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<?xml version="1.0" encoding="UTF-8"?>
<!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
  id="0"
  name="Alt-Ergo"
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  version="0.95.1"/>
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 <prover
  id="1"
  name="CVC3"
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  version="2.2"/>
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 <prover
  id="2"
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  name="CVC3"
  version="2.4.1"/>
 <prover
  id="3"
  name="CVC4"
  version="1.2"/>
 <prover
  id="4"
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  name="Coq"
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  version="8.4pl3"/>
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 <prover
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  id="5"
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  name="Z3"
  version="3.2"/>
 <file
  name="../dijkstra.mlw"
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  verified="true"
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  expanded="true">
  <theory
   name="DijkstraShortestPath"
   locfile="../dijkstra.mlw"
   loclnum="8" loccnumb="7" loccnume="27"
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   verified="true"
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   expanded="true">
   <goal
    name="WP_parameter relax"
    locfile="../dijkstra.mlw"
    loclnum="72" loccnumb="6" loccnume="11"
    expl="VC for relax"
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    sum="8f32f48bea01f4ed5752830a112387be"
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    proved="true"
    expanded="false"
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    shape="iainfix =V3amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix =V2aaddV1V2ANamemV1V2ANamemV1V4Oainfix =V3amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix &lt;ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V2Oainfix &gt;=ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V2OamemV1V4iainfix =V7amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix =V6aaddV1V2ANamemV1V2ANamemV1V4Oainfix =V7amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix =V6V2Aainfix &lt;ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V6Oainfix =V7V3Aainfix =V6V2Aainfix &gt;=ainfix +amixfix []V7V0aweightV0V1amixfix []V7V1AamemV1V6Oainfix =V7V3Aainfix =V6V2AamemV1V4Iainfix =V7amixfix [&lt;-]V3V1V5FIainfix =V6aaddV1V2Fiainfix =V3amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix =V2aaddV1V2ANamemV1V2ANamemV1V4Oainfix =V3amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix &lt;ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V2Oainfix &gt;=ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V2OamemV1V4ainfix =V8amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix =V2aaddV1V2ANamemV1V2ANamemV1V4Oainfix =V8amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix &lt;ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V2Oainfix =V8V3Aainfix &gt;=ainfix +amixfix []V8V0aweightV0V1amixfix []V8V1AamemV1V2Oainfix =V8V3AamemV1V4Iainfix =V8amixfix [&lt;-]V3V1V5Fainfix &lt;V5amixfix []V3V1amemV1V2Lainfix +amixfix []V3V0aweightV0V1NamemV1V4FF">
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    <label
     name="expl:VC for relax"/>
    <transf
     name="split_goal_wp"
     proved="true"
     expanded="false">
     <goal
      name="WP_parameter relax.1"
      locfile="../dijkstra.mlw"
      loclnum="72" loccnumb="6" loccnume="11"
      expl="1. postcondition"
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      sum="aeb81bc9317d1907e9bf84f8b9ddaaff"
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      proved="true"
      expanded="false"
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      shape="postconditionainfix =V6amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix =V2aaddV1V2ANamemV1V2ANamemV1V4Oainfix =V6amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix &lt;ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V2Oainfix =V6V3Aainfix &gt;=ainfix +amixfix []V6V0aweightV0V1amixfix []V6V1AamemV1V2Oainfix =V6V3AamemV1V4Iainfix =V6amixfix [&lt;-]V3V1V5FIainfix &lt;V5amixfix []V3V1IamemV1V2Lainfix +amixfix []V3V0aweightV0V1INamemV1V4FF">
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      <label
       name="expl:VC for relax"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter relax.2"
      locfile="../dijkstra.mlw"
      loclnum="72" loccnumb="6" loccnume="11"
      expl="2. postcondition"
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      sum="eaef5f6a4e2eba27510c164fad3d20fb"
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      proved="true"
      expanded="false"
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      shape="postconditionainfix =V3amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix =V2aaddV1V2ANamemV1V2ANamemV1V4Oainfix =V3amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix &lt;ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V2Oainfix &gt;=ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V2OamemV1V4INainfix &lt;V5amixfix []V3V1IamemV1V2Lainfix +amixfix []V3V0aweightV0V1INamemV1V4FF">
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      <label
       name="expl:VC for relax"/>
      <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 relax.3"
      locfile="../dijkstra.mlw"
      loclnum="72" loccnumb="6" loccnume="11"
      expl="3. postcondition"
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      sum="2a013bc10ab4368dab267dcc92a9af2a"
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      proved="true"
      expanded="false"
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      shape="postconditionainfix =V7amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix =V6aaddV1V2ANamemV1V2ANamemV1V4Oainfix =V7amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix =V6V2Aainfix &lt;ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V6Oainfix =V7V3Aainfix =V6V2Aainfix &gt;=ainfix +amixfix []V7V0aweightV0V1amixfix []V7V1AamemV1V6Oainfix =V7V3Aainfix =V6V2AamemV1V4Iainfix =V7amixfix [&lt;-]V3V1V5FIainfix =V6aaddV1V2FINamemV1V2Lainfix +amixfix []V3V0aweightV0V1INamemV1V4FF">
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      <label
       name="expl:VC for relax"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter relax.4"
      locfile="../dijkstra.mlw"
      loclnum="72" loccnumb="6" loccnume="11"
      expl="4. postcondition"
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      sum="15ce5553d218667d241e6ed6b89e0166"
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      proved="true"
      expanded="false"
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      shape="postconditionainfix =V3amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix =V2aaddV1V2ANamemV1V2ANamemV1V4Oainfix =V3amixfix [&lt;-]V3V1ainfix +amixfix []V3V0aweightV0V1Aainfix &lt;ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V2Oainfix &gt;=ainfix +amixfix []V3V0aweightV0V1amixfix []V3V1AamemV1V2OamemV1V4INNamemV1V4FF">
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      <label
       name="expl:VC for relax"/>
      <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>
    </transf>
   </goal>
   <goal
    name="Length_nonneg"
    locfile="../dijkstra.mlw"
    loclnum="108" loccnumb="8" loccnume="21"
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    sum="438bec4c8d4639d6a7a61143ff2aa83b"
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    proved="true"
    expanded="false"
    shape="ainfix &gt;=V2c0IapathV0V1V2FF">
    <proof
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     prover="4"
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     timelimit="5"
     memlimit="1000"
     edited="dijkstra_DijkstraShortestPath_Length_nonneg_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="1.07"/>
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    </proof>
   </goal>
   <goal
    name="Path_inversion"
    locfile="../dijkstra.mlw"
    loclnum="113" loccnumb="8" loccnume="22"
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    sum="7bb8eeb7acc4eef51735d794db4f89d9"
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    proved="true"
    expanded="false"
    shape="amemV1ag_succV3AapathV0V3ainfix -V2aweightV3V1EOainfix =V2c0Aainfix =V1V0IapathV0V1V2FF">
    <proof
     prover="0"
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
     <result status="valid" time="0.02"/>
    </proof>
   </goal>
   <goal
    name="Path_shortest_path"
    locfile="../dijkstra.mlw"
    loclnum="118" loccnumb="8" loccnume="26"
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    sum="22bf835a46cf6f0fb08d60ca0e1afbc6"
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    proved="true"
    expanded="false"
    shape="ainfix &lt;=V3V2Aashortest_pathV0V1V3EIapathV0V1V2FF">
    <proof
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     prover="4"
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     timelimit="5"
     memlimit="1000"
     edited="dijkstra_DijkstraShortestPath_Path_shortest_path_1.v"
     obsolete="false"
     archived="false">
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     <result status="valid" time="1.26"/>
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    </proof>
   </goal>
   <goal
    name="Main_lemma"
    locfile="../dijkstra.mlw"
    loclnum="124" loccnumb="8" loccnume="18"
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    sum="3f29de55aede380ca7b4f654b5ae02bf"
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    proved="true"
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    expanded="false"
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    shape="ainfix &lt;ainfix +V4aweightV3V1V2AamemV1ag_succV3Aashortest_pathV0V3V4EEOainfix &gt;V2c0Aainfix =V1V0INashortest_pathV0V1V2IapathV0V1V2FF">
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    <proof
     prover="0"
     timelimit="5"
     memlimit="1000"
     obsolete="false"
     archived="false">
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     <result status="valid" time="1.72"/>
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    </proof>
   </goal>
   <goal
    name="Completeness_lemma"
    locfile="../dijkstra.mlw"
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    loclnum="132" loccnumb="8" loccnume="26"
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    sum="0702a6e9f4432dae5ceec580977d832f"
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    proved="true"
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    expanded="false"
    shape="amemV2V0IapathV1V2V3FFIamemV1V0FIamemV5V0IamemV5ag_succV4FIamemV4V0FF">
    <proof
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     prover="4"
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     timelimit="5"
     memlimit="1000"
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     edited="dijkstra_DijkstraShortestPath_Completeness_lemma_1.v"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="1.17"/>
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    </proof>
   </goal>
   <goal
    name="WP_parameter shortest_path_code"
    locfile="../dijkstra.mlw"
    loclnum="186" loccnumb="6" loccnume="24"
    expl="VC for shortest_path_code"
