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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="4">
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<prover id="0" name="CVC4" version="1.2" timelimit="15" memlimit="1000"/>
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<prover id="1" name="Coq" version="8.4pl4" timelimit="30" memlimit="1000"/>
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<prover id="2" name="CVC3" version="2.4.1" timelimit="5" memlimit="1000"/>
<prover id="3" name="Alt-Ergo" version="0.95.1" timelimit="5" memlimit="1000"/>
<prover id="4" name="CVC3" version="2.2" timelimit="15" memlimit="1000"/>
<prover id="5" name="Z3" version="3.2" timelimit="5" memlimit="1000"/>
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<prover id="6" name="Alt-Ergo" version="0.95.2" timelimit="6" memlimit="1000"/>
<prover id="7" name="CVC4" version="1.3" timelimit="6" memlimit="1000"/>
<file name="../dijkstra.mlw">
<theory name="DijkstraShortestPath" sum="afa04af5de17123ae1f4e1a114b65d61">
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 <goal name="WP_parameter relax" expl="VC for relax">
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 <transf name="split_goal_wp">
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  <goal name="WP_parameter relax.1" expl="1. postcondition">
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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="WP_parameter relax.2" expl="2. postcondition">
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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="WP_parameter relax.3" expl="3. postcondition">
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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="WP_parameter relax.4" expl="4. postcondition">
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  <proof prover="3"><result status="valid" time="0.03"/></proof>
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  </goal>
 </transf>
 </goal>
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 <goal name="Length_nonneg">
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 <transf name="induction_pr">
  <goal name="Length_nonneg.1" expl="1.">
  <proof prover="6"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="Length_nonneg.2" expl="2.">
  <proof prover="7"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
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 </goal>
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 <goal name="Path_inversion">
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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="Path_shortest_path">
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 <proof prover="1" timelimit="5" edited="dijkstra_DijkstraShortestPath_Path_shortest_path_1.v"><result status="valid" time="1.26"/></proof>
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 </goal>
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 <goal name="Main_lemma">
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 <proof prover="3"><result status="valid" time="1.72"/></proof>
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 </goal>
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 <goal name="Completeness_lemma">
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 <transf name="induction_pr">
  <goal name="Completeness_lemma.1" expl="1.">
  <proof prover="6"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="Completeness_lemma.2" expl="2.">
  <proof prover="7"><result status="valid" time="0.03"/></proof>
  </goal>
 </transf>
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 </goal>
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 <goal name="WP_parameter shortest_path_code" expl="VC for shortest_path_code">
 <transf name="split_goal_wp">
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  <goal name="WP_parameter shortest_path_code.1" expl="1. loop invariant init">
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  <proof prover="2"><result status="valid" time="0.20"/></proof>
  <proof prover="5"><result status="valid" time="0.14"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.2" expl="2. loop invariant init">
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  <proof prover="2"><result status="valid" time="0.03"/></proof>
  <proof prover="3"><result status="valid" time="0.02"/></proof>
  <proof prover="5"><result status="valid" time="0.03"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.3" expl="3. loop invariant init">
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  <proof prover="5"><result status="valid" time="0.04"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.4" expl="4. precondition">
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  <proof prover="3"><result status="valid" time="0.01"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.5" expl="5. assertion">
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  <proof prover="0"><result status="valid" time="0.02"/></proof>
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  <proof prover="2"><result status="valid" time="0.07"/></proof>
  <proof prover="3" timelimit="15"><result status="valid" time="0.05"/></proof>
  <proof prover="4"><result status="valid" time="0.03"/></proof>
  <proof prover="5" timelimit="15"><result status="valid" time="0.58"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.6" expl="6. loop invariant init">
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  <proof prover="3"><result status="valid" time="0.00"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.7" expl="7. loop invariant init">
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  <transf name="inline_goal">
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   <goal name="WP_parameter shortest_path_code.7.1" expl="1. loop invariant init">
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   <transf name="split_goal_wp">
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    <goal name="WP_parameter shortest_path_code.7.1.1" expl="1.">
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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="WP_parameter shortest_path_code.7.1.2" expl="2.">
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    <proof prover="3"><result status="valid" time="0.01"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.7.1.3" expl="3.">
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    <proof prover="3" timelimit="30"><result status="valid" time="0.02"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.7.1.4" expl="4.">
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    <proof prover="3" timelimit="30"><result status="valid" time="0.01"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.7.1.5" expl="5.">
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    <proof prover="3" timelimit="30"><result status="valid" time="0.16"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.7.1.6" expl="6.">
