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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"http://why3.lri.fr/why3session.dtd">
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<why3session shape_version="6">
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<prover id="0" name="CVC4" version="1.5" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="1" name="CVC4" version="1.6" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="2" name="Z3" version="4.5.0" timelimit="5" steplimit="0" memlimit="1000"/>
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<prover id="3" name="Eprover" version="1.9.1-001" timelimit="5" steplimit="0" memlimit="2000"/>
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<prover id="4" name="Alt-Ergo" version="2.0.0" timelimit="5" steplimit="0" memlimit="1000"/>
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<file proved="true">
<path name=".."/>
<path name="lineardecision.mlw"/>
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<theory name="LinearEquationsCoeffs" proved="true">
 <goal name="neg_mul" proved="true">
 <proof prover="3"><result status="valid" time="0.06"/></proof>
 </goal>
</theory>
<theory name="LinearEquationsDecision" proved="true">
 <goal name="VC valid_expr" expl="VC for valid_expr" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC expr_bound" expl="VC for expr_bound" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC expr_bound_w" expl="VC for expr_bound_w" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC expr_bound_w.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC expr_bound_w.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC expr_bound_w.2" expl="precondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="12"/></proof>
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  </goal>
  <goal name="VC expr_bound_w.3" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC expr_bound_w.4" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC expr_bound_w.5" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="13"/></proof>
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  </goal>
  <goal name="VC expr_bound_w.6" expl="postcondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="34"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="eq_bound_w" proved="true">
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 <proof prover="4"><result status="valid" time="0.00" steps="19"/></proof>
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 </goal>
 <goal name="VC ctx_bound_w" expl="VC for ctx_bound_w" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC ctx_bound_w.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC ctx_bound_w.1" expl="precondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="12"/></proof>
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  </goal>
  <goal name="VC ctx_bound_w.2" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC ctx_bound_w.3" expl="postcondition" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="31"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC apply_r" expl="VC for apply_r" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC apply_r.0" expl="array creation size" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="13"/></proof>
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  </goal>
  <goal name="VC apply_r.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC apply_r.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC apply_r.3" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="18"/></proof>
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  </goal>
  <goal name="VC apply_r.4" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="19"/></proof>
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  </goal>
  <goal name="VC apply_r.5" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="18"/></proof>
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  </goal>
  <goal name="VC apply_r.6" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="18"/></proof>
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  </goal>
  <goal name="VC apply_r.7" expl="exceptional postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="6"/></proof>
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  </goal>
  <goal name="VC apply_r.8" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC apply_r.9" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="11"/></proof>
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  </goal>
  <goal name="VC apply_r.10" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="10"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC apply_l" expl="VC for apply_l" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC apply_l.0" expl="array creation size" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="8"/></proof>
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  </goal>
  <goal name="VC apply_l.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC apply_l.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC apply_l.3" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="18"/></proof>
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  </goal>
  <goal name="VC apply_l.4" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="19"/></proof>
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  </goal>
  <goal name="VC apply_l.5" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="18"/></proof>
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  </goal>
  <goal name="VC apply_l.6" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="18"/></proof>
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  </goal>
  <goal name="VC apply_l.7" expl="exceptional postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="6"/></proof>
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  </goal>
  <goal name="VC apply_l.8" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC apply_l.9" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="11"/></proof>
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  </goal>