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    sum="4b24f354a67f8b0aa7531f9922ac5988"
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    proved="true"
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    expanded="true"
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    shape="iNapathV0V10V11FINamemV10V8FAashortest_pathV0V12amixfix []V7V12IamemV12V8Fiainfix &lt;ainfix -acardinalavacardinalV15ainfix -acardinalavacardinalV8Aainfix &lt;=c0ainfix -acardinalavacardinalV8AamemV21V15Iainfix &lt;V22amixfix []V18V20IapathV0V21V22FFIaminV20V17V18FAainv_succV0V15V17V18AainvV0V15V17V18ainfix &lt;acardinalV23acardinalV16Aainfix &lt;=c0acardinalV16Aainv_succ2V0V15V25V26V14V23AainvV0V15V25V26AasubsetV23ag_succV14Aainfix &lt;=amixfix []V26V24ainfix +amixfix []V26V14aweightV14V24Iainfix =V26amixfix [&lt;-]V18V24ainfix +amixfix []V18V14aweightV14V24Aainfix =V25aaddV24V17ANamemV24V17ANamemV24V15Oainfix =V26amixfix [&lt;-]V18V24ainfix +amixfix []V18V14aweightV14V24Aainfix =V25V17Aainfix &lt;ainfix +amixfix []V18V14aweightV14V24amixfix []V18V24AamemV24V25Oainfix =V26V18Aainfix =V25V17Aainfix &gt;=ainfix +amixfix []V26V14aweightV14V24amixfix []V26V24AamemV24V25Oainfix =V26V18Aainfix =V25V17AamemV24V15FIainfix =V23aremoveV24V16AamemV24V16FFANais_emptyV16ainfix =V19aTrueINais_emptyV16qainfix =V19aTrueFIainv_succ2V0V15V17V18V14V16AainvV0V15V17V18AasubsetV16ag_succV14FAainv_succ2V0V15V13V7V14ag_succV14AainvV0V15V13V7Aasubsetag_succV14ag_succV14Iainfix =V15aaddV14V8FAashortest_pathV0V14amixfix []V7V14Iainfix =V13aremoveV14V6AaminV14V6V7FFANais_emptyV6Nainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV28V8Iainfix &lt;V29amixfix []V7V27IapathV0V28V29FFIaminV27V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FAamemV31V5Iainfix &lt;V32amixfix []V4V30IapathV0V31V32FFIaminV30V3V4FAainv_succV0V5V3V4AainvV0V5V3V4Iainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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    <label
     name="expl:VC for shortest_path_code"/>
    <transf
     name="split_goal_wp"
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     proved="true"
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     expanded="true">
     <goal
      name="WP_parameter shortest_path_code.1"
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
      expl="1. loop invariant init"
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      sum="a5fff86cb29c55cc9b50f5bca67d29f2"
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      proved="true"
      expanded="false"
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      shape="loop invariant initainvV0V5V3V4Iainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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      <label
       name="expl:VC for shortest_path_code"/>
      <proof
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       prover="2"
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       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.20"/>
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      </proof>
      <proof
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       prover="5"
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       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.14"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter shortest_path_code.2"
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
      expl="2. loop invariant init"
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      sum="f29d3d490b1e78dc76b9c9f69d6fd759"
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      proved="true"
      expanded="false"
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      shape="loop invariant initainv_succV0V5V3V4Iainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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      <label
       name="expl:VC for shortest_path_code"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
      <proof
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       prover="2"
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       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
      </proof>
      <proof
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       prover="5"
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       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter shortest_path_code.3"
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
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      expl="3. loop invariant init"
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      sum="5729a0d294abb5f230273432430dc021"
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      proved="true"
      expanded="false"
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      shape="loop invariant initamemV7V5Iainfix &lt;V8amixfix []V4V6IapathV0V7V8FFIaminV6V3V4FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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      <label
       name="expl:VC for shortest_path_code"/>
      <proof
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       prover="5"
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       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.04"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter shortest_path_code.4"
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
      expl="4. precondition"
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      sum="3374fbe6abcf8c96f18f5d73128e5651"
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      proved="true"
      expanded="false"
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      shape="preconditionNais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV11V8Iainfix &lt;V12amixfix []V7V10IapathV0V11V12FFIaminV10V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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      <label
       name="expl:VC for shortest_path_code"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
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      name="WP_parameter shortest_path_code.5"
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      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
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      expl="5. assertion"
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      sum="109480cbb5d4c43dce6a9c9f335cf1fc"
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      proved="true"
      expanded="false"
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      shape="assertionashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV13V8Iainfix &lt;V14amixfix []V7V12IapathV0V13V14FFIaminV12V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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      <label
       name="expl:VC for shortest_path_code"/>
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      <proof
       prover="0"
       timelimit="15"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.05"/>
      </proof>
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      <proof
       prover="1"
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       timelimit="15"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
      </proof>
      <proof
       prover="2"
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       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.07"/>
      </proof>
      <proof
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       prover="3"
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       timelimit="15"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
      <proof
       prover="5"
       timelimit="15"
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       memlimit="1000"
       obsolete="false"
       archived="false">
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MARCHE Claude committed
391
       <result status="valid" time="0.58"/>
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      </proof>
     </goal>
     <goal
395
      name="WP_parameter shortest_path_code.6"
396 397
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
398
      expl="6. loop invariant init"
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MARCHE Claude committed
399
      sum="0e5264bbc6b4bfc9736946a1ce81d85c"
400 401
      proved="true"
      expanded="false"
402
      shape="loop invariant initasubsetag_succV11ag_succV11Iainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV14V8Iainfix &lt;V15amixfix []V7V13IapathV0V14V15FFIaminV13V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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      <label
       name="expl:VC for shortest_path_code"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
415
      name="WP_parameter shortest_path_code.7"
416 417
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
418
      expl="7. loop invariant init"
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MARCHE Claude committed
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      sum="497a214e6d30bdc3f9149e846266cf01"
420 421
      proved="true"
      expanded="false"
422
      shape="loop invariant initainvV0V12V10V7Iainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV14V8Iainfix &lt;V15amixfix []V7V13IapathV0V14V15FFIaminV13V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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      <label
       name="expl:VC for shortest_path_code"/>
      <transf
       name="inline_goal"
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       proved="true"
       expanded="false">
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       <goal
430
        name="WP_parameter shortest_path_code.7.1"
431 432 433
        locfile="../dijkstra.mlw"
        loclnum="186" loccnumb="6" loccnume="24"
        expl="1. loop invariant init"
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MARCHE Claude committed
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        sum="7bc37f73f4ce309feaf1fc5c74a694c3"
435 436
        proved="true"
        expanded="false"
437
        shape="loop invariant initapathV0V13amixfix []V7V13IamemV13V10FAashortest_pathV0V14amixfix []V7V14IamemV14V12FAfIamemV15V12IamemV15V10FAasubsetV10avAasubsetV12avAainfix =amixfix []V7V0c0Aainv_srcV0V12V10Iainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V16IapathV0V11V16FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V17IamemV17V6FAamemV11V6FFINNamemV18V6FINainfix =V9aTrueINamemV19V6Fqainfix =V9aTrueFIamemV21V8Iainfix &lt;V22amixfix []V7V20IapathV0V21V22FFIainfix &lt;=amixfix []V7V20amixfix []V7V23IamemV23V6FAamemV20V6FAainfix &lt;=amixfix []V7V25ainfix +amixfix []V7V24aweightV24V25AamemV25V6OamemV25V8IamemV25ag_succV24FIamemV24V8FAapathV0V26amixfix []V7V26IamemV26V6FAashortest_pathV0V27amixfix []V7V27IamemV27V8FAfIamemV28V8IamemV28V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV29V5FFIamemV1avAamemV0avFF">
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        <label
         name="expl:VC for shortest_path_code"/>
        <transf
         name="split_goal_wp"
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         proved="true"
         expanded="false">
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         <goal
445
          name="WP_parameter shortest_path_code.7.1.1"
446 447 448
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="1."
