort.7"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="7. loop invariant init"
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      sum="4461d32369f09fbb90095f2b77a97032"
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      proved="true"
      expanded="false"
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      shape="ainfix =anum_ofaTuple2V4V6c0c0anum_ofaTuple2V5V6c0V0Iainfix &lt;V6c0Aainfix &lt;=c0V6FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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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 counting_sort.8"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="8. precondition"
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      sum="2163bfd9bf4618a1374c248c478733a4"
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      proved="true"
      expanded="false"
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      shape="ainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V10c0V6anum_ofaTuple2V5V10c0V0Iainfix &lt;V10V9Aainfix &lt;=c0V10FAainfix &lt;agetV7V11V9Aainfix &lt;=c0agetV7V11Iainfix &lt;V11V6Aainfix &lt;=c0V11FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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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 counting_sort.9"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="9. loop invariant preservation"
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      sum="86626cd7f8e90dc1f9e8395ddb9fb179"
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      proved="true"
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      expanded="false"
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      shape="ainfix =V6anum_ofaTuple2V5ainfix +V9c1c0V0Iainfix &gt;c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V11c0V6anum_ofaTuple2V5V11c0V0Iainfix &lt;V11V9Aainfix &lt;=c0V11FAainfix &lt;agetV7V12V9Aainfix &lt;=c0agetV7V12Iainfix &lt;V12V6Aainfix &lt;=c0V12FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.03"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.10"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="10. loop invariant preservation"
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      sum="cd6bab74150e109035658cc7de7c8698"
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      proved="true"
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      expanded="false"
      shape="asorted_subV7c0V6Iainfix &gt;c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V11c0V6anum_ofaTuple2V5V11c0V0Iainfix &lt;V11V9Aainfix &lt;=c0V11FAainfix &lt;agetV7V12V9Aainfix &lt;=c0agetV7V12Iainfix &lt;V12V6Aainfix &lt;=c0V12FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
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     </goal>
     <goal
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      name="WP_parameter counting_sort.11"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="11. loop invariant preservation"
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      sum="6f36a2eed8e4b0cf594b5a26d1967a88"
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      proved="true"
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      expanded="false"
      shape="ainfix &lt;agetV7V11ainfix +V9c1Aainfix &lt;=c0agetV7V11Iainfix &lt;V11V6Aainfix &lt;=c0V11FIainfix &gt;c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V12c0V6anum_ofaTuple2V5V12c0V0Iainfix &lt;V12V9Aainfix &lt;=c0V12FAainfix &lt;agetV7V13V9Aainfix &lt;=c0agetV7V13Iainfix &lt;V13V6Aainfix &lt;=c0V13FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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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"
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       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 counting_sort.12"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="12. loop invariant preservation"
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      sum="6f355b2c333a3e32aaf6209a7c3fe695"
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      proved="true"
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      expanded="false"