  <goal name="VC apply_l.10" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="10"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC sprod" expl="VC for sprod" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC sprod.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC sprod.1" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="11"/></proof>
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  </goal>
  <goal name="VC sprod.2" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="11"/></proof>
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  </goal>
  <goal name="VC sprod.3" expl="exceptional postcondition" proved="true">
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  <proof prover="2"><result status="valid" time="0.01"/></proof>
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  </goal>
  <goal name="VC sprod.4" expl="exceptional postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="6"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC m_append" expl="VC for m_append" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC m_append.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC m_append.1" expl="precondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="42"/></proof>
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  </goal>
  <goal name="VC m_append.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC m_append.3" expl="loop invariant init" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="13"/></proof>
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  </goal>
  <goal name="VC m_append.4" expl="loop invariant init" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="13"/></proof>
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  </goal>
  <goal name="VC m_append.5" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC m_append.6" expl="loop invariant init" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="26"/></proof>
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  </goal>
  <goal name="VC m_append.7" expl="loop invariant init" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="23"/></proof>
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  </goal>
  <goal name="VC m_append.8" expl="loop invariant init" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="19"/></proof>
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  </goal>
  <goal name="VC m_append.9" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="24"/></proof>
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  </goal>
  <goal name="VC m_append.10" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="24"/></proof>
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  </goal>
  <goal name="VC m_append.11" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="35"/></proof>
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  </goal>
  <goal name="VC m_append.12" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="32"/></proof>
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  </goal>
  <goal name="VC m_append.13" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="32"/></proof>
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  </goal>
  <goal name="VC m_append.14" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="21"/></proof>
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  </goal>
  <goal name="VC m_append.15" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="22"/></proof>
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  </goal>
  <goal name="VC m_append.16" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="76"/></proof>
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  </goal>
  <goal name="VC m_append.17" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="29"/></proof>
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  </goal>
  <goal name="VC m_append.18" expl="out of loop bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="31"/></proof>
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  </goal>
  <goal name="VC m_append.19" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
  <goal name="VC m_append.20" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="16"/></proof>
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  </goal>
  <goal name="VC m_append.21" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="24"/></proof>
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  </goal>
  <goal name="VC m_append.22" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="21"/></proof>
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  </goal>
  <goal name="VC m_append.23" expl="out of loop bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="16"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC v_append" expl="VC for v_append" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC v_append.0" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC v_append.1" expl="array creation size" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="9"/></proof>
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  </goal>
  <goal name="VC v_append.2" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC v_append.3" expl="loop invariant init" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="11"/></proof>
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  </goal>
  <goal name="VC v_append.4" expl="loop invariant init" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="13"/></proof>
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  </goal>
  <goal name="VC v_append.5" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
  <goal name="VC v_append.6" expl="index in array bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="15"/></proof>
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  </goal>
  <goal name="VC v_append.7" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.22" steps="396"/></proof>
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  </goal>
  <goal name="VC v_append.8" expl="loop invariant preservation" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.14" steps="144"/></proof>
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  </goal>
  <goal name="VC v_append.9" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="13"/></proof>
