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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="0.95.1"/>
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 <prover
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  id="1"
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  name="CVC3"
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  version="2.4.1"/>
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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="Z3"
  version="2.19"/>
 <file
  name="../power.mlw"
  verified="true"
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  expanded="true">
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  <theory
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   name="FastExponentiation"
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   locfile="../power.mlw"
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   loclnum="4" loccnumb="7" loccnume="25"
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   verified="true"
   expanded="true">
   <goal
    name="WP_parameter fast_exp"
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    locfile="../power.mlw"
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    loclnum="12" loccnumb="10" loccnume="18"
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    expl="VC for fast_exp"
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    sum="fa86ea7df489dc9c55e374b4874f41ba"
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    proved="true"
    expanded="true"
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    shape="iainfix =V1c0ainfix =c1apowerV0V1ainfix =iainfix =amodV1c2c0ainfix *V3V3ainfix *ainfix *V3V3V0apowerV0V1LapowerV0V2Aainfix &lt;=c0V2Aainfix &lt;V2V1Aainfix &lt;=c0V1LadivV1c2Iainfix &lt;=c0V1F">
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    <label
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     name="expl:VC for fast_exp"/>
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    <proof
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     prover="0"
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     timelimit="3"
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     memlimit="0"
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     obsolete="false"
     archived="false">
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     <result status="valid" time="0.24"/>
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    </proof>
   </goal>
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   <goal
    name="WP_parameter fast_exp_imperative"
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    locfile="../power.mlw"
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    loclnum="26" loccnumb="6" loccnume="25"
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    expl="VC for fast_exp_imperative"
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    sum="1f40fd2584867343a220b3e05c991538"
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    proved="true"
    expanded="true"
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    shape="iainfix &gt;V2c0iainfix =amodV2c2c1ainfix &lt;V7V2Aainfix &lt;=c0V2Aainfix =ainfix *V5apowerV6V7apowerV0V1Aainfix &lt;=c0V7Iainfix =V7adivV2c2FIainfix =V6ainfix *V3V3FIainfix =V5ainfix *V4V3Fainfix &lt;V9V2Aainfix &lt;=c0V2Aainfix =ainfix *V4apowerV8V9apowerV0V1Aainfix &lt;=c0V9Iainfix =V9adivV2c2FIainfix =V8ainfix *V3V3Fainfix =V4apowerV0V1Iainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FAainfix =ainfix *c1apowerV0V1apowerV0V1Aainfix &lt;=c0V1Iainfix &lt;=c0V1F">
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    <label
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     name="expl:VC for fast_exp_imperative"/>
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    <transf
     name="split_goal"
     proved="true"
     expanded="true">
     <goal
      name="WP_parameter fast_exp_imperative.1"
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      locfile="../power.mlw"
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      loclnum="26" loccnumb="6" loccnume="25"
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      expl="1. loop invariant init"
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      sum="5d0c4a27e12c87f953185df5d72efb01"
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      proved="true"
      expanded="true"
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      shape="ainfix =ainfix *c1apowerV0V1apowerV0V1Aainfix &lt;=c0V1Iainfix &lt;=c0V1F">
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      <label
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       name="expl:VC for fast_exp_imperative"/>
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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"/>
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      </proof>
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      <proof
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       prover="1"
       timelimit="10"
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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="3"
       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>
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     <goal
      name="WP_parameter fast_exp_imperative.2"
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      locfile="../power.mlw"
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      loclnum="26" loccnumb="6" loccnume="25"
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      expl="2. loop invariant preservation"
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      sum="612d9cc28d9cc95705002e1ca109ec83"
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      proved="true"
      expanded="true"
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      shape="ainfix =ainfix *V5apowerV6V7apowerV0V1Aainfix &lt;=c0V7Iainfix =V7adivV2c2FIainfix =V6ainfix *V3V3FIainfix =V5ainfix *V4V3FIainfix =amodV2c2c1Iainfix &gt;V2c0Iainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FIainfix &lt;=c0V1F">
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      <label
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       name="expl:VC for fast_exp_imperative"/>
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      <transf
       name="split_goal"
       proved="true"
       expanded="true">
       <goal
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        name="WP_parameter fast_exp_imperative.2.1"
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        locfile="../power.mlw"
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        loclnum="26" loccnumb="6" loccnume="25"
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        expl="1."
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        sum="55120266e6138a76bc44e230c722b651"
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        proved="true"
        expanded="true"
        shape="ainfix &lt;=c0V7Iainfix =V7adivV2c2FIainfix =V6ainfix *V3V3FIainfix =V5ainfix *V4V3FIainfix =amodV2c2c1Iainfix &gt;V2c0Iainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FIainfix &lt;=c0V1F">
        <label
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         name="expl:VC for fast_exp_imperative"/>
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        <proof
         prover="0"
         timelimit="10"
         memlimit="1000"
         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 fast_exp_imperative.2.2"
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        locfile="../power.mlw"
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        loclnum="26" loccnumb="6" loccnume="25"
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        expl="2."