      shape="ainfix =anum_ofaTuple2V8V11c0V6anum_ofaTuple2V5V11c0V0Iainfix &lt;V11ainfix +V9c1Aainfix &lt;=c0V11FIainfix &gt;c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V12c0V6anum_ofaTuple2V5V12c0V0Iainfix &lt;V12V9Aainfix &lt;=c0V12FAainfix &lt;agetV7V13V9Aainfix &lt;=c0agetV7V13Iainfix &lt;V13V6Aainfix &lt;=c0V13FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
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       timelimit="5"
       memlimit="1000"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="1.82"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter counting_sort.13"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="13. loop invariant init"
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      sum="f760d728bd8e8690756df53cb28c1952"
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      proved="true"
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      expanded="false"
      shape="ainfix =ainfix +ainfix -V6c1c1anum_ofaTuple2V5V9c0V0Iainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V11c0V6anum_ofaTuple2V5V11c0V0Iainfix &lt;V11V9Aainfix &lt;=c0V11FAainfix &lt;agetV7V12V9Aainfix &lt;=c0agetV7V12Iainfix &lt;V12V6Aainfix &lt;=c0V12FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
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       timelimit="5"
       memlimit="1000"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.14"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="14. loop invariant init"
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      sum="611b8b7a9d3113ea54a3d8620d7fce56"
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      proved="true"
      expanded="false"
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      shape="asorted_subV7c0V6Iainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V11c0V6anum_ofaTuple2V5V11c0V0Iainfix &lt;V11V9Aainfix &lt;=c0V11FAainfix &lt;agetV7V12V9Aainfix &lt;=c0agetV7V12Iainfix &lt;V12V6Aainfix &lt;=c0V12FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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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 counting_sort.15"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="15. loop invariant init"
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      sum="c8bc50b1602ab13bef734bbddbccdcf1"
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      proved="true"
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      expanded="false"
      shape="ainfix &lt;=agetV7V11V9Aainfix &lt;=c0agetV7V11Iainfix &lt;V11V6Aainfix &lt;=c0V11FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V12c0V6anum_ofaTuple2V5V12c0V0Iainfix &lt;V12V9Aainfix &lt;=c0V12FAainfix &lt;agetV7V13V9Aainfix &lt;=c0agetV7V13Iainfix &lt;V13V6Aainfix &lt;=c0V13FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
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       prover="0"
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       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
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      name="WP_parameter counting_sort.16"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="16. loop invariant init"
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      sum="992d5e59febaa18790c6f56b747c698c"
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      proved="true"
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      expanded="false"
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      shape="ainfix =anum_ofaTuple2V8V11c0V6anum_ofaTuple2V5V11c0V0Iainfix &lt;V11V9Aainfix &lt;=c0V11FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V12c0V6anum_ofaTuple2V5V12c0V0Iainfix &lt;V12V9Aainfix &lt;=c0V12FAainfix &lt;agetV7V13V9Aainfix &lt;=c0agetV7V13Iainfix &lt;V13V6Aainfix &lt;=c0V13FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.17"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="17. loop invariant init"
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      sum="050f97c7ea4c075062b4e7c3548a7f2c"
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      proved="true"
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      expanded="false"
      shape="ainfix =anum_ofaTuple2V8V9c0V6ainfix -c1c1Iainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V11c0V6anum_ofaTuple2V5V11c0V0Iainfix &lt;V11V9Aainfix &lt;=c0V11FAainfix &lt;agetV7V12V9Aainfix &lt;=c0agetV7V12Iainfix &lt;V12V6Aainfix &lt;=c0V12FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