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449
          sum="fc68898478cf52023b26df9cf91dad54"
450 451
          proved="true"
          expanded="false"
452
          shape="ainv_srcV0V12V10Iainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V13IapathV0V11V13FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V14IamemV14V6FAamemV11V6FFINNamemV15V6FINainfix =V9aTrueINamemV16V6Fqainfix =V9aTrueFIamemV18V8Iainfix &lt;V19amixfix []V7V17IapathV0V18V19FFIainfix &lt;=amixfix []V7V17amixfix []V7V20IamemV20V6FAamemV17V6FAainfix &lt;=amixfix []V7V22ainfix +amixfix []V7V21aweightV21V22AamemV22V6OamemV22V8IamemV22ag_succV21FIamemV21V8FAapathV0V23amixfix []V7V23IamemV23V6FAashortest_pathV0V24amixfix []V7V24IamemV24V8FAfIamemV25V8IamemV25V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV26V5FFIamemV1avAamemV0avFF">
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          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.03"/>
          </proof>
         </goal>
         <goal
465
          name="WP_parameter shortest_path_code.7.1.2"
466 467 468
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="2."
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MARCHE Claude committed
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          sum="faaa935bdf8c64b9e94b95c35ed2a975"
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          proved="true"
          expanded="false"
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          shape="ainfix =amixfix []V7V0c0Iainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V13IapathV0V11V13FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V14IamemV14V6FAamemV11V6FFINNamemV15V6FINainfix =V9aTrueINamemV16V6Fqainfix =V9aTrueFIamemV18V8Iainfix &lt;V19amixfix []V7V17IapathV0V18V19FFIainfix &lt;=amixfix []V7V17amixfix []V7V20IamemV20V6FAamemV17V6FAainfix &lt;=amixfix []V7V22ainfix +amixfix []V7V21aweightV21V22AamemV22V6OamemV22V8IamemV22ag_succV21FIamemV21V8FAapathV0V23amixfix []V7V23IamemV23V6FAashortest_pathV0V24amixfix []V7V24IamemV24V8FAfIamemV25V8IamemV25V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV26V5FFIamemV1avAamemV0avFF">
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          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.01"/>
          </proof>
         </goal>
         <goal
485
          name="WP_parameter shortest_path_code.7.1.3"
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          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="3."
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MARCHE Claude committed
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          sum="2f9b9e202f8b4771cb2ed69ac7efc23b"
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          proved="true"
          expanded="false"
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          shape="asubsetV12avIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V13IapathV0V11V13FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V14IamemV14V6FAamemV11V6FFINNamemV15V6FINainfix =V9aTrueINamemV16V6Fqainfix =V9aTrueFIamemV18V8Iainfix &lt;V19amixfix []V7V17IapathV0V18V19FFIainfix &lt;=amixfix []V7V17amixfix []V7V20IamemV20V6FAamemV17V6FAainfix &lt;=amixfix []V7V22ainfix +amixfix []V7V21aweightV21V22AamemV22V6OamemV22V8IamemV22ag_succV21FIamemV21V8FAapathV0V23amixfix []V7V23IamemV23V6FAashortest_pathV0V24amixfix []V7V24IamemV24V8FAfIamemV25V8IamemV25V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV26V5FFIamemV1avAamemV0avFF">
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          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="30"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.02"/>
          </proof>
         </goal>
         <goal
505
          name="WP_parameter shortest_path_code.7.1.4"
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          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="4."
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          sum="e720fb07385b10048a8210f3859baee7"
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          proved="true"
          expanded="false"
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          shape="asubsetV10avIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V13IapathV0V11V13FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V14IamemV14V6FAamemV11V6FFINNamemV15V6FINainfix =V9aTrueINamemV16V6Fqainfix =V9aTrueFIamemV18V8Iainfix &lt;V19amixfix []V7V17IapathV0V18V19FFIainfix &lt;=amixfix []V7V17amixfix []V7V20IamemV20V6FAamemV17V6FAainfix &lt;=amixfix []V7V22ainfix +amixfix []V7V21aweightV21V22AamemV22V6OamemV22V8IamemV22ag_succV21FIamemV21V8FAapathV0V23amixfix []V7V23IamemV23V6FAashortest_pathV0V24amixfix []V7V24IamemV24V8FAfIamemV25V8IamemV25V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV26V5FFIamemV1avAamemV0avFF">
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          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="30"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.01"/>
          </proof>
         </goal>
         <goal
525
          name="WP_parameter shortest_path_code.7.1.5"
526 527 528
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="5."
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          sum="51472b9a45d0c486afe7a80a34ca789a"
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          proved="true"
          expanded="false"
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          shape="fIamemV13V12IamemV13V10FIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V14IapathV0V11V14FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V15IamemV15V6FAamemV11V6FFINNamemV16V6FINainfix =V9aTrueINamemV17V6Fqainfix =V9aTrueFIamemV19V8Iainfix &lt;V20amixfix []V7V18IapathV0V19V20FFIainfix &lt;=amixfix []V7V18amixfix []V7V21IamemV21V6FAamemV18V6FAainfix &lt;=amixfix []V7V23ainfix +amixfix []V7V22aweightV22V23AamemV23V6OamemV23V8IamemV23ag_succV22FIamemV22V8FAapathV0V24amixfix []V7V24IamemV24V6FAashortest_pathV0V25amixfix []V7V25IamemV25V8FAfIamemV26V8IamemV26V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV27V5FFIamemV1avAamemV0avFF">
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          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="30"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.16"/>
          </proof>
         </goal>
         <goal
545
          name="WP_parameter shortest_path_code.7.1.6"
546 547 548
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="6."
