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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v2//EN" "http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="4">
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 <prover
  id="0"
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  name="Alt-Ergo"
  version="0.95.2"/>
 <prover
  id="1"
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  name="CVC3"
  version="2.4.1"/>
 <prover
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  id="2"
  name="CVC4"
  version="1.3"/>
 <prover
  id="3"
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  name="Z3"
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  version="4.3.1"/>
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 <file
  name="../binary_sqrt.mlw"
  verified="true"
  expanded="true">
  <theory
   name="BinarySqrt"
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   locfile="../binary_sqrt.mlw"
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   loclnum="8" loccnumb="7" loccnume="17"
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   verified="true"
   expanded="true">
   <goal
    name="WP_parameter sqrt"
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    locfile="../binary_sqrt.mlw"
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    loclnum="16" loccnumb="10" loccnume="14"
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    expl="VC for sqrt"
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    sum="2f48142e66f86f828944b2b4444e121e"
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    proved="true"
    expanded="true"
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    shape="iainfix &lt;V0ainfix *ainfix +iV6ainfix +V6V1ainfix &lt;=ainfix *ainfix +V6V1ainfix +V6V1V0V1ainfix +iV6ainfix +V6V1ainfix &lt;=ainfix *ainfix +V6V1ainfix +V6V1V0V1Aainfix &lt;=ainfix *iV6ainfix +V6V1ainfix &lt;=ainfix *ainfix +V6V1ainfix +V6V1V0iV6ainfix +V6V1ainfix &lt;=ainfix *ainfix +V6V1ainfix +V6V1V0V0Iainfix &lt;V0ainfix *ainfix +V6V5ainfix +V6V5Aainfix &lt;=ainfix *V6V6V0FAainfix =V5ainfix *afrom_intV4V3Aainfix &gt;=V4c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0Aainfix &lt;ainfix -aceilainfix /amaxV0c1.0V3V4ainfix -aceilainfix /amaxV0c1.0V3V2Aainfix &lt;=c0ainfix -aceilainfix /amaxV0c1.0V3V2Lainfix *c2.0V1Lainfix *c2V2Aainfix &lt;=afrom_intV2ainfix /amaxV0c1.0V3Aainfix &lt;=ainfix /ainfix *afrom_intV2V3V3ainfix /amaxV0c1.0V3Aainfix &lt;=ainfix *ainfix *afrom_intV2V3ainfix /c1.0V3ainfix *amaxV0c1.0ainfix /c1.0V3Aainfix &gt;ainfix /c1.0V3c0.0Aainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0ainfix &lt;V0ainfix *ainfix +c0.0V1ainfix +c0.0V1Aainfix &lt;=ainfix *c0.0c0.0V0ainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
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    <label
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     name="expl:VC for sqrt"/>
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    <transf
     name="split_goal"
     proved="true"
     expanded="true">
     <goal
      name="WP_parameter sqrt.1"
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      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="1. postcondition"
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      sum="930cac52353417990bb887760a9e0d6f"
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      proved="true"
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      expanded="false"
      shape="postconditionainfix &lt;V0ainfix *ainfix +c0.0V1ainfix +c0.0V1Aainfix &lt;=ainfix *c0.0c0.0V0Iainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
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      <label
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       name="expl:VC for sqrt"/>
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      <proof
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       prover="3"
       timelimit="5"
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       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt.2"
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      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="2. assertion"
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      sum="95aa6b7bd6934a32cb478bf426b496ec"
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      proved="true"
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      expanded="false"
      shape="assertionainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0INainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
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      <label
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       name="expl:VC for sqrt"/>
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      <proof
       prover="0"
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       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="1"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
       prover="3"
       timelimit="5"
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       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.00"/>
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      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt.3"
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      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="3. assertion"
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      sum="814f4beff6fe1fa8ff5b578637992816"
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      proved="true"
      expanded="false"
      shape="assertionainfix &gt;ainfix /c1.0V3c0.0Iainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0INainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt"/>
      <proof
       prover="3"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt.4"
      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="4. assertion"
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      sum="dfb7031800efc58e780215fd62ea66f5"
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      proved="true"