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       prover="0"
       timelimit="5"
       memlimit="1000"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="1.71"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter counting_sort.18"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="18. precondition"
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      sum="897dee71b2404c227a13cc69f696df57"
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      proved="true"
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      expanded="false"
      shape="ainfix &lt;V11V1Aainfix &lt;=c0V11Iainfix =anum_ofaTuple2V13V9c0V11ainfix -V14c1Aainfix =anum_ofaTuple2V13V15c0V11anum_ofaTuple2V5V15c0V0Iainfix &lt;V15V9Aainfix &lt;=c0V15FAainfix &lt;=agetV12V16V9Aainfix &lt;=c0agetV12V16Iainfix &lt;V16V11Aainfix &lt;=c0V16FAasorted_subV12c0V11Aainfix =ainfix +ainfix -V11V14c1anum_ofaTuple2V5V9c0V0Iainfix &lt;=V14V10Aainfix &lt;=c1V14FLamk arrayV1V12FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V17c0V6anum_ofaTuple2V5V17c0V0Iainfix &lt;V17V9Aainfix &lt;=c0V17FAainfix &lt;agetV7V18V9Aainfix &lt;=c0agetV7V18Iainfix &lt;V18V6Aainfix &lt;=c0V18FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
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       timelimit="5"
       memlimit="1000"
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       obsolete="false"
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       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 counting_sort.19"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="19. loop invariant preservation"
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      sum="e1c337311d32f4e06277c70c606fc285"
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      proved="true"
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      expanded="false"
      shape="ainfix =ainfix +ainfix -V17ainfix +V14c1c1anum_ofaTuple2V5V9c0V0Iainfix =V17ainfix +V11c1FIainfix =V15asetV12V11V9Lamk arrayV1V15FIainfix &lt;V11V1Aainfix &lt;=c0V11Iainfix =anum_ofaTuple2V13V9c0V11ainfix -V14c1Aainfix =anum_ofaTuple2V13V18c0V11anum_ofaTuple2V5V18c0V0Iainfix &lt;V18V9Aainfix &lt;=c0V18FAainfix &lt;=agetV12V19V9Aainfix &lt;=c0agetV12V19Iainfix &lt;V19V11Aainfix &lt;=c0V19FAasorted_subV12c0V11Aainfix =ainfix +ainfix -V11V14c1anum_ofaTuple2V5V9c0V0Iainfix &lt;=V14V10Aainfix &lt;=c1V14FLamk arrayV1V12FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V20c0V6anum_ofaTuple2V5V20c0V0Iainfix &lt;V20V9Aainfix &lt;=c0V20FAainfix &lt;agetV7V21V9Aainfix &lt;=c0agetV7V21Iainfix &lt;V21V6Aainfix &lt;=c0V21FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
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       timelimit="5"
       memlimit="1000"
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       obsolete="false"
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       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter counting_sort.20"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="20. loop invariant preservation"
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      sum="226c5a8be66e85a5b2e2a7ba1be55e06"
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      proved="true"
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      expanded="false"
      shape="asorted_subV15c0V17Iainfix =V17ainfix +V11c1FIainfix =V15asetV12V11V9Lamk arrayV1V15FIainfix &lt;V11V1Aainfix &lt;=c0V11Iainfix =anum_ofaTuple2V13V9c0V11ainfix -V14c1Aainfix =anum_ofaTuple2V13V18c0V11anum_ofaTuple2V5V18c0V0Iainfix &lt;V18V9Aainfix &lt;=c0V18FAainfix &lt;=agetV12V19V9Aainfix &lt;=c0agetV12V19Iainfix &lt;V19V11Aainfix &lt;=c0V19FAasorted_subV12c0V11Aainfix =ainfix +ainfix -V11V14c1anum_ofaTuple2V5V9c0V0Iainfix &lt;=V14V10Aainfix &lt;=c1V14FLamk arrayV1V12FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V20c0V6anum_ofaTuple2V5V20c0V0Iainfix &lt;V20V9Aainfix &lt;=c0V20FAainfix &lt;agetV7V21V9Aainfix &lt;=c0agetV7V21Iainfix &lt;V21V6Aainfix &lt;=c0V21FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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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"
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       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
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     <goal
