mirror of
https://github.com/AdaCore/why3.git
synced 2026-02-12 12:34:55 -08:00
385 lines
18 KiB
XML
385 lines
18 KiB
XML
<?xml version="1.0" encoding="UTF-8"?>
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<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
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"http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="6">
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<prover id="0" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="1" name="CVC5" version="1.0.0" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="3" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="4" name="Z3" version="4.11.2" timelimit="1" steplimit="0" memlimit="1000"/>
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<file format="whyml" proved="true">
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<path name=".."/><path name="sumrange.mlw"/>
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<theory name="ArraySum" proved="true">
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<goal name="sum'vc" expl="VC for sum" proved="true">
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<proof prover="3"><result status="valid" time="0.01" steps="2630"/></proof>
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</goal>
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<goal name="sum_right" proved="true">
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<transf name="introduce_premises" proved="true" >
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<goal name="sum_right.0" proved="true">
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<transf name="assert" proved="true" arg1="(forall x. 0 < x < j -> sum a (j-x) j = sum a (j-x) (j-1) + a[j-1])">
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<goal name="sum_right.0.0" expl="asserted formula" proved="true">
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<transf name="introduce_premises" proved="true" >
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<goal name="sum_right.0.0.0" expl="asserted formula" proved="true">
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<transf name="induction" proved="true" arg1="x">
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<goal name="sum_right.0.0.0.0" expl="base case (asserted formula)" proved="true">
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<proof prover="3"><result status="valid" time="0.00" steps="2549"/></proof>
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</goal>
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<goal name="sum_right.0.0.0.1" expl="recursive case (asserted formula)" proved="true">
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<transf name="instantiate" proved="true" arg1="Hrec" arg2="(x - 1)">
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<goal name="sum_right.0.0.0.1.0" expl="recursive case (asserted formula)" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="5493"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="sum_right.0.1" proved="true">
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<transf name="instantiate" proved="true" arg1="h" arg2="(j-i)">
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<goal name="sum_right.0.1.0" proved="true">
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<proof prover="4"><result status="valid" time="0.07" steps="529970"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</theory>
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<theory name="Simple" proved="true">
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<goal name="query'vc" expl="VC for query" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="query'vc.0" expl="loop invariant init" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="3486"/></proof>
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</goal>
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<goal name="query'vc.1" expl="index in array bounds" proved="true">
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<proof prover="3"><result status="valid" time="0.01" steps="3480"/></proof>
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</goal>
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<goal name="query'vc.2" expl="loop invariant preservation" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="4106"/></proof>
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</goal>
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<goal name="query'vc.3" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.00" steps="2951"/></proof>
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</goal>
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<goal name="query'vc.4" expl="out of loop bounds" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="2918"/></proof>
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</goal>
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</transf>
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</goal>
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</theory>
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<theory name="ExtraLemmas" proved="true">
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<goal name="sum_concat" proved="true">
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<transf name="introduce_premises" proved="true" >
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<goal name="sum_concat.0" proved="true">
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<transf name="induction" proved="true" arg1="k">
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<goal name="sum_concat.0.0" expl="base case" proved="true">
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<proof prover="3"><result status="valid" time="0.01" steps="3292"/></proof>
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</goal>
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<goal name="sum_concat.0.1" expl="recursive case" proved="true">
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<transf name="instantiate" proved="true" arg1="Hrec" arg2="k">
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<goal name="sum_concat.0.1.0" expl="recursive case" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="5303"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="sum_frame" proved="true">
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<transf name="introduce_premises" proved="true" >
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<goal name="sum_frame.0" proved="true">
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<transf name="assert" proved="true" arg1="(forall x. 0 <= x <= j-i -> sum a1 (j-x) j = sum a2 (j-x) j)">
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<goal name="sum_frame.0.0" expl="asserted formula" proved="true">
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<transf name="introduce_premises" proved="true" >
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<goal name="sum_frame.0.0.0" expl="asserted formula" proved="true">
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<transf name="induction" proved="true" arg1="x">
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<goal name="sum_frame.0.0.0.0" expl="base case (asserted formula)" proved="true">
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<proof prover="3"><result status="valid" time="0.01" steps="3975"/></proof>
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</goal>
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<goal name="sum_frame.0.0.0.1" expl="recursive case (asserted formula)" proved="true">
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<transf name="instantiate" proved="true" arg1="Hrec" arg2="(x - 1)">
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<goal name="sum_frame.0.0.0.1.0" expl="recursive case (asserted formula)" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="6230"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="sum_frame.0.1" proved="true">
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<transf name="instantiate" proved="true" arg1="h" arg2="(j-i)">
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<goal name="sum_frame.0.1.0" proved="true">
