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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v2//EN" "http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="2">
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 <prover
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  id="0"
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  name="Alt-Ergo"
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  version="0.94"/>
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 <prover
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  id="1"
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  name="CVC3"
  version="2.2"/>
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 <prover
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  id="2"
  name="Coq"
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  version="8.3pl4"/>
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 <prover
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  id="3"
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  name="Eprover"
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  version="1.4"/>
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 <prover
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  id="4"
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  name="Spass"
  version="3.7"/>
 <prover
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  id="5"
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  name="Vampire"
  version="0.6"/>
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 <prover
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  id="6"
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  name="Z3"
  version="2.19"/>
 <file
  name="../fibonacci.mlw"
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  verified="true"
  expanded="true">
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  <theory
   name="Fibonacci"
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   locfile="../fibonacci.mlw"
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   loclnum="2" loccnumb="7" loccnume="16"
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   verified="true"
   expanded="true">
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   <label
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    name="Fibonacci numbers"/>
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  </theory>
  <theory
   name="FibonacciTest"
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   locfile="../fibonacci.mlw"
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   loclnum="14" loccnumb="7" loccnume="20"
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   verified="true"
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   expanded="false">
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   <goal
    name="isfib_2_1"
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    locfile="../fibonacci.mlw"
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    loclnum="18" loccnumb="8" loccnume="17"
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    sum="d9eabf8d7568cdd6e09c64f34668cca8"
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    proved="true"
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    expanded="false"
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    shape="ainfix =afibc2c1">
    <proof
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     prover="1"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.00"/>
    </proof>
   </goal>
   <goal
    name="isfib_6_8"
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    locfile="../fibonacci.mlw"
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    loclnum="19" loccnumb="8" loccnume="17"
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    sum="9d93314ed80fc04190c1765d6323461d"
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    proved="true"
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    expanded="false"
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    shape="ainfix =afibc6c8">
    <proof
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     prover="1"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.00"/>
    </proof>
   </goal>
   <goal
    name="not_isfib_2_2"
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    locfile="../fibonacci.mlw"
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    loclnum="21" loccnumb="8" loccnume="21"
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    sum="a40d1bc22627a0babb88a4481a9541a5"
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    proved="true"
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    expanded="false"
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    shape="ainfix =afibc2c2N">
    <proof
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     prover="0"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.01"/>
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    </proof>
    <proof
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     prover="1"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.00"/>
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    </proof>
    <proof
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     prover="3"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.01"/>
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    </proof>
    <proof
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     prover="4"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.02"/>
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    </proof>
    <proof
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     prover="5"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.03"/>
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    </proof>
   </goal>
  </theory>
  <theory
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   name="FibonacciLinear"
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   locfile="../fibonacci.mlw"
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   loclnum="25" loccnumb="7" loccnume="22"
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   verified="true"
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   expanded="false">
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   <goal
    name="WP_parameter fib"
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    locfile="../fibonacci.mlw"
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    loclnum="31" loccnumb="6" loccnume="9"
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    expl="VC for fib"
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    sum="350a514a1ca03b5d98dc329a7b5c6f2d"
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    proved="true"
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    expanded="false"
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    shape="ainfix =afibV0V2Iainfix =afibainfix +ainfix -V0c1c1V2Aainfix =afibainfix +ainfix +ainfix -V0c1c1c1V1Aainfix &lt;=ainfix +ainfix -V0c1c1V0Aainfix &lt;=c0ainfix +ainfix -V0c1c1Aainfix =afibainfix +V3c1V4Aainfix =afibainfix +ainfix +V3c1c1V5Aainfix &lt;=ainfix +V3c1V0Aainfix &lt;=c0ainfix +V3c1Iainfix =V5ainfix +V1V2FIainfix =V4V1FIainfix =afibV3V2Aainfix =afibainfix +V3c1V1Aainfix &lt;=V3V0Aainfix &lt;=c0V3Iainfix &lt;=V3ainfix -V0c1Aainfix &lt;=c0V3FFAainfix =afibc0c0Aainfix =afibainfix +c0c1c1Aainfix &lt;=c0V0Aainfix &lt;=c0c0Iainfix &lt;=c0ainfix -V0c1Aainfix =afibV0c0Iainfix &gt;c0ainfix -V0c1Iainfix &gt;=V0c0F">
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    <label
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     name="expl:VC for fib"/>
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    <proof
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     prover="1"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.00"/>
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    </proof>
   </goal>
  </theory>
  <theory
   name="Mat22"
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   locfile="../fibonacci.mlw"
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   loclnum="46" loccnumb="7" loccnume="12"
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   verified="true"
   expanded="true">
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   <label
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    name="2x2 integer matrices"/>
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  </theory>
  <theory
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   name="FibonacciLogarithmic"
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   locfile="../fibonacci.mlw"
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   loclnum="68" loccnumb="7" loccnume="27"
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   verified="true"
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   expanded="true">
   <goal
    name="WP_parameter logfib"
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    locfile="../fibonacci.mlw"
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    loclnum="82" loccnumb="10" loccnume="16"
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    expl="VC for logfib"
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    sum="be18b57a378e8f58833c62cc4852ff5c"
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    proved="true"
    expanded="true"
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    shape="iainfix =V0c0ainfix =apoweramk tc1c1c1c0V0amk tainfix +c1c0c0c0c1iainfix =amodV0c2c0ainfix =apoweramk tc1c1c1c0V0amk tainfix +V3V4V4V4V3Lainfix *V2ainfix +V1ainfix +V1V2Lainfix +ainfix *V1V1ainfix *V2V2ainfix =apoweramk tc1c1c1c0V0amk tainfix +V5V6V6V6V5Lainfix +ainfix *ainfix +V1V2ainfix +V1V2ainfix *V2V2Lainfix *V2ainfix +V1ainfix +V1V2Iainfix =apoweramk tc1c1c1c0adivV0c2amk tainfix +V1V2V2V2V1FAainfix &gt;=adivV0c2c0Aainfix &lt;adivV0c2V0Aainfix &lt;=c0V0Iainfix &gt;=V0c0F">