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          sum="52afe2b1e607ba153472eb2bb2f14d10"
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          proved="true"
          expanded="false"
552
          shape="ashortest_pathV0V13amixfix []V7V13IamemV13V12FIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V14IapathV0V11V14FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V15IamemV15V6FAamemV11V6FFINNamemV16V6FINainfix =V9aTrueINamemV17V6Fqainfix =V9aTrueFIamemV19V8Iainfix &lt;V20amixfix []V7V18IapathV0V19V20FFIainfix &lt;=amixfix []V7V18amixfix []V7V21IamemV21V6FAamemV18V6FAainfix &lt;=amixfix []V7V23ainfix +amixfix []V7V22aweightV22V23AamemV23V6OamemV23V8IamemV23ag_succV22FIamemV22V8FAapathV0V24amixfix []V7V24IamemV24V6FAashortest_pathV0V25amixfix []V7V25IamemV25V8FAfIamemV26V8IamemV26V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV27V5FFIamemV1avAamemV0avFF">
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          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="30"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.41"/>
          </proof>
         </goal>
         <goal
565
          name="WP_parameter shortest_path_code.7.1.7"
566 567 568
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="7."
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          sum="7028acfffbaa6e2edeb6ae6fac2e99fb"
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          proved="true"
          expanded="false"
572
          shape="apathV0V13amixfix []V7V13IamemV13V10FIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V14IapathV0V11V14FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V15IamemV15V6FAamemV11V6FFINNamemV16V6FINainfix =V9aTrueINamemV17V6Fqainfix =V9aTrueFIamemV19V8Iainfix &lt;V20amixfix []V7V18IapathV0V19V20FFIainfix &lt;=amixfix []V7V18amixfix []V7V21IamemV21V6FAamemV18V6FAainfix &lt;=amixfix []V7V23ainfix +amixfix []V7V22aweightV22V23AamemV23V6OamemV23V8IamemV23ag_succV22FIamemV22V8FAapathV0V24amixfix []V7V24IamemV24V6FAashortest_pathV0V25amixfix []V7V25IamemV25V8FAfIamemV26V8IamemV26V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV27V5FFIamemV1avAamemV0avFF">
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          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="30"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.08"/>
          </proof>
         </goal>
        </transf>
       </goal>
      </transf>
     </goal>
     <goal
589
      name="WP_parameter shortest_path_code.8"
590 591
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
592
      expl="8. loop invariant init"
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      sum="b0a024f143aa083025ee5ee24f459b1b"
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      proved="true"
      expanded="false"
596
      shape="loop invariant initainv_succ2V0V12V10V7V11ag_succV11Iainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV14V8Iainfix &lt;V15amixfix []V7V13IapathV0V14V15FFIaminV13V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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      <label
       name="expl:VC for shortest_path_code"/>
      <transf
       name="split_goal_wp"
       proved="true"
       expanded="false">
       <goal
604
        name="WP_parameter shortest_path_code.8.1"
605 606 607
        locfile="../dijkstra.mlw"
        loclnum="186" loccnumb="6" loccnume="24"
        expl="1. loop invariant init"
MARCHE Claude's avatar
MARCHE Claude committed
608
        sum="b0a024f143aa083025ee5ee24f459b1b"
609 610
        proved="true"
        expanded="false"
611
        shape="loop invariant initainv_succ2V0V12V10V7V11ag_succV11Iainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV14V8Iainfix &lt;V15amixfix []V7V13IapathV0V14V15FFIaminV13V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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        <label
         name="expl:VC for shortest_path_code"/>
        <proof
         prover="0"
         timelimit="5"
         memlimit="1000"
         obsolete="false"
         archived="false">
         <result status="valid" time="0.18"/>
        </proof>
       </goal>
      </transf>
     </goal>
     <goal
626
      name="WP_parameter shortest_path_code.9"
627 628
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
629
      expl="9. precondition"
MARCHE Claude's avatar
MARCHE Claude committed
630
      sum="03dc5dabadbc87b526c7f13865e52dca"
631 632
      proved="true"
      expanded="false"
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      shape="preconditionNais_emptyV13Iainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV18V8Iainfix &lt;V19amixfix []V7V17IapathV0V18V19FFIaminV17V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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      <label
       name="expl:VC for shortest_path_code"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
644 645 646 647 648 649
     </goal>
     <goal
      name="WP_parameter shortest_path_code.10"
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
      expl="10. assertion"
MARCHE Claude's avatar
MARCHE Claude committed
650
      sum="f618dae38a5ad80ac7c4ac22a72e332c"
651 652
      proved="true"
      expanded="false"
653
      shape="assertionainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &gt;=ainfix +amixfix []V20V11aweightV11V18amixfix []V20V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINais_emptyV13Iainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV22V8Iainfix &lt;V23amixfix []V7V21IapathV0V22V23FFIaminV21V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
654 655
      <label
       name="expl:VC for shortest_path_code"/>
656
      <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
657
       prover="5"
658 659
       timelimit="5"
       memlimit="1000"
660
       obsolete="false"
661
       archived="false">
662
       <result status="valid" time="0.08"/>
663 664 665
      </proof>
     </goal>
     <goal
666
      name="WP_parameter shortest_path_code.11"
667 668
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
669
      expl="11. loop invariant preservation"
MARCHE Claude's avatar
MARCHE Claude committed
670
      sum="0bc4442164596c8bd83d88ff8ff3c4de"
671 672
      proved="true"
      expanded="false"
673
      shape="loop invariant preservationasubsetV17ag_succV11Iainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &gt;=ainfix +amixfix []V20V11aweightV11V18amixfix []V20V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINais_emptyV13Iainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV22V8Iainfix &lt;V23amixfix []V7V21IapathV0V22V23FFIaminV21V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
674 675 676 677 678 679 680 681 682 683 684 685
      <label
       name="expl:VC for shortest_path_code"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
686
      name="WP_parameter shortest_path_code.12"
687 688
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
689
      expl="12. loop invariant preservation"
MARCHE Claude's avatar
MARCHE Claude committed
690
      sum="6ead39a58d7f984f32ffd36e6448a5e5"
691
      proved="true"
692
      expanded="false"
693
      shape="loop invariant preservationainvV0V12V19V20Iainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &gt;=ainfix +amixfix []V20V11aweightV11V18amixfix []V20V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINais_emptyV13Iainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV22V8Iainfix &lt;V23amixfix []V7V21IapathV0V22V23FFIaminV21V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
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      <label
       name="expl:VC for shortest_path_code"/>
      <transf
       name="inline_goal"
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       proved="true"
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       expanded="false">
700
       <goal
701
        name="WP_parameter shortest_path_code.12.1"
702 703 704
        locfile="../dijkstra.mlw"
        loclnum="186" loccnumb="6" loccnume="24"
        expl="1. loop invariant preservation"
MARCHE Claude's avatar
MARCHE Claude committed
705
        sum="40565c279964e9ba571cf247c0e2e358"
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        proved="true"
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        expanded="false"
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        shape="loop invariant preservationapathV0V21amixfix []V20V21IamemV21V19FAashortest_pathV0V22amixfix []V20V22IamemV22V12FAfIamemV23V12IamemV23V19FAasubsetV19avAasubsetV12avAainfix =amixfix []V20V0c0Aainv_srcV0V12V19Iainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV24V13FIainfix =V16aTrueINNamemV25V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V27ainfix +amixfix []V15V26aweightV26V27AamemV27V14OamemV27V12INamemV27V13Aainfix =V26V11ONainfix =V26V11IamemV27ag_succV26FIamemV26V12FAapathV0V28amixfix []V15V28IamemV28V14FAashortest_pathV0V29amixfix []V15V29IamemV29V12FAfIamemV30V12IamemV30V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV31ag_succV11IamemV31V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V32IapathV0V11V32FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V33IamemV33V6FAamemV11V6FFINNamemV34V6FINainfix =V9aTrueINamemV35V6Fqainfix =V9aTrueFIamemV37V8Iainfix &lt;V38amixfix []V7V36IapathV0V37V38FFIainfix &lt;=amixfix []V7V36amixfix []V7V39IamemV39V6FAamemV36V6FAainfix &lt;=amixfix []V7V41ainfix +amixfix []V7V40aweightV40V41AamemV41V6OamemV41V8IamemV41ag_succV40FIamemV40V8FAapathV0V42amixfix []V7V42IamemV42V6FAashortest_pathV0V43amixfix []V7V43IamemV43V8FAfIamemV44V8IamemV44V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV45V5FFIamemV1avAamemV0avFF">
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        <label
         name="expl:VC for shortest_path_code"/>
        <transf
         name="split_goal_wp"
713
         proved="true"
714
         expanded="false">
715
         <goal
716
          name="WP_parameter shortest_path_code.12.1.1"
717 718 719
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="1."