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<proof prover="3"><result status="valid" time="0.00" steps="3275"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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<goal name="sum_update" proved="true">
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<transf name="introduce_premises" proved="true" >
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<goal name="sum_update.0" proved="true">
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<transf name="induction" proved="true" arg1="h" arg2="from" arg3="i+1">
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<goal name="sum_update.0.0" expl="base case" proved="true">
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<transf name="compute_in_goal" proved="true" >
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<goal name="sum_update.0.0.0" expl="base case" proved="true">
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<proof prover="3"><result status="valid" time="0.07" steps="16040"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="sum_update.0.1" expl="recursive case" proved="true">
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<transf name="compute_in_goal" proved="true" >
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<goal name="sum_update.0.1.0" expl="recursive case" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="9017"/></proof>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</transf>
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</goal>
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</theory>
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<theory name="CumulativeArray" proved="true">
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<goal name="create'vc" expl="VC for create" proved="true">
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<proof prover="4"><result status="valid" time="0.01" steps="22848"/></proof>
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</goal>
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<goal name="query'vc" expl="VC for query" proved="true">
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<proof prover="3"><result status="valid" time="0.06" steps="12547"/></proof>
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</goal>
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<goal name="update'vc" expl="VC for update" proved="true">
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<proof prover="4"><result status="valid" time="0.02" steps="71868"/></proof>
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</goal>
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</theory>
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<theory name="CumulativeTree" proved="true">
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<goal name="tree_of_array'vc" expl="VC for tree_of_array" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="tree_of_array'vc.0" expl="index in array bounds" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="7001"/></proof>
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</goal>
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<goal name="tree_of_array'vc.1" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.01" steps="6432"/></proof>
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</goal>
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<goal name="tree_of_array'vc.2" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="8080"/></proof>
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</goal>
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<goal name="tree_of_array'vc.3" expl="variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="7123"/></proof>
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</goal>
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<goal name="tree_of_array'vc.4" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="7126"/></proof>
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</goal>
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<goal name="tree_of_array'vc.5" expl="variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="7236"/></proof>
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</goal>
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<goal name="tree_of_array'vc.6" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="7221"/></proof>
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</goal>
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<goal name="tree_of_array'vc.7" expl="assertion" proved="true">
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<proof prover="1"><result status="valid" time="0.08" steps="21250"/></proof>
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</goal>
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<goal name="tree_of_array'vc.8" expl="postcondition" proved="true">
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<proof prover="1"><result status="valid" time="0.11" steps="30325"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="create'vc" expl="VC for create" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="6435"/></proof>
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</goal>
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<goal name="query_aux'vc" expl="VC for query_aux" proved="true">
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<proof prover="3"><result status="valid" time="0.25" steps="40747"/></proof>
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</goal>
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<goal name="query'vc" expl="VC for query" proved="true">
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<proof prover="1"><result status="valid" time="0.06" steps="15792"/></proof>
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</goal>
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<goal name="is_tree_for_frame" proved="true">
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<transf name="induction_ty_lex" proved="true" >
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<goal name="is_tree_for_frame.0" proved="true">
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<proof prover="0"><result status="valid" time="1.17" steps="931"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="update_aux'vc" expl="VC for update_aux" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="update_aux'vc.0" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.05" steps="7293"/></proof>
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</goal>
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<goal name="update_aux'vc.1" expl="variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="7952"/></proof>
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</goal>
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<goal name="update_aux'vc.2" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="7505"/></proof>
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</goal>
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<goal name="update_aux'vc.3" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="7603"/></proof>
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</goal>
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<goal name="update_aux'vc.4" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="9082"/></proof>
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</goal>
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<goal name="update_aux'vc.5" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="9710"/></proof>
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</goal>
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<goal name="update_aux'vc.6" expl="variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="7963"/></proof>
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</goal>
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<goal name="update_aux'vc.7" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="7527"/></proof>
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</goal>
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<goal name="update_aux'vc.8" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="7702"/></proof>
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</goal>
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<goal name="update_aux'vc.9" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="9726"/></proof>