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  </goal>
  <goal name="VC v_append.10" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="17"/></proof>
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  </goal>
  <goal name="VC v_append.11" expl="postcondition" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="14"/></proof>
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  </goal>
  <goal name="VC v_append.12" expl="out of loop bounds" proved="true">
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  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="18"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC infix ==" expl="VC for infix ==" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC infix ==.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC infix ==.1" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC infix ==.2" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC infix ==.3" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC infix ==.4" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC infix ==.5" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.01" steps="14"/></proof>
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  </goal>
  <goal name="VC infix ==.6" expl="loop invariant preservation" proved="true">
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  <proof prover="4"><result status="valid" time="0.02" steps="17"/></proof>
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  </goal>
  <goal name="VC infix ==.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC infix ==.8" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC max_var" expl="VC for max_var" proved="true">
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 <proof prover="4"><result status="valid" time="0.04" steps="271"/></proof>
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 </goal>
 <goal name="VC max_var_e" expl="VC for max_var_e" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC max_var_ctx" expl="VC for max_var_ctx" proved="true">
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 <proof prover="4"><result status="valid" time="0.04" steps="203"/></proof>
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 </goal>
 <goal name="VC opp_expr" expl="VC for opp_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC opp_expr.0" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC opp_expr.0.0" expl="assertion" proved="true">
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MARCHE Claude committed
326
   <proof prover="4"><result status="valid" time="0.01" steps="9"/></proof>
327 328
   </goal>
   <goal name="VC opp_expr.0.1" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
329
   <proof prover="4"><result status="valid" time="0.01" steps="9"/></proof>
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   </goal>
   <goal name="VC opp_expr.0.2" expl="assertion" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="VC opp_expr.0.2.0" expl="assertion" proved="true">
    <transf name="apply" proved="true" arg1="neg_mul">
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="VC opp_expr.0.3" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
340
   <proof prover="4"><result status="valid" time="0.02" steps="9"/></proof>
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   </goal>
  </transf>
  </goal>
  <goal name="VC opp_expr.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC opp_expr.2" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC opp_expr.3" expl="assertion" proved="true">
  <proof prover="3" memlimit="1000"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC opp_expr.4" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC opp_expr.4.0" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
356
   <proof prover="4"><result status="valid" time="0.01" steps="9"/></proof>
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   </goal>
   <goal name="VC opp_expr.4.1" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02"/></proof>
   </goal>
   <goal name="VC opp_expr.4.2" expl="assertion" proved="true">
   <proof prover="2"><result status="valid" time="0.02"/></proof>
   </goal>
   <goal name="VC opp_expr.4.3" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
365
   <proof prover="4"><result status="valid" time="0.02" steps="9"/></proof>
366 367 368 369 370 371 372 373 374
   </goal>
   <goal name="VC opp_expr.4.4" expl="VC for opp_expr" proved="true">
   <proof prover="2"><result status="valid" time="0.02"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC opp_expr.5" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC opp_expr.5.0" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
375
   <proof prover="4"><result status="valid" time="0.01" steps="14"/></proof>
376 377 378 379
   </goal>
   <goal name="VC opp_expr.5.1" expl="postcondition" proved="true">
   <transf name="compute_in_goal" proved="true" >
    <goal name="VC opp_expr.5.1.0" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
380
    <proof prover="4"><result status="valid" time="0.04" steps="25"/></proof>
381 382 383 384
    </goal>
   </transf>
   </goal>
   <goal name="VC opp_expr.5.2" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
385
   <proof prover="4"><result status="valid" time="0.02" steps="10"/></proof>
386 387 388 389
   </goal>
  </transf>
  </goal>
  <goal name="VC opp_expr.6" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
390
  <proof prover="4"><result status="valid" time="0.02" steps="125"/></proof>
391 392
  </goal>
  <goal name="VC opp_expr.7" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
393
  <proof prover="4"><result status="valid" time="0.02" steps="115"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC norm_eq_aux" expl="VC for norm_eq_aux" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC norm_eq_aux.0" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
400
  <proof prover="4"><result status="valid" time="0.01" steps="24"/></proof>
401 402
  </goal>
  <goal name="VC norm_eq_aux.1" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
403