MARCHE Claude's avatar
MARCHE Claude committed
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          sum="9b051eb437dc7927ae463dbe2c5cfc98"
721 722
          proved="true"
          expanded="false"
723
          shape="ainv_srcV0V12V19Iainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV21V13FIainfix =V16aTrueINNamemV22V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V24ainfix +amixfix []V15V23aweightV23V24AamemV24V14OamemV24V12INamemV24V13Aainfix =V23V11ONainfix =V23V11IamemV24ag_succV23FIamemV23V12FAapathV0V25amixfix []V15V25IamemV25V14FAashortest_pathV0V26amixfix []V15V26IamemV26V12FAfIamemV27V12IamemV27V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV28ag_succV11IamemV28V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V29IapathV0V11V29FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V30IamemV30V6FAamemV11V6FFINNamemV31V6FINainfix =V9aTrueINamemV32V6Fqainfix =V9aTrueFIamemV34V8Iainfix &lt;V35amixfix []V7V33IapathV0V34V35FFIainfix &lt;=amixfix []V7V33amixfix []V7V36IamemV36V6FAamemV33V6FAainfix &lt;=amixfix []V7V38ainfix +amixfix []V7V37aweightV37V38AamemV38V6OamemV38V8IamemV38ag_succV37FIamemV37V8FAapathV0V39amixfix []V7V39IamemV39V6FAashortest_pathV0V40amixfix []V7V40IamemV40V8FAfIamemV41V8IamemV41V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV42V5FFIamemV1avAamemV0avFF">
724 725 726 727 728 729 730 731
          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
732
           <result status="valid" time="0.44"/>
733 734 735
          </proof>
         </goal>
         <goal
736
          name="WP_parameter shortest_path_code.12.1.2"
737 738 739
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="2."
MARCHE Claude's avatar
MARCHE Claude committed
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          sum="eba747aacbb3063fee227c0d5d67d224"
741 742
          proved="true"
          expanded="false"
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          shape="ainfix =amixfix []V20V0c0Iainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV21V13FIainfix =V16aTrueINNamemV22V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V24ainfix +amixfix []V15V23aweightV23V24AamemV24V14OamemV24V12INamemV24V13Aainfix =V23V11ONainfix =V23V11IamemV24ag_succV23FIamemV23V12FAapathV0V25amixfix []V15V25IamemV25V14FAashortest_pathV0V26amixfix []V15V26IamemV26V12FAfIamemV27V12IamemV27V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV28ag_succV11IamemV28V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V29IapathV0V11V29FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V30IamemV30V6FAamemV11V6FFINNamemV31V6FINainfix =V9aTrueINamemV32V6Fqainfix =V9aTrueFIamemV34V8Iainfix &lt;V35amixfix []V7V33IapathV0V34V35FFIainfix &lt;=amixfix []V7V33amixfix []V7V36IamemV36V6FAamemV33V6FAainfix &lt;=amixfix []V7V38ainfix +amixfix []V7V37aweightV37V38AamemV38V6OamemV38V8IamemV38ag_succV37FIamemV37V8FAapathV0V39amixfix []V7V39IamemV39V6FAashortest_pathV0V40amixfix []V7V40IamemV40V8FAfIamemV41V8IamemV41V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV42V5FFIamemV1avAamemV0avFF">
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          <label
           name="expl:VC for shortest_path_code"/>
          <proof
Andrei Paskevich's avatar
Andrei Paskevich committed
747
           prover="2"
748 749 750 751
           timelimit="10"
           memlimit="1000"
           obsolete="false"
           archived="false">
752
           <result status="valid" time="0.28"/>
753 754 755
          </proof>
         </goal>
         <goal
756
          name="WP_parameter shortest_path_code.12.1.3"
757 758 759
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="3."
MARCHE Claude's avatar
MARCHE Claude committed
760
          sum="50a7c3695c6997192ed94fac6678d3c0"
761 762
          proved="true"
          expanded="false"
763
          shape="asubsetV12avIainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV21V13FIainfix =V16aTrueINNamemV22V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V24ainfix +amixfix []V15V23aweightV23V24AamemV24V14OamemV24V12INamemV24V13Aainfix =V23V11ONainfix =V23V11IamemV24ag_succV23FIamemV23V12FAapathV0V25amixfix []V15V25IamemV25V14FAashortest_pathV0V26amixfix []V15V26IamemV26V12FAfIamemV27V12IamemV27V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV28ag_succV11IamemV28V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V29IapathV0V11V29FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V30IamemV30V6FAamemV11V6FFINNamemV31V6FINainfix =V9aTrueINamemV32V6Fqainfix =V9aTrueFIamemV34V8Iainfix &lt;V35amixfix []V7V33IapathV0V34V35FFIainfix &lt;=amixfix []V7V33amixfix []V7V36IamemV36V6FAamemV33V6FAainfix &lt;=amixfix []V7V38ainfix +amixfix []V7V37aweightV37V38AamemV38V6OamemV38V8IamemV38ag_succV37FIamemV37V8FAapathV0V39amixfix []V7V39IamemV39V6FAashortest_pathV0V40amixfix []V7V40IamemV40V8FAfIamemV41V8IamemV41V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV42V5FFIamemV1avAamemV0avFF">
764 765 766 767 768 769 770 771 772 773 774 775
          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
           <result status="valid" time="0.03"/>
          </proof>
         </goal>
         <goal
776
          name="WP_parameter shortest_path_code.12.1.4"
777 778 779
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="4."
MARCHE Claude's avatar
MARCHE Claude committed
780
          sum="b407af2bab0ab4011f046d9953091dc4"
781 782
          proved="true"
          expanded="false"
783
          shape="asubsetV19avIainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV21V13FIainfix =V16aTrueINNamemV22V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V24ainfix +amixfix []V15V23aweightV23V24AamemV24V14OamemV24V12INamemV24V13Aainfix =V23V11ONainfix =V23V11IamemV24ag_succV23FIamemV23V12FAapathV0V25amixfix []V15V25IamemV25V14FAashortest_pathV0V26amixfix []V15V26IamemV26V12FAfIamemV27V12IamemV27V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV28ag_succV11IamemV28V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V29IapathV0V11V29FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V30IamemV30V6FAamemV11V6FFINNamemV31V6FINainfix =V9aTrueINamemV32V6Fqainfix =V9aTrueFIamemV34V8Iainfix &lt;V35amixfix []V7V33IapathV0V34V35FFIainfix &lt;=amixfix []V7V33amixfix []V7V36IamemV36V6FAamemV33V6FAainfix &lt;=amixfix []V7V38ainfix +amixfix []V7V37aweightV37V38AamemV38V6OamemV38V8IamemV38ag_succV37FIamemV37V8FAapathV0V39amixfix []V7V39IamemV39V6FAashortest_pathV0V40amixfix []V7V40IamemV40V8FAfIamemV41V8IamemV41V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV42V5FFIamemV1avAamemV0avFF">
784 785 786
          <label
           name="expl:VC for shortest_path_code"/>
          <proof
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Andrei Paskevich committed
787
           prover="2"
788 789 790 791
           timelimit="10"
           memlimit="1000"
           obsolete="false"
           archived="false">
792
           <result status="valid" time="1.94"/>
793 794 795
          </proof>
         </goal>
         <goal
796
          name="WP_parameter shortest_path_code.12.1.5"
797 798 799
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="5."