      expanded="false"
      shape="assertionainfix &lt;=ainfix *ainfix *afrom_intV2V3ainfix /c1.0V3ainfix *amaxV0c1.0ainfix /c1.0V3Iainfix &gt;ainfix /c1.0V3c0.0Iainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0INainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.02"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt.5"
      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="5. assertion"
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      sum="143b48cb7cee72f474c8858297f5eb19"
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      proved="true"
      expanded="false"
      shape="assertionainfix &lt;=ainfix /ainfix *afrom_intV2V3V3ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix *ainfix *afrom_intV2V3ainfix /c1.0V3ainfix *amaxV0c1.0ainfix /c1.0V3Iainfix &gt;ainfix /c1.0V3c0.0Iainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0INainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.03"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt.6"
      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="6. assertion"
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      sum="4396794d87686e427bb0aebb559385b6"
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      proved="true"
      expanded="false"
      shape="assertionainfix &lt;=afrom_intV2ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix /ainfix *afrom_intV2V3V3ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix *ainfix *afrom_intV2V3ainfix /c1.0V3ainfix *amaxV0c1.0ainfix /c1.0V3Iainfix &gt;ainfix /c1.0V3c0.0Iainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0INainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt"/>
      <proof
       prover="3"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="4.39"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt.7"
      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="7. variant decrease"
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      sum="5b06530b9d368209d903e9d91d9e4182"
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      proved="true"
      expanded="false"
      shape="variant decreaseainfix &lt;ainfix -aceilainfix /amaxV0c1.0V3V4ainfix -aceilainfix /amaxV0c1.0V3V2Aainfix &lt;=c0ainfix -aceilainfix /amaxV0c1.0V3V2Lainfix *c2.0V1Lainfix *c2V2Iainfix &lt;=afrom_intV2ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix /ainfix *afrom_intV2V3V3ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix *ainfix *afrom_intV2V3ainfix /c1.0V3ainfix *amaxV0c1.0ainfix /c1.0V3Iainfix &gt;ainfix /c1.0V3c0.0Iainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0INainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.27"/>
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      </proof>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.04"/>
      </proof>
      <proof
       prover="3"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt.8"
      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="8. precondition"
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      sum="af396d9f812039d722ce55092f1611e3"
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      proved="true"
      expanded="false"
      shape="preconditionainfix &lt;=c0.0V0Lainfix *c2.0V1Lainfix *c2V2Iainfix &lt;=afrom_intV2ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix /ainfix *afrom_intV2V3V3ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix *ainfix *afrom_intV2V3ainfix /c1.0V3ainfix *amaxV0c1.0ainfix /c1.0V3Iainfix &gt;ainfix /c1.0V3c0.0Iainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0INainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="3"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt.9"
      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="9. precondition"
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      sum="228255f4c81393d5b46ebd149782cb23"
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      proved="true"
      expanded="false"
      shape="preconditionainfix &gt;=V4c1Aainfix &gt;V3c0.0Lainfix *c2.0V1Lainfix *c2V2Iainfix &lt;=afrom_intV2ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix /ainfix *afrom_intV2V3V3ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix *ainfix *afrom_intV2V3ainfix /c1.0V3ainfix *amaxV0c1.0ainfix /c1.0V3Iainfix &gt;ainfix /c1.0V3c0.0Iainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0INainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="3"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt.10"
      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="10. precondition"
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      sum="aac0c6fd62909777cc134f89f5a8a500"
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      proved="true"
      expanded="false"
      shape="preconditionainfix =V5ainfix *afrom_intV4V3Lainfix *c2.0V1Lainfix *c2V2Iainfix &lt;=afrom_intV2ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix /ainfix *afrom_intV2V3V3ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix *ainfix *afrom_intV2V3ainfix /c1.0V3ainfix *amaxV0c1.0ainfix /c1.0V3Iainfix &gt;ainfix /c1.0V3c0.0Iainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0INainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt"/>
      <proof
       prover="3"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt.11"
      locfile="../binary_sqrt.mlw"
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      loclnum="16" loccnumb="10" loccnume="14"
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      expl="11. postcondition"
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      sum="99fdae98c4c5124065b35bd678dd849a"
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      proved="true"
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      expanded="false"