  <proof prover="4"><result status="valid" time="0.01" steps="10"/></proof>
404 405 406 407 408
  </goal>
  <goal name="VC norm_eq_aux.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC norm_eq_aux.3" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
409
  <proof prover="4"><result status="valid" time="0.02" steps="9"/></proof>
410 411
  </goal>
  <goal name="VC norm_eq_aux.4" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
412
  <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
413 414 415 416 417 418 419 420
  </goal>
  <goal name="VC norm_eq_aux.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC norm_eq_aux.6" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC norm_eq_aux.7" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
421
  <proof prover="4"><result status="valid" time="0.02" steps="25"/></proof>
422 423
  </goal>
  <goal name="VC norm_eq_aux.8" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
424
  <proof prover="4"><result status="valid" time="0.02" steps="54"/></proof>
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  </goal>
  <goal name="VC norm_eq_aux.9" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC norm_eq_aux.10" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC norm_eq" expl="VC for norm_eq" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC norm_eq.0" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
437
  <proof prover="4"><result status="valid" time="0.02" steps="42"/></proof>
438 439 440 441 442 443 444
  </goal>
  <goal name="VC norm_eq.1" expl="assertion" proved="true">
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC norm_eq.2" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC norm_eq.2.0" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
445
   <proof prover="4"><result status="valid" time="0.02" steps="39"/></proof>
446 447
   </goal>
   <goal name="VC norm_eq.2.1" expl="VC for norm_eq" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
448
   <proof prover="4"><result status="valid" time="0.03" steps="32"/></proof>
449 450
   </goal>
   <goal name="VC norm_eq.2.2" expl="VC for norm_eq" proved="true">
451
   <proof prover="0"><result status="valid" time="0.16"/></proof>
452 453
   </goal>
   <goal name="VC norm_eq.2.3" expl="VC for norm_eq" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
454
   <proof prover="4"><result status="valid" time="0.02" steps="38"/></proof>
455 456
   </goal>
   <goal name="VC norm_eq.2.4" expl="VC for norm_eq" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
457
   <proof prover="4"><result status="valid" time="0.02" steps="19"/></proof>
458 459
   </goal>
   <goal name="VC norm_eq.2.5" expl="VC for norm_eq" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
460
   <proof prover="4"><result status="valid" time="0.02" steps="14"/></proof>
461 462 463 464 465 466
   </goal>
  </transf>
  </goal>
  <goal name="VC norm_eq.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC norm_eq.3.0" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
467
   <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
468 469
   </goal>
   <goal name="VC norm_eq.3.1" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
470
   <proof prover="0"><result status="valid" time="0.10"/></proof>
471 472 473 474
   </goal>
  </transf>
  </goal>
  <goal name="VC norm_eq.4" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
475
  <proof prover="4"><result status="valid" time="0.02" steps="33"/></proof>
476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505
  </goal>
  <goal name="VC norm_eq.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC interp_ctx_impl" expl="VC for interp_ctx_impl" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC interp_ctx_impl.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC interp_ctx_impl.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC interp_ctx_impl.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC interp_ctx_valid" expl="VC for interp_ctx_valid" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC interp_ctx_valid.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC interp_ctx_valid.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC interp_ctx_wr" expl="VC for interp_ctx_wr" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
506
 <proof prover="4"><result status="valid" time="0.02" steps="140"/></proof>
507 508
 </goal>
 <goal name="VC interp_ctx_wl" expl="VC for interp_ctx_wl" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
509
 <proof prover="4"><result status="valid" time="0.02" steps="115"/></proof>
510 511 512 513 514 515 516
 </goal>
 <goal name="VC mul_expr" expl="VC for mul_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC mul_expr.0" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.12"/></proof>
  </goal>
  <goal name="VC mul_expr.1" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
517
  <proof prover="4"><result status="valid" time="0.02" steps="10"/></proof>
518 519
  </goal>
  <goal name="VC mul_expr.2" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
520
  <proof prover="4"><result status="valid" time="0.01" steps="16"/></proof>
521 522
  </goal>
  <goal name="VC mul_expr.3" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
523
  <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
524 525 526 527 528
  </goal>
  <goal name="VC mul_expr.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC mul_expr.5" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
529
  <proof prover="4"><result status="valid" time="0.02" steps="18"/></proof>
530 531
  </goal>
  <goal name="VC mul_expr.6" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
532
  <proof prover="4"><result status="valid" time="0.01" steps="27"/></proof>
533 534 535 536 537
  </goal>
  <goal name="VC mul_expr.7" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC mul_expr.8" expl="variant decrease" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
538
  <proof prover="4"><result status="valid" time="0.02" steps="46"/></proof>
539 540
  </goal>
  <goal name="VC mul_expr.9" expl="variant decrease" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
541