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      name="WP_parameter counting_sort.21"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="21. loop invariant preservation"
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      sum="974414371344113a392841e2481f2b30"
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      proved="true"
      expanded="false"
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      shape="ainfix &lt;=agetV15V18V9Aainfix &lt;=c0agetV15V18Iainfix &lt;V18V17Aainfix &lt;=c0V18FIainfix =V17ainfix +V11c1FIainfix =V15asetV12V11V9Lamk arrayV1V15FIainfix &lt;V11V1Aainfix &lt;=c0V11Iainfix =anum_ofaTuple2V13V9c0V11ainfix -V14c1Aainfix =anum_ofaTuple2V13V19c0V11anum_ofaTuple2V5V19c0V0Iainfix &lt;V19V9Aainfix &lt;=c0V19FAainfix &lt;=agetV12V20V9Aainfix &lt;=c0agetV12V20Iainfix &lt;V20V11Aainfix &lt;=c0V20FAasorted_subV12c0V11Aainfix =ainfix +ainfix -V11V14c1anum_ofaTuple2V5V9c0V0Iainfix &lt;=V14V10Aainfix &lt;=c1V14FLamk arrayV1V12FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V21c0V6anum_ofaTuple2V5V21c0V0Iainfix &lt;V21V9Aainfix &lt;=c0V21FAainfix &lt;agetV7V22V9Aainfix &lt;=c0agetV7V22Iainfix &lt;V22V6Aainfix &lt;=c0V22FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.22"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="22. loop invariant preservation"
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      sum="8c5ca59c6f07266f95ebd56cd1f77e87"
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      proved="true"
      expanded="false"
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      shape="ainfix =anum_ofaTuple2V16V18c0V17anum_ofaTuple2V5V18c0V0Iainfix &lt;V18V9Aainfix &lt;=c0V18FIainfix =V17ainfix +V11c1FIainfix =V15asetV12V11V9Lamk arrayV1V15FIainfix &lt;V11V1Aainfix &lt;=c0V11Iainfix =anum_ofaTuple2V13V9c0V11ainfix -V14c1Aainfix =anum_ofaTuple2V13V19c0V11anum_ofaTuple2V5V19c0V0Iainfix &lt;V19V9Aainfix &lt;=c0V19FAainfix &lt;=agetV12V20V9Aainfix &lt;=c0agetV12V20Iainfix &lt;V20V11Aainfix &lt;=c0V20FAasorted_subV12c0V11Aainfix =ainfix +ainfix -V11V14c1anum_ofaTuple2V5V9c0V0Iainfix &lt;=V14V10Aainfix &lt;=c1V14FLamk arrayV1V12FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V21c0V6anum_ofaTuple2V5V21c0V0Iainfix &lt;V21V9Aainfix &lt;=c0V21FAainfix &lt;agetV7V22V9Aainfix &lt;=c0agetV7V22Iainfix &lt;V22V6Aainfix &lt;=c0V22FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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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 counting_sort.23"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="23. loop invariant preservation"
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      sum="ba2ad8ef1e180ebc62e7a1bfecc6067a"
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      proved="true"
      expanded="false"
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      shape="ainfix =anum_ofaTuple2V16V9c0V17ainfix -ainfix +V14c1c1Iainfix =V17ainfix +V11c1FIainfix =V15asetV12V11V9Lamk arrayV1V15FIainfix &lt;V11V1Aainfix &lt;=c0V11Iainfix =anum_ofaTuple2V13V9c0V11ainfix -V14c1Aainfix =anum_ofaTuple2V13V18c0V11anum_ofaTuple2V5V18c0V0Iainfix &lt;V18V9Aainfix &lt;=c0V18FAainfix &lt;=agetV12V19V9Aainfix &lt;=c0agetV12V19Iainfix &lt;V19V11Aainfix &lt;=c0V19FAasorted_subV12c0V11Aainfix =ainfix +ainfix -V11V14c1anum_ofaTuple2V5V9c0V0Iainfix &lt;=V14V10Aainfix &lt;=c1V14FLamk arrayV1V12FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V20c0V6anum_ofaTuple2V5V20c0V0Iainfix &lt;V20V9Aainfix &lt;=c0V20FAainfix &lt;agetV7V21V9Aainfix &lt;=c0agetV7V21Iainfix &lt;V21V6Aainfix &lt;=c0V21FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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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 counting_sort.24"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="24. loop invariant preservation"
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      sum="22b8acf13a99b60fab2aa2c477a3a735"
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      proved="true"
      expanded="false"
