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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="1.4" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="1" name="Alt-Ergo" version="1.30" timelimit="2" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="3" name="Z3" version="4.5.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="4" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
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<file name="../dijkstra.mlw" proved="true">
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<theory name="DijkstraShortestPath" proved="true" sum="501f8eee126b36613e1204b6238c589f">
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 <goal name="WP_parameter relax" expl="VC for relax" proved="true">
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 <proof prover="1"><result status="valid" time="0.01" steps="11"/></proof>
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 </goal>
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 <goal name="Length_nonneg" proved="true">
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 <transf name="induction_pr" proved="true" >
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  <goal name="Length_nonneg.0" proved="true">
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  <proof prover="1"><result status="valid" time="0.00" steps="4"/></proof>
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  </goal>
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  <goal name="Length_nonneg.1" proved="true">
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  <proof prover="0"><result status="valid" time="0.02"/></proof>
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  </goal>
 </transf>
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 </goal>
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 <goal name="Path_inversion" proved="true">
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 <proof prover="1"><result status="valid" time="0.01" steps="9"/></proof>
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 </goal>
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 <goal name="Path_shortest_path" proved="true">
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 <transf name="induction" proved="true" arg1="d">
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  <goal name="Path_shortest_path.0" proved="true">
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  <proof prover="4"><result status="valid" time="0.02"/></proof>
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  </goal>
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  <goal name="Path_shortest_path.1" proved="true">
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  <proof prover="4" timelimit="5"><result status="valid" time="0.06"/></proof>
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  </goal>
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 </transf>
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 </goal>
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 <goal name="Main_lemma" proved="true">
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 <proof prover="1"><result status="valid" time="0.04" steps="173"/></proof>
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 </goal>
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 <goal name="Completeness_lemma" proved="true">
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 <transf name="induction_pr" proved="true" >
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  <goal name="Completeness_lemma.0" proved="true">
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  <proof prover="1"><result status="valid" time="0.00" steps="5"/></proof>
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  </goal>
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  <goal name="Completeness_lemma.1" proved="true">
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  <proof prover="0"><result status="valid" time="0.04"/></proof>
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  </goal>
 </transf>
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 </goal>
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 <goal name="inside_or_exit" proved="true">
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 <transf name="induction_pr" proved="true" >
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  <goal name="inside_or_exit.0" proved="true">
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  <proof prover="1"><result status="valid" time="0.01" steps="5"/></proof>
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  </goal>
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  <goal name="inside_or_exit.1" proved="true">
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  <transf name="case" proved="true" arg1="(mem z s)">
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   <goal name="inside_or_exit.1.0" proved="true">
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   <proof prover="4"><result status="valid" time="0.02"/></proof>
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   </goal>
   <goal name="inside_or_exit.1.1" proved="true">
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   <proof prover="4"><result status="valid" time="0.84"/></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" expl="VC for shortest_path_code" proved="true">
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 <transf name="split_goal_wp" proved="true" >
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  <goal name="WP_parameter shortest_path_code.0" expl="loop invariant init" proved="true">
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  <proof prover="1"><result status="valid" time="0.04" steps="164"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.1" expl="loop invariant init" proved="true">
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  <proof prover="1"><result status="valid" time="0.01" steps="11"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.2" expl="loop invariant init" proved="true">
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  <proof prover="1"><result status="valid" time="0.02" steps="35"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.3" expl="precondition" 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="WP_parameter shortest_path_code.4" expl="assertion" proved="true">
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  <proof prover="1"><result status="valid" time="0.02" steps="86"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.5" expl="loop invariant init" proved="true">
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  <proof prover="1"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.6" expl="loop invariant init" proved="true">
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  <proof prover="1" timelimit="1"><result status="valid" time="0.08" steps="321"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.7" expl="loop invariant init" proved="true">
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  <proof prover="1" timelimit="60"><result status="valid" time="0.02" steps="110"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.8" expl="precondition" proved="true">
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  <proof prover="1"><result status="valid" time="0.01" steps="19"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.9" expl="assertion" proved="true">