  <proof prover="4"><result status="valid" time="0.01" steps="49"/></proof>
542 543
  </goal>
  <goal name="VC mul_expr.10" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
544
  <proof prover="4"><result status="valid" time="0.03" steps="20"/></proof>
545 546
  </goal>
  <goal name="VC mul_expr.11" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
547
  <proof prover="4"><result status="valid" time="0.02" steps="61"/></proof>
548 549 550 551 552 553 554 555 556 557 558 559
  </goal>
  <goal name="VC mul_expr.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC mul_expr.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC add_expr" expl="VC for add_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC add_expr.0" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
560
  <proof prover="3"><result status="valid" time="0.22"/></proof>
561 562
  </goal>
  <goal name="VC add_expr.1" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
563
  <proof prover="4"><result status="valid" time="0.03" steps="17"/></proof>
564 565 566 567 568 569 570 571 572
  </goal>
  <goal name="VC add_expr.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC add_expr.3.0" expl="postcondition" proved="true">
   <transf name="introduce_premises" proved="true" >
    <goal name="VC add_expr.3.0.0" expl="postcondition" proved="true">
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Raphael Rieu-Helft committed
573
    <proof prover="3"><result status="valid" time="0.69"/></proof>
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    </goal>
   </transf>
   </goal>
   <goal name="VC add_expr.3.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.05"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC add_expr.4" expl="postcondition" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="VC add_expr.4.0" expl="postcondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
585
   <proof prover="0" timelimit="1"><result status="valid" time="0.19"/></proof>
586 587
   </goal>
   <goal name="VC add_expr.4.1" expl="postcondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
588
   <proof prover="3"><result status="valid" time="0.45"/></proof>
589 590 591 592 593 594 595 596 597 598
   </goal>
  </transf>
  </goal>
  <goal name="VC add_expr.5" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.6" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.7" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
599
  <proof prover="4"><result status="valid" time="0.02" steps="61"/></proof>
600 601
  </goal>
  <goal name="VC add_expr.8" expl="postcondition" proved="true">
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  <transf name="split_goal_right" proved="true" >
   <goal name="VC add_expr.8.0" expl="postcondition" proved="true">
   <transf name="split_goal_right" proved="true" >
    <goal name="VC add_expr.8.0.0" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
606
    <proof prover="4"><result status="valid" time="0.02" steps="56"/></proof>
607 608
    </goal>
    <goal name="VC add_expr.8.0.1" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
609
    <proof prover="4"><result status="valid" time="0.01" steps="21"/></proof>
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    </goal>
   </transf>
   </goal>
   <goal name="VC add_expr.8.1" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
614
   <proof prover="4"><result status="valid" time="0.03" steps="20"/></proof>
615 616
   </goal>
  </transf>
617 618 619 620 621 622 623 624
  </goal>
  <goal name="VC add_expr.9" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.10" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.11" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
625
  <proof prover="4"><result status="valid" time="0.02" steps="61"/></proof>
626 627
  </goal>
  <goal name="VC add_expr.12" expl="postcondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
628
  <proof prover="4"><result status="valid" time="0.71" steps="204"/></proof>
629 630 631 632 633 634 635 636
  </goal>
  <goal name="VC add_expr.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.15" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
637
  <proof prover="4"><result status="valid" time="0.02" steps="19"/></proof>
638 639 640 641 642 643 644 645 646 647 648
  </goal>
  <goal name="VC add_expr.16" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.17" expl="postcondition" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="VC add_expr.17.0" expl="postcondition" proved="true">
   <transf name="revert" proved="true" arg1="H">
    <goal name="VC add_expr.17.0.0" expl="postcondition" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="VC add_expr.17.0.0.0" expl="postcondition" proved="true">
649
     <proof prover="0" timelimit="1"><result status="valid" time="0.14"/></proof>
650 651
     </goal>
     <goal name="VC add_expr.17.0.0.1" expl="postcondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
652
     <proof prover="3"><result status="valid" time="0.43"/></proof>
653 654 655 656 657 658 659 660 661 662 663 664 665 666
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="VC add_expr.18" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.19" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.20" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
667
  <proof prover="4"><result status="valid" time="0.02" steps="58"/></proof>
668 669
  </goal>
  <goal name="VC add_expr.21" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
670
  <proof prover="4"><result status="valid" time="0.19" steps="242"/></proof>
671 672 673 674 675 676 677 678
  </goal>
  <goal name="VC add_expr.22" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.23" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.24" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
679
  <proof prover="4"><result status="valid" time="0.02" steps="58"/></proof>
680 681
  </goal>
  <goal name="VC add_expr.25" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
682
  <proof prover="4"><result status="valid" time="0.15" steps="191"/></proof>
683 684 685 686 687 688 689 690 691 692 693 694 695 696
  </goal>
