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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"https://www.why3.org/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="Z3" version="4.8.10" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.4.0" timelimit="1" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="binomial.mlw"/>
<theory name="Top" proved="true">
<goal name="infix /'vc" expl="VC for infix /" proved="true">
<proof prover="0"><result status="valid" time="0.010000" steps="6"/></proof>
</goal>
<goal name="comb'vc" expl="VC for comb" proved="true">
<proof prover="0"><result status="valid" time="0.010000" steps="2900"/></proof>
</goal>
<goal name="prop1'vc" expl="VC for prop1" proved="true">
<proof prover="0"><result status="valid" time="0.020000" steps="5222"/></proof>
</goal>
<goal name="prop2'vc" expl="VC for prop2" proved="true">
<transf name="split_vc" proved="true" >
<goal name="prop2'vc.0" expl="variant decrease" proved="true">
<proof prover="0"><result status="valid" time="0.010000" steps="2339"/></proof>
</goal>
<goal name="prop2'vc.1" expl="precondition" proved="true">
<proof prover="0"><result status="valid" time="0.020000" steps="2357"/></proof>
</goal>
<goal name="prop2'vc.2" expl="variant decrease" proved="true">
<proof prover="0"><result status="valid" time="0.020000" steps="3208"/></proof>
</goal>
<goal name="prop2'vc.3" expl="precondition" proved="true">
<proof prover="0"><result status="valid" time="0.010000" steps="3235"/></proof>
</goal>
<goal name="prop2'vc.4" expl="postcondition" proved="true">
<proof prover="1"><result status="valid" time="0.090000" steps="785"/></proof>
</goal>
</transf>
</goal>
<goal name="compute'vc" expl="VC for compute" proved="true">
<transf name="split_vc" proved="true" >
<goal name="compute'vc.0" expl="loop invariant init" proved="true">
<proof prover="0"><result status="valid" time="0.020000" steps="317"/></proof>
</goal>
<goal name="compute'vc.1" expl="loop invariant init" proved="true">
<proof prover="0"><result status="valid" time="0.020000" steps="3822"/></proof>
</goal>
<goal name="compute'vc.2" expl="check division by zero" proved="true">
<proof prover="0"><result status="valid" time="0.010000" steps="508"/></proof>
</goal>
<goal name="compute'vc.3" expl="precondition" proved="true">
<proof prover="0"><result status="valid" time="0.020000" steps="9265"/></proof>
</goal>
<goal name="compute'vc.4" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.010000" steps="8720"/></proof>
</goal>
<goal name="compute'vc.5" expl="loop invariant preservation" proved="true">
<proof prover="0"><result status="valid" time="0.241054" steps="4243789"/></proof>
</goal>
<goal name="compute'vc.6" expl="postcondition" proved="true">
<proof prover="0"><result status="valid" time="0.020000" steps="5037"/></proof>
</goal>
<goal name="compute'vc.7" expl="VC for compute" proved="true">
<proof prover="0"><result status="valid" time="0.010000" steps="1672"/></proof>
</goal>
</transf>
</goal>
</theory>
</file>
</why3session>
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