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MARCHE Claude committed
800
          sum="fb8e2b29225461fadb8357aa0c10e3ee"
801 802
          proved="true"
          expanded="false"
803
          shape="fIamemV21V12IamemV21V19FIainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV22V13FIainfix =V16aTrueINNamemV23V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V25ainfix +amixfix []V15V24aweightV24V25AamemV25V14OamemV25V12INamemV25V13Aainfix =V24V11ONainfix =V24V11IamemV25ag_succV24FIamemV24V12FAapathV0V26amixfix []V15V26IamemV26V14FAashortest_pathV0V27amixfix []V15V27IamemV27V12FAfIamemV28V12IamemV28V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV29ag_succV11IamemV29V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V30IapathV0V11V30FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V31IamemV31V6FAamemV11V6FFINNamemV32V6FINainfix =V9aTrueINamemV33V6Fqainfix =V9aTrueFIamemV35V8Iainfix &lt;V36amixfix []V7V34IapathV0V35V36FFIainfix &lt;=amixfix []V7V34amixfix []V7V37IamemV37V6FAamemV34V6FAainfix &lt;=amixfix []V7V39ainfix +amixfix []V7V38aweightV38V39AamemV39V6OamemV39V8IamemV39ag_succV38FIamemV38V8FAapathV0V40amixfix []V7V40IamemV40V6FAashortest_pathV0V41amixfix []V7V41IamemV41V8FAfIamemV42V8IamemV42V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV43V5FFIamemV1avAamemV0avFF">
804 805 806 807 808 809 810 811
          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
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Andrei Paskevich committed
812
           <result status="valid" time="2.23"/>
813 814 815
          </proof>
         </goal>
         <goal
816
          name="WP_parameter shortest_path_code.12.1.6"
817 818 819
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="6."
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MARCHE Claude committed
820
          sum="0610c5461a6a5613321152f6a0130365"
821 822
          proved="true"
          expanded="false"
823
          shape="ashortest_pathV0V21amixfix []V20V21IamemV21V12FIainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV22V13FIainfix =V16aTrueINNamemV23V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V25ainfix +amixfix []V15V24aweightV24V25AamemV25V14OamemV25V12INamemV25V13Aainfix =V24V11ONainfix =V24V11IamemV25ag_succV24FIamemV24V12FAapathV0V26amixfix []V15V26IamemV26V14FAashortest_pathV0V27amixfix []V15V27IamemV27V12FAfIamemV28V12IamemV28V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV29ag_succV11IamemV29V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V30IapathV0V11V30FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V31IamemV31V6FAamemV11V6FFINNamemV32V6FINainfix =V9aTrueINamemV33V6Fqainfix =V9aTrueFIamemV35V8Iainfix &lt;V36amixfix []V7V34IapathV0V35V36FFIainfix &lt;=amixfix []V7V34amixfix []V7V37IamemV37V6FAamemV34V6FAainfix &lt;=amixfix []V7V39ainfix +amixfix []V7V38aweightV38V39AamemV39V6OamemV39V8IamemV39ag_succV38FIamemV38V8FAapathV0V40amixfix []V7V40IamemV40V6FAashortest_pathV0V41amixfix []V7V41IamemV41V8FAfIamemV42V8IamemV42V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV43V5FFIamemV1avAamemV0avFF">
824 825 826 827 828 829 830 831
          <label
           name="expl:VC for shortest_path_code"/>
          <proof
           prover="0"
           timelimit="5"
           memlimit="1000"
           obsolete="false"
           archived="false">
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MARCHE Claude committed
832
           <result status="valid" time="0.42"/>
833 834 835
          </proof>
         </goal>
         <goal
836
          name="WP_parameter shortest_path_code.12.1.7"
837 838 839
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="7."
MARCHE Claude's avatar
MARCHE Claude committed
840
          sum="75a24182b38eca60cd2ea9550a71bb4f"
841
          proved="true"
842
          expanded="false"
843
          shape="apathV0V21amixfix []V20V21IamemV21V19FIainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV22V13FIainfix =V16aTrueINNamemV23V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V25ainfix +amixfix []V15V24aweightV24V25AamemV25V14OamemV25V12INamemV25V13Aainfix =V24V11ONainfix =V24V11IamemV25ag_succV24FIamemV24V12FAapathV0V26amixfix []V15V26IamemV26V14FAashortest_pathV0V27amixfix []V15V27IamemV27V12FAfIamemV28V12IamemV28V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV29ag_succV11IamemV29V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V30IapathV0V11V30FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V31IamemV31V6FAamemV11V6FFINNamemV32V6FINainfix =V9aTrueINamemV33V6Fqainfix =V9aTrueFIamemV35V8Iainfix &lt;V36amixfix []V7V34IapathV0V35V36FFIainfix &lt;=amixfix []V7V34amixfix []V7V37IamemV37V6FAamemV34V6FAainfix &lt;=amixfix []V7V39ainfix +amixfix []V7V38aweightV38V39AamemV39V6OamemV39V8IamemV39ag_succV38FIamemV38V8FAapathV0V40amixfix []V7V40IamemV40V6FAashortest_pathV0V41amixfix []V7V41IamemV41V8FAfIamemV42V8IamemV42V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV43V5FFIamemV1avAamemV0avFF">
844 845 846
          <label
           name="expl:VC for shortest_path_code"/>
          <proof
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Andrei Paskevich committed
847
           prover="4"
848
           timelimit="30"
849 850 851 852
           memlimit="1000"
           edited="dijkstra_DijkstraShortestPath_WP_parameter_shortest_path_code_2.v"
           obsolete="false"
           archived="false">
Andrei Paskevich's avatar
Andrei Paskevich committed
853
           <result status="valid" time="12.63"/>
854 855 856 857 858 859 860
          </proof>
         </goal>
        </transf>
       </goal>
      </transf>
     </goal>
     <goal
861
      name="WP_parameter shortest_path_code.13"
862 863
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
864
      expl="13. loop invariant preservation"
MARCHE Claude's avatar
MARCHE Claude committed
865
      sum="6297bbd76ea297ce9ee1c2aec2ec1edd"
866 867
      proved="true"
      expanded="false"
868
      shape="loop invariant preservationainv_succ2V0V12V19V20V11V17Iainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &gt;=ainfix +amixfix []V20V11aweightV11V18amixfix []V20V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINais_emptyV13Iainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV22V8Iainfix &lt;V23amixfix []V7V21IapathV0V22V23FFIaminV21V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
869 870 871 872 873 874 875
      <label
       name="expl:VC for shortest_path_code"/>
      <transf
       name="split_goal_wp"
       proved="true"
       expanded="false">
       <goal
876
        name="WP_parameter shortest_path_code.13.1"
877 878 879
        locfile="../dijkstra.mlw"
        loclnum="186" loccnumb="6" loccnume="24"
        expl="1. loop invariant preservation"
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MARCHE Claude committed
880
        sum="6297bbd76ea297ce9ee1c2aec2ec1edd"
881 882
        proved="true"
        expanded="false"
883
        shape="loop invariant preservationainv_succ2V0V12V19V20V11V17Iainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &gt;=ainfix +amixfix []V20V11aweightV11V18amixfix []V20V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINais_emptyV13Iainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV22V8Iainfix &lt;V23amixfix []V7V21IapathV0V22V23FFIaminV21V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