  <goal name="VC add_expr.26" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.27" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.28" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.29" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.30" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
697
  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
698 699
  </goal>
  <goal name="VC add_expr.31" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
700
  <proof prover="4"><result status="valid" time="0.02" steps="19"/></proof>
701 702 703 704 705 706 707 708
  </goal>
  <goal name="VC add_expr.32" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.33" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.34" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
709
  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
710 711
  </goal>
  <goal name="VC add_expr.35" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
712
  <proof prover="4"><result status="valid" time="0.02" steps="20"/></proof>
713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729
  </goal>
  <goal name="VC add_expr.36" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.37" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.38" expl="unreachable point" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.39" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.40" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.41" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
730
  <proof prover="4"><result status="valid" time="0.02" steps="13"/></proof>
731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749
  </goal>
  <goal name="VC add_expr.42" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.43" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC add_expr.44" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_expr.45" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC add_expr.46" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC mul_eq" expl="VC for mul_eq" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
750
 <proof prover="4"><result status="valid" time="0.01" steps="29"/></proof>
751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784
 </goal>
 <goal name="VC add_eq" expl="VC for add_eq" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC add_eq.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC add_eq.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.16"/></proof>
  </goal>
  <goal name="VC add_eq.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC add_eq.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_eq.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC add_eq.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC zero_expr" expl="VC for zero_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC zero_expr.0" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC zero_expr.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC zero_expr.2" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC zero_expr.2.0" expl="postcondition" proved="true">
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MARCHE Claude committed
785
   <proof prover="4"><result status="valid" time="0.02" steps="26"/></proof>
786 787
   </goal>
   <goal name="VC zero_expr.2.1" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
788
   <proof prover="3"><result status="valid" time="0.23"/></proof>
789 790
   </goal>
   <goal name="VC zero_expr.2.2" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
791
   <proof prover="4"><result status="valid" time="0.03" steps="31"/></proof>
792 793 794 795 796 797
   </goal>
  </transf>
  </goal>
  <goal name="VC zero_expr.3" expl="postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC zero_expr.3.0" expl="postcondition" proved="true">
798
   <proof prover="0"><result status="valid" time="0.06"/></proof>
799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814
   </goal>
  </transf>
  </goal>
  <goal name="VC zero_expr.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC sub_expr" expl="VC for sub_expr" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC sub_expr.0" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC sub_expr.0.0" expl="assertion" proved="true">
   <proof prover="3"><result status="valid" time="0.04"/></proof>
   </goal>
   <goal name="VC sub_expr.0.1" expl="VC for sub_expr" proved="true">
815
   <proof prover="0"><result status="valid" time="0.05"/></proof>
816 817
   </goal>
   <goal name="VC sub_expr.0.2" expl="VC for sub_expr" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
818
   <proof prover="4"><result status="valid" time="0.01" steps="8"/></proof>
819 820
   </goal>
   <goal name="VC sub_expr.0.3" expl="VC for sub_expr" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
821
   <proof prover="4"><result status="valid" time="0.01" steps="34"/></proof>
822 823
   </goal>
   <goal name="VC sub_expr.0.4" expl="VC for sub_expr" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
824
   <proof prover="4"><result status="valid" time="0.02" steps="11"/></proof>
825 826 827 828
   </goal>
  </transf>
  </goal>
  <goal name="VC sub_expr.1" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
829
  <proof prover="4"><result status="valid" time="0.01" steps="8"/></proof>
830 831 832 833 834 835 836 837 838 839 840 841
  </goal>
  <goal name="VC sub_expr.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC sub_expr.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC same_eq" expl="VC for same_eq" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC same_eq.0" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
842
  <proof prover="0"><result status="valid" time="0.09"/></proof>
843 844
  </goal>
  <goal name="VC same_eq.1" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
845
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884
  </goal>
  <goal name="VC same_eq.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC same_eq.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC same_eq.4" expl="exceptional postcondition" proved="true">
  <transf name="split_goal_right" proved="true" >
  </transf>
  </goal>