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        sum="1770687516ae686c6f733fc7f399080c"
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        proved="true"
        expanded="true"
        shape="ainfix =ainfix *V5apowerV6V7apowerV0V1Iainfix =V7adivV2c2FIainfix =V6ainfix *V3V3FIainfix =V5ainfix *V4V3FIainfix =amodV2c2c1Iainfix &gt;V2c0Iainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FIainfix &lt;=c0V1F">
        <label
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         name="expl:VC for fast_exp_imperative"/>
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        <proof
         prover="2"
         timelimit="10"
         memlimit="1000"
         edited="power_M_WP_parameter_fast_exp_imperative_1.v"
         obsolete="false"
         archived="false">
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         <result status="valid" time="0.56"/>
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        </proof>
       </goal>
      </transf>
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     </goal>
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     <goal
      name="WP_parameter fast_exp_imperative.3"
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      locfile="../power.mlw"
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      loclnum="26" loccnumb="6" loccnume="25"
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      expl="3. loop variant decrease"
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      sum="aaab1dfa72ea0e2fd6c92b907125000c"
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      proved="true"
      expanded="true"
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      shape="ainfix &lt;V7V2Aainfix &lt;=c0V2Iainfix =V7adivV2c2FIainfix =V6ainfix *V3V3FIainfix =V5ainfix *V4V3FIainfix =amodV2c2c1Iainfix &gt;V2c0Iainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FIainfix &lt;=c0V1F">
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      <label
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       name="expl:VC for fast_exp_imperative"/>
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      <proof
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       prover="0"
       timelimit="10"
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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>
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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>
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      <proof
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       prover="3"
       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>
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     <goal
      name="WP_parameter fast_exp_imperative.4"
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      locfile="../power.mlw"
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      loclnum="26" loccnumb="6" loccnume="25"
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      expl="4. loop invariant preservation"
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      sum="ecd6ecd12d1efc98ee313f5c6cb7ca9f"
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      proved="true"
      expanded="true"
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      shape="ainfix =ainfix *V4apowerV5V6apowerV0V1Aainfix &lt;=c0V6Iainfix =V6adivV2c2FIainfix =V5ainfix *V3V3FIainfix =amodV2c2c1NIainfix &gt;V2c0Iainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FIainfix &lt;=c0V1F">
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      <label
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       name="expl:VC for fast_exp_imperative"/>
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      <transf
       name="split_goal"
       proved="true"
       expanded="true">
       <goal
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        name="WP_parameter fast_exp_imperative.4.1"
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        locfile="../power.mlw"
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        loclnum="26" loccnumb="6" loccnume="25"
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        expl="1."
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        sum="33a6f270a530b1f0bc6530ee6bbc0e35"
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        proved="true"
        expanded="true"
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        shape="ainfix &lt;=c0V6Iainfix =V6adivV2c2FIainfix =V5ainfix *V3V3FIainfix =amodV2c2c1NIainfix &gt;V2c0Iainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FIainfix &lt;=c0V1F">
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        <label
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         name="expl:VC for fast_exp_imperative"/>
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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="0.02"/>
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        </proof>
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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>
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        <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="0.02"/>
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        </proof>
       </goal>
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       <goal
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        name="WP_parameter fast_exp_imperative.4.2"
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        locfile="../power.mlw"
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        loclnum="26" loccnumb="6" loccnume="25"
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        expl="2."
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        sum="e2807afe6fc54e502780fe361d651774"
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        proved="true"
        expanded="true"
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        shape="ainfix =ainfix *V4apowerV5V6apowerV0V1Iainfix =V6adivV2c2FIainfix =V5ainfix *V3V3FIainfix =amodV2c2c1NIainfix &gt;V2c0Iainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FIainfix &lt;=c0V1F">
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        <label
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         name="expl:VC for fast_exp_imperative"/>
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        <proof
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         prover="2"
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         timelimit="10"
         memlimit="1000"
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         edited="power_WP_M_WP_parameter_fast_exp_imperative_3.v"
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         obsolete="false"
         archived="false">
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         <result status="valid" time="0.62"/>
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        </proof>
       </goal>
      </transf>
     </goal>
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     <goal
      name="WP_parameter fast_exp_imperative.5"
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      locfile="../power.mlw"
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      loclnum="26" loccnumb="6" loccnume="25"
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      expl="5. loop variant decrease"
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      sum="8569b52ac392b0cfe600928c5ac8143b"
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      proved="true"
      expanded="true"
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      shape="ainfix &lt;V6V2Aainfix &lt;=c0V2Iainfix =V6adivV2c2FIainfix =V5ainfix *V3V3FIainfix =amodV2c2c1NIainfix &gt;V2c0Iainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FIainfix &lt;=c0V1F">
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      <label
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       name="expl:VC for fast_exp_imperative"/>
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      <proof
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       prover="0"
       timelimit="10"
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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>
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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>
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      <proof
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       prover="3"
       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>
     </goal>
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     <goal
      name="WP_parameter fast_exp_imperative.6"
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      locfile="../power.mlw"
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      loclnum="26" loccnumb="6" loccnume="25"
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      expl="6. postcondition"
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      sum="b6f5c50baa92e4d3d366415b67d94a03"
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      proved="true"
      expanded="true"
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      shape="ainfix =V4apowerV0V1Iainfix &gt;V2c0NIainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FIainfix &lt;=c0V1F">
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      <label
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       name="expl:VC for fast_exp_imperative"/>
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      <transf
       name="split_goal"
       proved="true"
       expanded="true">
       <goal
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        name="WP_parameter fast_exp_imperative.6.1"
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        locfile="../power.mlw"
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        loclnum="26" loccnumb="6" loccnume="25"
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        expl="1. postcondition"
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        sum="b6f5c50baa92e4d3d366415b67d94a03"
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        proved="true"
        expanded="true"
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        shape="ainfix =V4apowerV0V1Iainfix &gt;V2c0NIainfix =ainfix *V4apowerV3V2apowerV0V1Aainfix &lt;=c0V2FIainfix &lt;=c0V1F">
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        <label
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         name="expl:VC for fast_exp_imperative"/>
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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>
       </goal>
      </transf>
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     </goal>
    </transf>
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   </goal>
  </theory>
 </file>
</why3session>