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  <proof prover="2"><result status="valid" time="0.18"/></proof>
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  <transf name="remove" proved="true" arg1="real,tuple0,unit,ref,zero,one,(&gt;),(-),( * ),(-),(==),singleton,union,inter,diff,choose,(!),Assoc,Unit_def_l,Unit_def_r,Inv_def_l,Inv_def_r,Comm,Assoc1,Mul_distr_l,Mul_distr_r,Comm1,Unitary,NonTrivialRing,Refl,Trans,Antisymm,Total,ZeroLessOne,CompatOrderAdd,CompatOrderMult,Select_eq,Select_neq,extensionality,subset_refl,subset_trans,empty_def1,mem_empty,remove_def1,add_remove,remove_add,subset_remove,union_def1,inter_def1,diff_def1,subset_diff,choose_def,cardinal_nonneg,cardinal_empty,cardinal_add,cardinal_remove,subset_eq,cardinal1,G_succ_sound,Weight_nonneg,Length_nonneg,Path_inversion,Path_shortest_path,Main_lemma,Completeness_lemma,inside_or_exit">
   <goal name="WP_parameter shortest_path_code.9.0" expl="assertion" proved="true">
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   <proof prover="2" timelimit="1"><result status="valid" time="0.02"/></proof>
   <proof prover="3"><result status="valid" time="0.03"/></proof>
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   </goal>
  </transf>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.10" expl="loop invariant preservation" proved="true">
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  <proof prover="1"><result status="valid" time="0.01" steps="40"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.11" expl="loop invariant preservation" proved="true">
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  <transf name="inline_goal" proved="true" >
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   <goal name="WP_parameter shortest_path_code.11.0" expl="loop invariant preservation" proved="true">
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   <transf name="split_goal_wp" proved="true" >
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    <goal name="WP_parameter shortest_path_code.11.0.0" expl="VC for shortest_path_code" proved="true">
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    <proof prover="1"><result status="valid" time="0.02" steps="64"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.11.0.1" expl="VC for shortest_path_code" proved="true">
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    <proof prover="0" timelimit="10" memlimit="4000"><result status="valid" time="1.40"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.11.0.2" expl="VC for shortest_path_code" proved="true">
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    <proof prover="1"><result status="valid" time="0.01" steps="25"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.11.0.3" expl="VC for shortest_path_code" proved="true">
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    <proof prover="3" timelimit="10" memlimit="4000"><result status="valid" time="8.42"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.11.0.4" expl="VC for shortest_path_code" proved="true">
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    <proof prover="1"><result status="valid" time="0.05" steps="191"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.11.0.5" expl="VC for shortest_path_code" proved="true">
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    <proof prover="1"><result status="valid" time="0.17" steps="495"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.11.0.6" expl="VC for shortest_path_code" proved="true">
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    <transf name="case" proved="true" arg1="(v = v1)">
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     <goal name="WP_parameter shortest_path_code.11.0.6.0" expl="VC for shortest_path_code" proved="true">
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     <proof prover="3"><result status="valid" time="0.70"/></proof>
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     </goal>
     <goal name="WP_parameter shortest_path_code.11.0.6.1" expl="VC for shortest_path_code" proved="true">
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     <proof prover="4"><result status="valid" time="0.12"/></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.12" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.20"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.13" expl="loop variant decrease" proved="true">
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  <proof prover="1"><result status="valid" time="0.02" steps="59"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.14" expl="loop invariant preservation" proved="true">
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  <proof prover="1"><result status="valid" time="0.01" steps="19"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.15" expl="loop invariant preservation" proved="true">
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  <proof prover="1"><result status="valid" time="0.10" steps="291"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.16" expl="loop invariant preservation" proved="true">
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  <transf name="cut" proved="true" arg1="(is_empty su)">
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   <goal name="WP_parameter shortest_path_code.16.0" expl="loop invariant preservation" proved="true">
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   <transf name="cut" proved="true" arg1="(inv_succ src visited q d)">
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    <goal name="WP_parameter shortest_path_code.16.0.0" expl="loop invariant preservation" proved="true">
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    <proof prover="3"><result status="valid" time="0.35"/></proof>
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    </goal>
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    <goal name="WP_parameter shortest_path_code.16.0.1" proved="true">
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    <proof prover="4"><result status="valid" time="0.13"/></proof>
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    </goal>
   </transf>
   </goal>
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   <goal name="WP_parameter shortest_path_code.16.1" proved="true">
   <proof prover="4"><result status="valid" time="0.02"/></proof>
   </goal>
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  </transf>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.17" expl="loop variant decrease" proved="true">
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  <proof prover="1"><result status="valid" time="0.04" steps="122"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.18" expl="postcondition" proved="true">
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  <proof prover="1"><result status="valid" time="0.01" steps="22"/></proof>
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  </goal>
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  <goal name="WP_parameter shortest_path_code.19" expl="postcondition" proved="true">
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  <proof prover="1"><result status="valid" time="0.18" steps="352"/></proof>
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  </goal>
 </transf>
 </goal>
</theory>
</file>
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</why3session>