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</goal>
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<goal name="update_aux'vc.10" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="9159"/></proof>
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</goal>
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<goal name="update_aux'vc.11" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.55" steps="78497"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="update'vc" expl="VC for update" proved="true">
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<proof prover="1"><result status="valid" time="0.10" steps="27615"/></proof>
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</goal>
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<goal name="depth_min" proved="true">
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<transf name="induction_ty_lex" proved="true" >
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<goal name="depth_min.0" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="8072"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="depth_is_log'vc" expl="VC for depth_is_log" proved="true">
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<proof prover="0" timelimit="1"><result status="valid" time="0.77" steps="1034"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc" expl="VC for update_aux_complexity" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="update_aux_complexity'vc.0" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="8590"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.1" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="8549"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.2" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.09" steps="14820"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.3" expl="variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="9315"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.4" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="8809"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.5" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.05" steps="8914"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.6" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="10454"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.7" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="11206"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.8" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="11797"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.9" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.12" steps="23192"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.10" expl="variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="9326"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.11" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="8831"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.12" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="9013"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.13" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="11222"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.14" expl="assertion" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="10531"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.15" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="11890"/></proof>
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</goal>
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<goal name="update_aux_complexity'vc.16" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.13" steps="22308"/></proof>
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</goal>
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</transf>
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</goal>
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<goal name="query_aux_complexity'vc" expl="VC for query_aux_complexity" proved="true">
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<transf name="split_goal_right" proved="true" >
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<goal name="query_aux_complexity'vc.0" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="9079"/></proof>
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</goal>
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<goal name="query_aux_complexity'vc.1" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.05" steps="10854"/></proof>
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</goal>
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<goal name="query_aux_complexity'vc.2" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="9266"/></proof>
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</goal>
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<goal name="query_aux_complexity'vc.3" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.06" steps="11536"/></proof>
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</goal>
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<goal name="query_aux_complexity'vc.4" expl="variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="10357"/></proof>
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</goal>
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<goal name="query_aux_complexity'vc.5" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.03" steps="9849"/></proof>
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</goal>
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<goal name="query_aux_complexity'vc.6" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="10057"/></proof>
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</goal>
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<goal name="query_aux_complexity'vc.7" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="11689"/></proof>
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</goal>
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<goal name="query_aux_complexity'vc.8" expl="postcondition" proved="true">
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<proof prover="3"><result status="valid" time="0.02" steps="8129"/></proof>
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</goal>
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<goal name="query_aux_complexity'vc.9" expl="variant decrease" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="10432"/></proof>
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</goal>
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<goal name="query_aux_complexity'vc.10" expl="precondition" proved="true">
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<proof prover="3"><result status="valid" time="0.04" steps="9933"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.11" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.04" steps="10212"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.12" expl="postcondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.05" steps="11814"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.13" expl="postcondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.02" steps="8155"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.14" expl="variant decrease" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.05" steps="10430"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.15" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.04" steps="9931"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.16" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.04" steps="10240"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.17" expl="variant decrease" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.04" steps="10632"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.18" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.04" steps="10100"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.19" expl="precondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.04" steps="10354"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.20" expl="postcondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.03" steps="12354"/></proof>
|
|
</goal>
|
|
<goal name="query_aux_complexity'vc.21" expl="postcondition" proved="true">
|
|
<proof prover="3"><result status="valid" time="0.06" steps="13457"/></proof>
|
|
</goal>
|
|
</transf>
|
|
</goal>
|
|
</theory>
|
|
</file>
|
|
</why3session>
|