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      shape="ainfix =V11anum_ofaTuple2V5ainfix +V9c1c0V0Iainfix =anum_ofaTuple2V13V9c0V11ainfix -ainfix +V10c1c1Aainfix =anum_ofaTuple2V13V14c0V11anum_ofaTuple2V5V14c0V0Iainfix &lt;V14V9Aainfix &lt;=c0V14FAainfix &lt;=agetV12V15V9Aainfix &lt;=c0agetV12V15Iainfix &lt;V15V11Aainfix &lt;=c0V15FAasorted_subV12c0V11Aainfix =ainfix +ainfix -V11ainfix +V10c1c1anum_ofaTuple2V5V9c0V0Lamk arrayV1V12FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V16c0V6anum_ofaTuple2V5V16c0V0Iainfix &lt;V16V9Aainfix &lt;=c0V16FAainfix &lt;agetV7V17V9Aainfix &lt;=c0agetV7V17Iainfix &lt;V17V6Aainfix &lt;=c0V17FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.24"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.25"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="25. loop invariant preservation"
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      sum="0d3d75cf48b11c13bb548f9eee6333e2"
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      proved="true"
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      expanded="false"
      shape="asorted_subV12c0V11Iainfix =anum_ofaTuple2V13V9c0V11ainfix -ainfix +V10c1c1Aainfix =anum_ofaTuple2V13V14c0V11anum_ofaTuple2V5V14c0V0Iainfix &lt;V14V9Aainfix &lt;=c0V14FAainfix &lt;=agetV12V15V9Aainfix &lt;=c0agetV12V15Iainfix &lt;V15V11Aainfix &lt;=c0V15FAasorted_subV12c0V11Aainfix =ainfix +ainfix -V11ainfix +V10c1c1anum_ofaTuple2V5V9c0V0Lamk arrayV1V12FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V16c0V6anum_ofaTuple2V5V16c0V0Iainfix &lt;V16V9Aainfix &lt;=c0V16FAainfix &lt;agetV7V17V9Aainfix &lt;=c0agetV7V17Iainfix &lt;V17V6Aainfix &lt;=c0V17FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
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     </goal>
     <goal
      name="WP_parameter counting_sort.26"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="26. loop invariant preservation"
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      sum="2e653037c84002a769d7e216a938903d"
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      proved="true"
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      expanded="false"
      shape="ainfix &lt;agetV12V14ainfix +V9c1Aainfix &lt;=c0agetV12V14Iainfix &lt;V14V11Aainfix &lt;=c0V14FIainfix =anum_ofaTuple2V13V9c0V11ainfix -ainfix +V10c1c1Aainfix =anum_ofaTuple2V13V15c0V11anum_ofaTuple2V5V15c0V0Iainfix &lt;V15V9Aainfix &lt;=c0V15FAainfix &lt;=agetV12V16V9Aainfix &lt;=c0agetV12V16Iainfix &lt;V16V11Aainfix &lt;=c0V16FAasorted_subV12c0V11Aainfix =ainfix +ainfix -V11ainfix +V10c1c1anum_ofaTuple2V5V9c0V0Lamk arrayV1V12FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V17c0V6anum_ofaTuple2V5V17c0V0Iainfix &lt;V17V9Aainfix &lt;=c0V17FAainfix &lt;agetV7V18V9Aainfix &lt;=c0agetV7V18Iainfix &lt;V18V6Aainfix &lt;=c0V18FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
      </proof>
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     </goal>
     <goal
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      name="WP_parameter counting_sort.27"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="27. loop invariant preservation"
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      sum="1ffa5b68a21e672c9e9ecc51d44c781f"
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      proved="true"
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      expanded="false"
      shape="ainfix =anum_ofaTuple2V13V14c0V11anum_ofaTuple2V5V14c0V0Iainfix &lt;V14ainfix +V9c1Aainfix &lt;=c0V14FIainfix =anum_ofaTuple2V13V9c0V11ainfix -ainfix +V10c1c1Aainfix =anum_ofaTuple2V13V15c0V11anum_ofaTuple2V5V15c0V0Iainfix &lt;V15V9Aainfix &lt;=c0V15FAainfix &lt;=agetV12V16V9Aainfix &lt;=c0agetV12V16Iainfix &lt;V16V11Aainfix &lt;=c0V16FAasorted_subV12c0V11Aainfix =ainfix +ainfix -V11ainfix +V10c1c1anum_ofaTuple2V5V9c0V0Lamk arrayV1V12FIainfix &lt;=c1V10Lagetaconstc0V9Iainfix &lt;V9akAainfix &lt;=c0V9Iainfix =anum_ofaTuple2V8V17c0V6anum_ofaTuple2V5V17c0V0Iainfix &lt;V17V9Aainfix &lt;=c0V17FAainfix &lt;agetV7V18V9Aainfix &lt;=c0agetV7V18Iainfix &lt;V18V6Aainfix &lt;=c0V18FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5V9c0V0Iainfix &lt;=V9ainfix -akc1Aainfix &lt;=c0V9FLamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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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="4.84"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter counting_sort.28"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="28. assertion"
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      sum="d8535dc6e90c77a63d6162d880c07ea6"