      shape="postconditionainfix &lt;V0ainfix *ainfix +iV6ainfix +V6V1ainfix &lt;=ainfix *ainfix +V6V1ainfix +V6V1V0V1ainfix +iV6ainfix +V6V1ainfix &lt;=ainfix *ainfix +V6V1ainfix +V6V1V0V1Aainfix &lt;=ainfix *iV6ainfix +V6V1ainfix &lt;=ainfix *ainfix +V6V1ainfix +V6V1V0iV6ainfix +V6V1ainfix &lt;=ainfix *ainfix +V6V1ainfix +V6V1V0V0Iainfix &lt;V0ainfix *ainfix +V6V5ainfix +V6V5Aainfix &lt;=ainfix *V6V6V0FIainfix =V5ainfix *afrom_intV4V3Aainfix &gt;=V4c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0Lainfix *c2.0V1Lainfix *c2V2Iainfix &lt;=afrom_intV2ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix /ainfix *afrom_intV2V3V3ainfix /amaxV0c1.0V3Iainfix &lt;=ainfix *ainfix *afrom_intV2V3ainfix /c1.0V3ainfix *amaxV0c1.0ainfix /c1.0V3Iainfix &gt;ainfix /c1.0V3c0.0Iainfix &lt;=ainfix *afrom_intV2V3amaxV0c1.0INainfix &lt;c1.0V1Aainfix &lt;V0V1Iainfix =V1ainfix *afrom_intV2V3Aainfix &gt;=V2c1Aainfix &gt;V3c0.0Aainfix &lt;=c0.0V0F">
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      <label
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       name="expl:VC for sqrt"/>
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      <proof
       prover="0"
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       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.38"/>
      </proof>
     </goal>
    </transf>
   </goal>
   <goal
    name="WP_parameter sqrt_main"
    locfile="../binary_sqrt.mlw"
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    loclnum="35" loccnumb="6" loccnume="15"
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    expl="VC for sqrt_main"
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    sum="c34a139793f399d5395639d3b7ce4df4"
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    proved="true"
    expanded="true"
    shape="ainfix &lt;V0ainfix *ainfix +V2V1ainfix +V2V1Aainfix &lt;=ainfix *V2V2V0Iainfix &lt;V0ainfix *ainfix +V2V1ainfix +V2V1Aainfix &lt;=ainfix *V2V2V0FAainfix =V1ainfix *afrom_intc1V1Aainfix &gt;=c1c1Aainfix &gt;V1c0.0Aainfix &lt;=c0.0V0Iainfix &gt;V1c0.0Aainfix &lt;=c0.0V0F">
    <label
     name="expl:VC for sqrt_main"/>
    <transf
     name="split_goal_wp"
     proved="true"
     expanded="true">
     <goal
      name="WP_parameter sqrt_main.1"
      locfile="../binary_sqrt.mlw"
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      loclnum="35" loccnumb="6" loccnume="15"
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      expl="1. precondition"
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      sum="a4f4b305f07cc5e971c99ce1c17331e4"
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      proved="true"
      expanded="false"
      shape="preconditionainfix &lt;=c0.0V0Iainfix &gt;V1c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt_main"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="1"
       timelimit="5"
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       memlimit="1000"
       obsolete="false"
       archived="false">
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       <result status="valid" time="0.02"/>
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      </proof>
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      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
       prover="3"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt_main.2"
      locfile="../binary_sqrt.mlw"
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      loclnum="35" loccnumb="6" loccnume="15"
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      expl="2. precondition"
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      sum="9b43683c9c4eff601a49aaa9410eeac0"
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      proved="true"
      expanded="false"
      shape="preconditionainfix &gt;=c1c1Aainfix &gt;V1c0.0Iainfix &gt;V1c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt_main"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
       prover="1"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
       prover="3"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt_main.3"
      locfile="../binary_sqrt.mlw"
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      loclnum="35" loccnumb="6" loccnume="15"
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      expl="3. precondition"
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      sum="735dc81a88955752d1d437dd00d880cf"
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      proved="true"
      expanded="false"
      shape="preconditionainfix =V1ainfix *afrom_intc1V1Iainfix &gt;V1c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt_main"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
       prover="1"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
      <proof
       prover="3"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
     </goal>
     <goal
      name="WP_parameter sqrt_main.4"
      locfile="../binary_sqrt.mlw"
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      loclnum="35" loccnumb="6" loccnume="15"
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      expl="4. postcondition"
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MARCHE Claude committed
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      sum="e85265bbf58abeb249a5a034be320f57"
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      proved="true"
      expanded="false"
      shape="postconditionainfix &lt;V0ainfix *ainfix +V2V1ainfix +V2V1Aainfix &lt;=ainfix *V2V2V0Iainfix &lt;V0ainfix *ainfix +V2V1ainfix +V2V1Aainfix &lt;=ainfix *V2V2V0FIainfix =V1ainfix *afrom_intc1V1Aainfix &gt;=c1c1Aainfix &gt;V1c0.0Aainfix &lt;=c0.0V0Iainfix &gt;V1c0.0Aainfix &lt;=c0.0V0F">
      <label
       name="expl:VC for sqrt_main"/>
      <proof
       prover="0"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="1"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="2"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.01"/>
      </proof>
      <proof
       prover="3"
       timelimit="5"
       memlimit="1000"
       obsolete="false"
       archived="false">
       <result status="valid" time="0.00"/>
      </proof>
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     </goal>
    </transf>
   </goal>
  </theory>
 </file>
</why3session>