884 885
        <label
         name="expl:VC for shortest_path_code"/>
886 887 888 889 890 891 892 893 894
        <transf
         name="inline_goal"
         proved="true"
         expanded="false">
         <goal
          name="WP_parameter shortest_path_code.13.1.1"
          locfile="../dijkstra.mlw"
          loclnum="186" loccnumb="6" loccnume="24"
          expl="1. loop invariant preservation"
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MARCHE Claude committed
895
          sum="76128a03a580ab98029ab0600abcf198"
896 897
          proved="true"
          expanded="false"
898
          shape="loop invariant preservationainfix &lt;=amixfix []V20V22ainfix +amixfix []V20V21aweightV21V22AamemV22V19OamemV22V12INamemV22V17Aainfix =V21V11ONainfix =V21V11IamemV22ag_succV21FIamemV21V12FIainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV23V13FIainfix =V16aTrueINNamemV24V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V26ainfix +amixfix []V15V25aweightV25V26AamemV26V14OamemV26V12INamemV26V13Aainfix =V25V11ONainfix =V25V11IamemV26ag_succV25FIamemV25V12FAapathV0V27amixfix []V15V27IamemV27V14FAashortest_pathV0V28amixfix []V15V28IamemV28V12FAfIamemV29V12IamemV29V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV30ag_succV11IamemV30V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V31IapathV0V11V31FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V32IamemV32V6FAamemV11V6FFINNamemV33V6FINainfix =V9aTrueINamemV34V6Fqainfix =V9aTrueFIamemV36V8Iainfix &lt;V37amixfix []V7V35IapathV0V36V37FFIainfix &lt;=amixfix []V7V35amixfix []V7V38IamemV38V6FAamemV35V6FAainfix &lt;=amixfix []V7V40ainfix +amixfix []V7V39aweightV39V40AamemV40V6OamemV40V8IamemV40ag_succV39FIamemV39V8FAapathV0V41amixfix []V7V41IamemV41V6FAashortest_pathV0V42amixfix []V7V42IamemV42V8FAfIamemV43V8IamemV43V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV44V5FFIamemV1avAamemV0avFF">
899 900 901 902 903 904 905 906 907 908 909
          <label
           name="expl:VC for shortest_path_code"/>
          <transf
           name="split_goal_wp"
           proved="true"
           expanded="false">
           <goal
            name="WP_parameter shortest_path_code.13.1.1.1"
            locfile="../dijkstra.mlw"
            loclnum="186" loccnumb="6" loccnume="24"
            expl="1. loop invariant preservation"
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MARCHE Claude committed
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            sum="81e47b5c002b688fff83bec6a14c08b4"
911 912
            proved="true"
            expanded="false"
913
            shape="loop invariant preservationamemV22V19OamemV22V12INamemV22V17Aainfix =V21V11ONainfix =V21V11IamemV22ag_succV21FIamemV21V12FIainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV23V13FIainfix =V16aTrueINNamemV24V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V26ainfix +amixfix []V15V25aweightV25V26AamemV26V14OamemV26V12INamemV26V13Aainfix =V25V11ONainfix =V25V11IamemV26ag_succV25FIamemV25V12FAapathV0V27amixfix []V15V27IamemV27V14FAashortest_pathV0V28amixfix []V15V28IamemV28V12FAfIamemV29V12IamemV29V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV30ag_succV11IamemV30V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V31IapathV0V11V31FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V32IamemV32V6FAamemV11V6FFINNamemV33V6FINainfix =V9aTrueINamemV34V6Fqainfix =V9aTrueFIamemV36V8Iainfix &lt;V37amixfix []V7V35IapathV0V36V37FFIainfix &lt;=amixfix []V7V35amixfix []V7V38IamemV38V6FAamemV35V6FAainfix &lt;=amixfix []V7V40ainfix +amixfix []V7V39aweightV39V40AamemV40V6OamemV40V8IamemV40ag_succV39FIamemV39V8FAapathV0V41amixfix []V7V41IamemV41V6FAashortest_pathV0V42amixfix []V7V42IamemV42V8FAfIamemV43V8IamemV43V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV44V5FFIamemV1avAamemV0avFF">
914 915 916
            <label
             name="expl:VC for shortest_path_code"/>
            <proof
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Andrei Paskevich committed
917
             prover="2"
918 919 920 921 922 923 924
             timelimit="5"
             memlimit="1000"
             obsolete="false"
             archived="false">
             <result status="valid" time="0.08"/>
            </proof>
            <proof
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Andrei Paskevich committed
925
             prover="5"
926 927 928 929
             timelimit="5"
             memlimit="1000"
             obsolete="false"
             archived="false">
930
             <result status="valid" time="3.26"/>
931 932 933 934 935 936 937
            </proof>
           </goal>
           <goal
            name="WP_parameter shortest_path_code.13.1.1.2"
            locfile="../dijkstra.mlw"
            loclnum="186" loccnumb="6" loccnume="24"
            expl="2. loop invariant preservation"
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MARCHE Claude committed
938
            sum="a65eaab5fa0db9096779d83f738ac02e"
939 940
            proved="true"
            expanded="false"
941
            shape="loop invariant preservationainfix &lt;=amixfix []V20V22ainfix +amixfix []V20V21aweightV21V22INamemV22V17Aainfix =V21V11ONainfix =V21V11IamemV22ag_succV21FIamemV21V12FIainfix =amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Oainfix &lt;amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20asetV15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINNamemV23V13FIainfix =V16aTrueINNamemV24V13Fqainfix =V16aTrueFIainfix &lt;=amixfix []V15V26ainfix +amixfix []V15V25aweightV25V26AamemV26V14OamemV26V12INamemV26V13Aainfix =V25V11ONainfix =V25V11IamemV26ag_succV25FIamemV25V12FAapathV0V27amixfix []V15V27IamemV27V14FAashortest_pathV0V28amixfix []V15V28IamemV28V12FAfIamemV29V12IamemV29V14FAasubsetV14avAasubsetV12avAainfix =amixfix []V15V0c0Aainv_srcV0V12V14AamemV30ag_succV11IamemV30V13FFIainfix =V12aaddV11V8FIainfix &lt;=amixfix []V7V11V31IapathV0V11V31FAapathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6Aainfix &lt;=amixfix []V7V11amixfix []V7V32IamemV32V6FAamemV11V6FFINNamemV33V6FINainfix =V9aTrueINamemV34V6Fqainfix =V9aTrueFIamemV36V8Iainfix &lt;V37amixfix []V7V35IapathV0V36V37FFIainfix &lt;=amixfix []V7V35amixfix []V7V38IamemV38V6FAamemV35V6FAainfix &lt;=amixfix []V7V40ainfix +amixfix []V7V39aweightV39V40AamemV40V6OamemV40V8IamemV40ag_succV39FIamemV39V8FAapathV0V41amixfix []V7V41IamemV41V6FAashortest_pathV0V42amixfix []V7V42IamemV42V8FAfIamemV43V8IamemV43V6FAasubsetV6avAasubsetV8avAainfix =amixfix []V7V0c0Aainv_srcV0V8V6FIainfix =V4asetV2V0c0Aainfix =V3aaddV0aemptyANamemV44V5FFIamemV1avAamemV0avFF">
942 943 944
            <label
             name="expl:VC for shortest_path_code"/>
            <proof
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Andrei Paskevich committed
945
             prover="2"
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             timelimit="5"
             memlimit="1000"
             obsolete="false"
             archived="false">
950
             <result status="valid" time="0.39"/>
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            </proof>
           </goal>
          </transf>
         </goal>
        </transf>
956 957 958 959
       </goal>