  <goal name="VC same_eq.5" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC same_eq.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC norm_context" expl="VC for norm_context" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC norm_context.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC norm_context.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC norm_context.2" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC norm_context.3" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC norm_context.4" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC print_lc" expl="VC for print_lc" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
885
 <proof prover="4"><result status="valid" time="0.01" steps="39"/></proof>
886 887 888 889 890 891 892 893 894 895
 </goal>
 <goal name="VC check_combination" expl="VC for check_combination" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC check_combination.0" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC check_combination.1" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC check_combination.2" expl="variant decrease" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
896
  <proof prover="4"><result status="valid" time="0.02" steps="35"/></proof>
897 898
  </goal>
  <goal name="VC check_combination.3" expl="precondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
899
  <proof prover="4"><result status="valid" time="0.02" steps="15"/></proof>
900 901
  </goal>
  <goal name="VC check_combination.4" expl="precondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
902
  <proof prover="4"><result status="valid" time="0.02" steps="60"/></proof>
903 904
  </goal>
  <goal name="VC check_combination.5" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
905
  <proof prover="4"><result status="valid" time="0.02" steps="74"/></proof>
906 907 908 909 910 911 912
  </goal>
  <goal name="VC check_combination.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC check_combination.7" expl="assertion" proved="true">
  <transf name="split_goal_right" proved="true" >
   <goal name="VC check_combination.7.0" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
913
   <proof prover="4"><result status="valid" time="0.03" steps="15"/></proof>
914 915
   </goal>
   <goal name="VC check_combination.7.1" expl="assertion" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
916
   <proof prover="4"><result status="valid" time="0.02" steps="30"/></proof>
917 918
   </goal>
   <goal name="VC check_combination.7.2" expl="VC for check_combination" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
919
   <proof prover="4"><result status="valid" time="0.03" steps="45"/></proof>
920 921 922 923
   </goal>
  </transf>
  </goal>
  <goal name="VC check_combination.8" expl="variant decrease" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
924
  <proof prover="4"><result status="valid" time="0.02" steps="35"/></proof>
925 926
  </goal>
  <goal name="VC check_combination.9" expl="precondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
927
  <proof prover="4"><result status="valid" time="0.02" steps="12"/></proof>
928 929
  </goal>
  <goal name="VC check_combination.10" expl="precondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
930
  <proof prover="4"><result status="valid" time="0.02" steps="60"/></proof>
931 932
  </goal>
  <goal name="VC check_combination.11" expl="postcondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
933
  <proof prover="4"><result status="valid" time="0.02" steps="74"/></proof>
934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950
  </goal>
  <goal name="VC check_combination.12" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC check_combination.13" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC check_combination.14" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="VC check_combination.15" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC check_combination.16" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC check_combination.17" expl="precondition" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
951
  <proof prover="4"><result status="valid" time="0.02" steps="8"/></proof>
952 953
  </goal>
  <goal name="VC check_combination.18" expl="postcondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
954
  <proof prover="3"><result status="valid" time="2.21"/></proof>
955 956
  </goal>
  <goal name="VC check_combination.19" expl="postcondition" proved="true">
957
  <proof prover="0"><result status="valid" time="0.02"/></proof>
958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973
  </goal>
  <goal name="VC check_combination.20" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="VC check_combination.21" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="VC check_combination.22" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
 </transf>
 </goal>
 <goal name="VC transpose" expl="VC for transpose" proved="true">
 <proof prover="2"><result status="valid" time="0.18"/></proof>
 </goal>
 <goal name="VC swap_rows" expl="VC for swap_rows" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
974
 <proof prover="2"><result status="valid" time="0.40"/></proof>
975 976
 </goal>
 <goal name="VC mul_row" expl="VC for mul_row" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
977
 <proof prover="4"><result status="valid" time="0.12" steps="293"/></proof>
978 979
 </goal>
 <goal name="VC addmul_row" expl="VC for addmul_row" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
980
 <proof prover="4"><result status="valid" time="0.14" steps="541"/></proof>
981 982 983 984 985
 </goal>
 <goal name="VC gauss_jordan" expl="VC for gauss_jordan" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC gauss_jordan.0" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.17"/></proof>
MARCHE Claude's avatar
MARCHE Claude committed
986
  <proof prover="4" memlimit="2000"><result status="valid" time="0.02" steps="17"/></proof>
987 988
  </goal>
  <goal name="VC gauss_jordan.1" expl="integer overflow" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
989
  <proof prover="4"><result status="valid" time="0.02" steps="20"/></proof>
