<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
<why3session shape_version="6">
<prover id="0" name="Coq" version="8.11.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="2.1.0" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="2" name="CVC3" version="2.4.1" timelimit="3" steplimit="0" memlimit="1000"/>
<prover id="4" name="Eprover" version="2.0" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="6" name="MetiTarski" version="2.4" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="7" name="Alt-Ergo" version="2.4.2" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="8" name="Z3" version="4.8.10" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="9" name="CVC5" version="1.0.5" timelimit="5" steplimit="0" memlimit="1000"/>
<file format="whyml" proved="true">
<path name=".."/><path name="lagrange_inequality.why"/>
<theory name="LagrangeInequality" proved="true">
 <goal name="norm2_pos" proved="true">
 <proof prover="6"><result status="valid" time="0.020000"/></proof>
 <proof prover="8"><result status="valid" time="0.000000" steps="225"/></proof>
 </goal>
 <goal name="Lagrange" proved="true">
 <proof prover="6"><result status="valid" time="0.010000"/></proof>
 <proof prover="8"><result status="valid" time="0.000000" steps="536"/></proof>
 </goal>
</theory>
<theory name="CauchySchwarzInequality" proved="true">
 <goal name="CauchySchwarz_aux" proved="true">
 <proof prover="6"><result status="valid" time="0.020000"/></proof>
 <proof prover="8"><result status="valid" time="0.010000" steps="1241"/></proof>
 </goal>
 <goal name="norm_pos" proved="true">
 <proof prover="1"><result status="valid" time="0.000000" steps="4"/></proof>
 <proof prover="6"><result status="valid" time="0.010000"/></proof>
 <proof prover="9"><result status="valid" time="0.178548" steps="12575"/></proof>
 </goal>
 <goal name="sqr_le_sqrt" proved="true">
 <proof prover="6"><result status="valid" time="0.040000"/></proof>
 </goal>
 <goal name="CauchySchwarz" proved="true">
 <proof prover="4"><result status="valid" time="0.100000"/></proof>
 </goal>
</theory>
<theory name="TriangleInequality" proved="true">
 <goal name="triangle_aux" proved="true">
 <transf name="split_vc" proved="true" >
  <goal name="triangle_aux.0" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="1115"/></proof>
  </goal>
  <goal name="triangle_aux.1" proved="true">
  <proof prover="7"><result status="valid" time="0.000000" steps="12"/></proof>
  </goal>
  <goal name="triangle_aux.2" proved="true">
  <proof prover="7"><result status="valid" time="0.030000" steps="419"/></proof>
  </goal>
  <goal name="triangle_aux.3" proved="true">
  <proof prover="9"><result status="valid" time="0.020000" steps="1424"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="sqr_sqrt_le" proved="true">
 <proof prover="1"><result status="valid" time="0.020000" steps="20"/></proof>
 <proof prover="2"><result status="valid" time="0.010000"/></proof>
 <proof prover="6"><result status="valid" time="0.060000"/></proof>
 </goal>
 <goal name="triangle" proved="true">
 <proof prover="0"><path name="lagrange_inequality_TriangleInequality_triangle_1.v"/><result status="valid" time="0.350000"/></proof>
 </goal>
</theory>
</file>
</why3session>