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    <label
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     name="expl:VC for logfib"/>
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    <transf
     name="split_goal"
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     proved="true"
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     expanded="true">
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     <goal
      name="WP_parameter logfib.1"
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      locfile="../fibonacci.mlw"
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      loclnum="82" loccnumb="10" loccnume="16"
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      expl="1. postcondition"
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      sum="54ff9f48d80a0d661479ac9f4110b022"
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      proved="true"
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      expanded="true"
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      shape="ainfix =apoweramk tc1c1c1c0V0amk tainfix +c1c0c0c0c1Iainfix =V0c0Iainfix &gt;=V0c0F">
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      <label
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       name="expl:VC for logfib"/>
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      <proof
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       prover="0"
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       timelimit="5"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="1"
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       timelimit="5"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.00"/>
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      </proof>
      <proof
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       prover="5"
       timelimit="3"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.00"/>
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      </proof>
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      <proof
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       prover="6"
       timelimit="5"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
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     </goal>
     <goal
      name="WP_parameter logfib.2"
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      locfile="../fibonacci.mlw"
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      loclnum="82" loccnumb="10" loccnume="16"
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      expl="2. variant decrease"
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      sum="024ee6b3b1eb5f5cb113823603c892cf"
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      proved="true"
      expanded="true"
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      shape="ainfix &lt;adivV0c2V0Aainfix &lt;=c0V0Iainfix =V0c0NIainfix &gt;=V0c0F">
      <label
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       name="expl:VC for logfib"/>
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      <proof
       prover="0"
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       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>
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     </goal>
     <goal
      name="WP_parameter logfib.3"
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      locfile="../fibonacci.mlw"
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      loclnum="82" loccnumb="10" loccnume="16"
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      expl="3. precondition"
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      sum="f98d6f543cdf82e62fc44c18db5e7230"
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      proved="true"
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      expanded="true"
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      shape="ainfix &gt;=adivV0c2c0Iainfix =V0c0NIainfix &gt;=V0c0F">
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      <label
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       name="expl:VC for logfib"/>
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      <proof
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       prover="1"
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       timelimit="5"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
      <proof
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       prover="6"
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       timelimit="5"
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       memlimit="0"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.01"/>
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      </proof>
     </goal>
     <goal
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      name="WP_parameter logfib.4"
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      locfile="../fibonacci.mlw"
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      loclnum="82" loccnumb="10" loccnume="16"
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      expl="4. postcondition"
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      sum="4124e6c67675b5e5aa3e4feca51111a1"
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      proved="true"
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      expanded="true"
      shape="iainfix =amodV0c2c0ainfix =apoweramk tc1c1c1c0V0amk tainfix +V3V4V4V4V3Lainfix *V2ainfix +V1ainfix +V1V2Lainfix +ainfix *V1V1ainfix *V2V2ainfix =apoweramk tc1c1c1c0V0amk tainfix +V5V6V6V6V5Lainfix +ainfix *ainfix +V1V2ainfix +V1V2ainfix *V2V2Lainfix *V2ainfix +V1ainfix +V1V2Iainfix =apoweramk tc1c1c1c0adivV0c2amk tainfix +V1V2V2V2V1FIainfix &gt;=adivV0c2c0Iainfix =V0c0NIainfix &gt;=V0c0F">
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      <label
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       name="expl:VC for logfib"/>
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      <proof
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       prover="2"
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       timelimit="10"
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       memlimit="0"
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       edited="fibonacci_WP_FibonacciLogarithmic_WP_parameter_logfib_1.v"
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       obsolete="false"
       archived="false">
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       <result status="valid" time="0.60"/>
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      </proof>
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     </goal>
    </transf>
   </goal>
   <goal
    name="fib_m"
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    locfile="../fibonacci.mlw"
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    loclnum="105" loccnumb="8" loccnume="13"
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    sum="a63b2ce2736615025314f4148f50ebfc"
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    proved="true"
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    expanded="true"
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    shape="ainfix =afibV0aa21V1Aainfix =afibainfix +V0c1aa11V1Lapoweram1110V0Iainfix &gt;=V0c0F">
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    <proof
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     prover="2"
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     timelimit="10"
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     memlimit="0"
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     edited="fibonacci_WP_FibonacciLogarithmic_fib_m_1.v"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.54"/>
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    </proof>
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   </goal>
   <goal
    name="WP_parameter fibo"
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    locfile="../fibonacci.mlw"
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    loclnum="109" loccnumb="6" loccnume="10"
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    expl="VC for fibo"
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    sum="c3f07c9fe36f4699cf6d127472aa26e7"
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    proved="true"
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    expanded="false"
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    shape="ainfix =V2afibV0Iainfix =apoweramk tc1c1c1c0V0amk tainfix +V1V2V2V2V1FAainfix &gt;=V0c0Iainfix &gt;=V0c0F">
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    <label
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     name="expl:VC for fibo"/>
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    <proof
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     prover="0"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.00"/>
    </proof>
    <proof
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     prover="1"
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     timelimit="5"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.00"/>
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    </proof>
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   </goal>
  </theory>
 </file>
</why3session>