      </transf>
     </goal>
     <goal
960
      name="WP_parameter shortest_path_code.14"
961 962
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
963
      expl="14. loop variant decrease"
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MARCHE Claude committed
964
      sum="96101beb1c98785e0e11afb2f70e3298"
965 966
      proved="true"
      expanded="false"
967
      shape="loop variant decreaseainfix &lt;acardinalV17acardinalV13Aainfix &lt;=c0acardinalV13Iainfix &lt;=amixfix []V20V18ainfix +amixfix []V20V11aweightV11V18Iainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19aaddV18V14ANamemV18V14ANamemV18V12Oainfix =V20amixfix [&lt;-]V15V18ainfix +amixfix []V15V11aweightV11V18Aainfix =V19V14Aainfix &lt;ainfix +amixfix []V15V11aweightV11V18amixfix []V15V18AamemV18V19Oainfix =V20V15Aainfix =V19V14Aainfix &gt;=ainfix +amixfix []V20V11aweightV11V18amixfix []V20V18AamemV18V19Oainfix =V20V15Aainfix =V19V14AamemV18V12FIainfix =V17aremoveV18V13AamemV18V13FFINais_emptyV13Iainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV22V8Iainfix &lt;V23amixfix []V7V21IapathV0V22V23FFIaminV21V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
968 969 970 971 972 973 974 975 976 977 978 979
      <label
       name="expl:VC for shortest_path_code"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
      </proof>
     </goal>
     <goal
980
      name="WP_parameter shortest_path_code.15"
981 982
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
983
      expl="15. loop invariant preservation"
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MARCHE Claude committed
984
      sum="f5c42c65434fc369b734c19353126d25"
985 986
      proved="true"
      expanded="false"
987
      shape="loop invariant preservationainvV0V12V14V15INainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV18V8Iainfix &lt;V19amixfix []V7V17IapathV0V18V19FFIaminV17V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
988 989 990 991 992 993 994 995 996 997 998 999
      <label
       name="expl:VC for shortest_path_code"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
1000
      name="WP_parameter shortest_path_code.16"
1001 1002
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
1003
      expl="16. loop invariant preservation"
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MARCHE Claude committed
1004
      sum="0ffeeac46cbb1fff045c9e567cd5c7c8"
1005 1006
      proved="true"
      expanded="false"
1007
      shape="loop invariant preservationainv_succV0V12V14V15INainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV18V8Iainfix &lt;V19amixfix []V7V17IapathV0V18V19FFIaminV17V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
1008 1009 1010
      <label
       name="expl:VC for shortest_path_code"/>
      <proof
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Andrei Paskevich committed
1011
       prover="5"
1012 1013 1014 1015
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
1016
       <result status="valid" time="0.03"/>
1017 1018 1019
      </proof>
     </goal>
     <goal
1020
      name="WP_parameter shortest_path_code.17"
1021 1022
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
1023
      expl="17. loop invariant preservation"
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MARCHE Claude committed
1024
      sum="c83f07fe73308623e3c22999a115098d"
1025
      proved="true"
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Andrei Paskevich committed
1026
      expanded="true"
1027
      shape="loop invariant preservationamemV18V12Iainfix &lt;V19amixfix []V15V17IapathV0V18V19FFIaminV17V14V15FINainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV21V8Iainfix &lt;V22amixfix []V7V20IapathV0V21V22FFIaminV20V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
1028 1029 1030
      <label
       name="expl:VC for shortest_path_code"/>
      <proof
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Andrei Paskevich committed
1031
       prover="4"
1032
       timelimit="30"
1033 1034 1035 1036
       memlimit="1000"
       edited="dijkstra_DijkstraShortestPath_WP_parameter_shortest_path_code_3.v"
       obsolete="false"
       archived="false">
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Andrei Paskevich committed
1037
       <result status="valid" time="2.40"/>
1038 1039 1040 1041 1042 1043 1044
      </proof>
     </goal>
     <goal
      name="WP_parameter shortest_path_code.18"
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
      expl="18. loop variant decrease"
MARCHE Claude's avatar
MARCHE Claude committed
1045
      sum="78905312faefa9b7223e5cbcdc0a15a5"
1046 1047
      proved="true"
      expanded="false"
1048
      shape="loop variant decreaseainfix &lt;ainfix -acardinalavacardinalV12ainfix -acardinalavacardinalV8Aainfix &lt;=c0ainfix -acardinalavacardinalV8INainfix =V16aTrueINais_emptyV13qainfix =V16aTrueFIainv_succ2V0V12V14V15V11V13AainvV0V12V14V15AasubsetV13ag_succV11FIainfix =V12aaddV11V8FIashortest_pathV0V11amixfix []V7V11Iainfix =V10aremoveV11V6AaminV11V6V7FFINais_emptyV6INainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV18V8Iainfix &lt;V19amixfix []V7V17IapathV0V18V19FFIaminV17V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
1049 1050 1051 1052 1053 1054 1055 1056
      <label
       name="expl:VC for shortest_path_code"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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MARCHE Claude committed
1057
       <result status="valid" time="0.07"/>
1058 1059 1060
      </proof>
     </goal>
     <goal
1061
      name="WP_parameter shortest_path_code.19"
1062 1063
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
1064
      expl="19. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
1065
      sum="4a8e7b6c317e81338b54de49d73dadb9"
1066 1067
      proved="true"
      expanded="false"
1068
      shape="postconditionashortest_pathV0V10amixfix []V7V10IamemV10V8FINNainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV12V8Iainfix &lt;V13amixfix []V7V11IapathV0V12V13FFIaminV11V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080
      <label
       name="expl:VC for shortest_path_code"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
      </proof>
     </goal>
     <goal
1081
      name="WP_parameter shortest_path_code.20"
1082 1083
      locfile="../dijkstra.mlw"
      loclnum="186" loccnumb="6" loccnume="24"
1084
      expl="20. postcondition"
MARCHE Claude's avatar
MARCHE Claude committed
1085
      sum="d5c644f754e568f21cbe00693bcda6f7"
1086 1087
      proved="true"
      expanded="false"
1088
      shape="postconditionNapathV0V10V11FINamemV10V8FINNainfix =V9aTrueIais_emptyV6qainfix =V9aTrueFIamemV13V8Iainfix &lt;V14amixfix []V7V12IapathV0V13V14FFIaminV12V6V7FAainv_succV0V8V6V7AainvV0V8V6V7FIainfix =V4amixfix [&lt;-]V2V0c0Aainfix =V3aaddV0aemptyAais_emptyV5FIamemV1avAamemV0avFF">
1089 1090 1091
      <label
       name="expl:VC for shortest_path_code"/>
      <proof
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Andrei Paskevich committed
1092
       prover="5"
1093 1094 1095 1096
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
1097
       <result status="valid" time="0.02"/>
1098 1099 1100 1101 1102 1103 1104
      </proof>
     </goal>
    </transf>
   </goal>
  </theory>
 </file>
</why3session>