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<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="6">
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<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="3" name="Z3" version="4.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="5" name="Eprover" version="2.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="6" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="7" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
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<file proved="true">
<path name=".."/>
<path name="gcd.mlw"/>
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<theory name="EuclideanAlgorithm" proved="true">
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 <goal name="VC euclid" expl="VC for euclid" proved="true">
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 <transf name="split_goal_right" proved="true" >
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  <goal name="VC euclid.0" expl="check modulo by zero" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="4"/></proof>
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  </goal>
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  <goal name="VC euclid.1" expl="variant decrease" proved="true">
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  <proof prover="6"><result status="valid" time="0.02" steps="20"/></proof>
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  </goal>
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  <goal name="VC euclid.2" expl="precondition" proved="true">
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  <proof prover="6"><result status="valid" time="0.00" steps="8"/></proof>
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  </goal>
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  <goal name="VC euclid.3" expl="postcondition" proved="true">
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  <proof prover="6"><result status="valid" time="0.03" steps="47"/></proof>
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  </goal>
 </transf>
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 </goal>
</theory>
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<theory name="EuclideanAlgorithmIterative" proved="true">
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 <goal name="VC euclid" expl="VC for euclid" proved="true">
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 <proof prover="5"><result status="valid" time="0.02"/></proof>
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 </goal>
</theory>
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<theory name="BinaryGcd" proved="true">
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 <goal name="even1" proved="true">
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 <proof prover="6"><result status="valid" time="0.01" steps="16"/></proof>
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 </goal>
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 <goal name="odd1" proved="true">
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 <proof prover="6"><result status="valid" time="0.02" steps="17"/></proof>
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 </goal>
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 <goal name="div_nonneg" proved="true">
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 <proof prover="6"><result status="valid" time="0.01" steps="5"/></proof>
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 </goal>
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 <goal name="gcd_even_even" proved="true">
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 <proof prover="6"><result status="valid" time="0.01" steps="31"/></proof>
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 </goal>
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 <goal name="gcd_even_odd" proved="true">
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 <proof prover="0" edited="gcd_BinaryGcd_gcd_even_odd_2.v"><result status="valid" time="1.00"/></proof>
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 </goal>
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 <goal name="gcd_even_odd2" proved="true">
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 <proof prover="6"><result status="valid" time="0.05" steps="29"/></proof>
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 </goal>
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 <goal name="odd_odd_div2" proved="true">
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 <proof prover="6"><result status="valid" time="0.01" steps="23"/></proof>
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 </goal>
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 <goal name="VC gcd_odd_odd" expl="VC for gcd_odd_odd" proved="true">
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 <proof prover="6"><result status="valid" time="0.02" steps="34"/></proof>
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 </goal>
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 <goal name="gcd_odd_odd2" proved="true">
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 <proof prover="6"><result status="valid" time="0.07" steps="37"/></proof>
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 </goal>
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 <goal name="VC binary_gcd" expl="VC for binary_gcd" proved="true">
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 <transf name="split_goal_right" proved="true" >
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  <goal name="VC binary_gcd.0" expl="variant decrease" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="7"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.1" expl="precondition" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="7"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.2" expl="precondition" proved="true">
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  <proof prover="6"><result status="valid" time="0.00" steps="8"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.3" expl="precondition" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="9"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.4" expl="check division by zero" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="10"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.5" expl="check division by zero" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="10"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.6" expl="variant decrease" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.7" expl="precondition" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="20"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.8" expl="check division by zero" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="10"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.9" expl="variant decrease" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.10" expl="precondition" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.11" expl="precondition" proved="true">
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  <proof prover="6"><result status="valid" time="0.00" steps="9"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.12" expl="check division by zero" proved="true">
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  <proof prover="6"><result status="valid" time="0.00" steps="10"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.13" expl="variant decrease" proved="true">
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  <proof prover="6"><result status="valid" time="0.02" steps="15"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.14" expl="precondition" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.15" expl="check division by zero" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="10"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.16" expl="variant decrease" proved="true">
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  <proof prover="6"><result status="valid" time="0.02" steps="17"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.17" expl="precondition" proved="true">
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  <proof prover="6"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
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  <goal name="VC binary_gcd.18" expl="postcondition" proved="true">
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  <transf name="split_goal_right" proved="true" >
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   <goal name="VC binary_gcd.18.0" expl="postcondition" proved="true">
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   <proof prover="6"><result status="valid" time="0.01" steps="8"/></proof>
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   </goal>
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   <goal name="VC binary_gcd.18.1" expl="postcondition" proved="true">
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   <proof prover="6"><result status="valid" time="0.01" steps="18"/></proof>
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   </goal>
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   <goal name="VC binary_gcd.18.2" expl="postcondition" proved="true">
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   <proof prover="6"><result status="valid" time="0.12" steps="91"/></proof>
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   </goal>
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   <goal name="VC binary_gcd.18.3" expl="postcondition" proved="true">
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   <proof prover="3"><result status="valid" time="0.03"/></proof>
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   </goal>
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   <goal name="VC binary_gcd.18.4" expl="postcondition" proved="true">
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   <proof prover="3"><result status="valid" time="0.02"/></proof>
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   </goal>
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   <goal name="VC binary_gcd.18.5" expl="postcondition" proved="true">
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   <proof prover="3"><result status="valid" time="0.03"/></proof>
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   </goal>
  </transf>
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  </goal>
 </transf>
 </goal>
</theory>
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<theory name="EuclideanAlgorithm63" proved="true">
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 <goal name="VC euclid" expl="VC for euclid" proved="true">
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 <proof prover="7"><result status="valid" time="0.09"/></proof>
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 </goal>
</theory>
</file>
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</why3session>