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      proved="true"
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      expanded="false"
      shape="ainfix =V6V1Iainfix =anum_ofaTuple2V8V9c0V6anum_ofaTuple2V5V9c0V0Iainfix &lt;V9ainfix +ainfix -akc1c1Aainfix &lt;=c0V9FAainfix &lt;agetV7V10ainfix +ainfix -akc1c1Aainfix &lt;=c0agetV7V10Iainfix &lt;V10V6Aainfix &lt;=c0V10FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5ainfix +ainfix -akc1c1c0V0Lamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
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      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
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       timelimit="20"
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       memlimit="0"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
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     <goal
      name="WP_parameter counting_sort.29"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="29. postcondition"
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      sum="dc1ec12573a6e114efdb59f97ba3f1c7"
      proved="true"
      expanded="false"
      shape="apermutV5V8Aasorted_subV7c0V1Iainfix =V6V1Iainfix =anum_ofaTuple2V8V9c0V6anum_ofaTuple2V5V9c0V0Iainfix &lt;V9ainfix +ainfix -akc1c1Aainfix &lt;=c0V9FAainfix &lt;agetV7V10ainfix +ainfix -akc1c1Aainfix &lt;=c0agetV7V10Iainfix &lt;V10V6Aainfix &lt;=c0V10FAasorted_subV7c0V6Aainfix =V6anum_ofaTuple2V5ainfix +ainfix -akc1c1c0V0Lamk arrayV1V7FIainfix &lt;=c0ainfix -akc1Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="20"
       memlimit="0"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.30"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="30. loop invariant init"
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      sum="ca4d80173741c9417953cd019c517746"
      proved="true"
      expanded="false"
      shape="ainfix =agetaconstc0V6anum_ofaTuple2V5V6c0c0Iainfix &lt;V6akAainfix &lt;=c0V6FIainfix &lt;=c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="20"
       memlimit="0"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.31"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="31. precondition"
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      sum="dcbdff10d5f0051d7dbccc9c7e1ee255"
      proved="true"
      expanded="false"
      shape="ainfix &lt;V7V0Aainfix &lt;=c0V7Iainfix =agetV6V8anum_ofaTuple2V5V8c0V7Iainfix &lt;V8akAainfix &lt;=c0V8FIainfix &lt;=V7ainfix -V0c1Aainfix &lt;=c0V7FFIainfix &lt;=c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.32"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="32. precondition"
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      sum="20dd082469ce388ce73f429a569ea95e"
      proved="true"
      expanded="false"
      shape="ainfix &lt;V8akAainfix &lt;=c0V8LagetV3V7Iainfix &lt;V7V0Aainfix &lt;=c0V7Iainfix =agetV6V9anum_ofaTuple2V5V9c0V7Iainfix &lt;V9akAainfix &lt;=c0V9FIainfix &lt;=V7ainfix -V0c1Aainfix &lt;=c0V7FFIainfix &lt;=c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
      <label
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       name="expl:VC for counting_sort"/>
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      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
      <proof
       prover="5"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.05"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter counting_sort.33"
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      locfile="../counting_sort.mlw"
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      loclnum="65" loccnumb="6" loccnume="19"
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      expl="33. precondition"
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      sum="4fec1ba6ae2cc8165cac5b991442a047"
      proved="true"
      expanded="false"
      shape="ainfix &lt;V8akAainfix &lt;=c0V8Iainfix &lt;V8akAainfix &lt;=c0V8LagetV3V7Iainfix &lt;V7V0Aainfix &lt;=c0V7Iainfix =agetV6V9anum_ofaTuple2V5V9c0V7Iainfix &lt;V9akAainfix &lt;=c0V9FIainfix &lt;=V7ainfix -V0c1Aainfix &lt;=c0V7FFIainfix &lt;=c0ainfix -V0c1Iainfix &gt;=akc0Iainfix =V0V1Aainfix &lt;=c0V0Aak_valuesV5Lamk arrayV0V3Lamk arrayV1V2FF">
      <label
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       name="expl:VC for counting_sort"/>