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    <proof prover="3" timelimit="30"><result status="valid" time="0.41"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.7.1.7" expl="7.">
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    <proof prover="3" timelimit="30"><result status="valid" time="0.08"/></proof>
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    </goal>
   </transf>
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   </goal>
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  </transf>
  </goal>
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  <goal name="WP_parameter shortest_path_code.8" expl="8. loop invariant init">
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  <transf name="split_goal_wp">
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   <goal name="WP_parameter shortest_path_code.8.1" expl="1. loop invariant init">
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   <proof prover="3"><result status="valid" time="0.18"/></proof>
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   </goal>
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  </transf>
  </goal>
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  <goal name="WP_parameter shortest_path_code.9" expl="9. precondition">
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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="WP_parameter shortest_path_code.10" expl="10. assertion">
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  <proof prover="5"><result status="valid" time="0.08"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.11" expl="11. loop invariant preservation">
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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="WP_parameter shortest_path_code.12" expl="12. loop invariant preservation">
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  <transf name="inline_goal">
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   <goal name="WP_parameter shortest_path_code.12.1" expl="1. loop invariant preservation">
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   <transf name="split_goal_wp">
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    <goal name="WP_parameter shortest_path_code.12.1.1" expl="1.">
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    <proof prover="3"><result status="valid" time="0.44"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.12.1.2" expl="2.">
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    <proof prover="2" timelimit="10"><result status="valid" time="0.28"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.12.1.3" expl="3.">
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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="WP_parameter shortest_path_code.12.1.4" expl="4.">
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    <proof prover="2" timelimit="10"><result status="valid" time="1.94"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.12.1.5" expl="5.">
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    <proof prover="3"><result status="valid" time="2.23"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.12.1.6" expl="6.">
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    <proof prover="3"><result status="valid" time="0.42"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.12.1.7" expl="7.">
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    <proof prover="1" edited="dijkstra_DijkstraShortestPath_WP_parameter_shortest_path_code_2.v"><result status="valid" time="12.63"/></proof>
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    </goal>
   </transf>
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   </goal>
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  </transf>
  </goal>
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  <goal name="WP_parameter shortest_path_code.13" expl="13. loop invariant preservation">
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  <transf name="split_goal_wp">
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   <goal name="WP_parameter shortest_path_code.13.1" expl="1. loop invariant preservation">
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   <transf name="inline_goal">
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    <goal name="WP_parameter shortest_path_code.13.1.1" expl="1. loop invariant preservation">
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    <transf name="split_goal_wp">
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     <goal name="WP_parameter shortest_path_code.13.1.1.1" expl="1. loop invariant preservation">
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     <proof prover="2"><result status="valid" time="0.08"/></proof>
     <proof prover="5"><result status="valid" time="3.26"/></proof>
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     </goal>
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     <goal name="WP_parameter shortest_path_code.13.1.1.2" expl="2. loop invariant preservation">
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     <proof prover="2"><result status="valid" time="0.39"/></proof>
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     </goal>
    </transf>
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    </goal>
   </transf>
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   </goal>
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  </transf>
  </goal>
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  <goal name="WP_parameter shortest_path_code.14" expl="14. loop variant decrease">
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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="WP_parameter shortest_path_code.15" expl="15. loop invariant preservation">
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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="WP_parameter shortest_path_code.16" expl="16. loop invariant preservation">
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  <proof prover="5"><result status="valid" time="0.03"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.17" expl="17. loop invariant preservation">
  <proof prover="1" edited="dijkstra_DijkstraShortestPath_WP_parameter_shortest_path_code_3.v"><result status="valid" time="2.40"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.18" expl="18. loop variant decrease">
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  <proof prover="3"><result status="valid" time="0.07"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.19" expl="19. postcondition">
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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="WP_parameter shortest_path_code.20" expl="20. postcondition">
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  <proof prover="5"><result status="valid" time="0.02"/></proof>
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  </goal>
 </transf>
 </goal>
</theory>
</file>
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</why3session>