990 991
  </goal>
  <goal name="VC gauss_jordan.2" expl="variant decrease" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
992
  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
993 994
  </goal>
  <goal name="VC gauss_jordan.3" expl="precondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
995
  <proof prover="4"><result status="valid" time="0.01" steps="18"/></proof>
996 997
  </goal>
  <goal name="VC gauss_jordan.4" expl="precondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
998
  <proof prover="4"><result status="valid" time="0.02" steps="20"/></proof>
999 1000
  </goal>
  <goal name="VC gauss_jordan.5" expl="postcondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1001
  <proof prover="4"><result status="valid" time="0.01" steps="49"/></proof>
1002 1003
  </goal>
  <goal name="VC gauss_jordan.6" expl="postcondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1004
  <proof prover="4"><result status="valid" time="0.02" steps="25"/></proof>
1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022
  </goal>
  <goal name="VC gauss_jordan.7" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC gauss_jordan.8" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC gauss_jordan.9" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC gauss_jordan.10" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC gauss_jordan.11" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC gauss_jordan.12" expl="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1023
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="15"/></proof>
1024 1025 1026 1027 1028 1029
  </goal>
  <goal name="VC gauss_jordan.13" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC gauss_jordan.14" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1030
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="21"/></proof>
1031 1032
  </goal>
  <goal name="VC gauss_jordan.15" expl="precondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1033
  <proof prover="4"><result status="valid" time="0.01" steps="23"/></proof>
1034 1035 1036 1037 1038 1039
  </goal>
  <goal name="VC gauss_jordan.16" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC gauss_jordan.17" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1040
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="27"/></proof>
1041 1042
  </goal>
  <goal name="VC gauss_jordan.18" expl="index in array bounds" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1043
  <proof prover="4"><result status="valid" time="0.01" steps="30"/></proof>
1044 1045
  </goal>
  <goal name="VC gauss_jordan.19" expl="precondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1046
  <proof prover="4"><result status="valid" time="0.02" steps="30"/></proof>
1047 1048 1049
  </goal>
  <goal name="VC gauss_jordan.20" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04"/></proof>
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1050
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="30"/></proof>
1051 1052 1053 1054 1055
  </goal>
  <goal name="VC gauss_jordan.21" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC gauss_jordan.22" expl="precondition" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1056
  <proof prover="4"><result status="valid" time="0.01" steps="55"/></proof>
1057 1058 1059 1060 1061
  </goal>
  <goal name="VC gauss_jordan.23" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC gauss_jordan.24" expl="index in array bounds" proved="true">
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Raphael Rieu-Helft committed
1062
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="45"/></proof>
1063 1064
  </goal>
  <goal name="VC gauss_jordan.25" expl="precondition" proved="true">
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Raphael Rieu-Helft committed
1065
  <proof prover="4"><result status="valid" time="0.01" steps="65"/></proof>
1066 1067 1068
  </goal>
  <goal name="VC gauss_jordan.26" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
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Raphael Rieu-Helft committed
1069
  <proof prover="4" memlimit="2000"><result status="valid" time="0.00" steps="8"/></proof>
1070 1071 1072 1073 1074
  </goal>
  <goal name="VC gauss_jordan.27" expl="assertion" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="VC gauss_jordan.27.0" expl="assertion" proved="true">
   <transf name="split_vc" proved="true" >
1075
    <goal name="VC gauss_jordan.27.0.0" expl="assertion" proved="true">
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Raphael Rieu-Helft committed
1076
    <proof prover="0"><result status="valid" time="0.23"/></proof>
1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088
    </goal>
    <goal name="VC gauss_jordan.27.0.1" expl="VC for gauss_jordan" proved="true">
    <proof prover="2"><result status="valid" time="0.04"/></proof>
    </goal>
    <goal name="VC gauss_jordan.27.0.2" expl="VC for gauss_jordan" proved="true">
    <proof prover="2"><result status="valid" time="0.14"/></proof>
    </goal>
    <goal name="VC gauss_jordan.27.0.3" expl="VC for gauss_jordan" proved="true">
    <transf name="revert" proved="true" arg1="H">
     <goal name="VC gauss_jordan.27.0.3.0" expl="VC for gauss_jordan" proved="true">
     <transf name="split_vc" proved="true" >
      <goal name="VC gauss_jordan.27.0.3.0.0" expl="VC for gauss_jordan" proved="true">
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Raphael Rieu-Helft committed
1089
      <proof prover="4"><result status="valid" time="0.14" steps="439"/></proof>
1090 1091 1092 1093 1094 1095
      </goal>
     </transf>
     </goal>
    </transf>
    </goal>
    <goal name="VC gauss_jordan.27.0.4" expl="VC for gauss_jordan" proved="true">
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Raphael Rieu-Helft committed
1096
    <proof prover="0"><result status="valid" time="0.30"/></proof>
1097 1098 1099 1100 1101 1102
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="VC gauss_jordan.28" expl="loop invariant preservation" proved="true">
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Raphael Rieu-Helft committed
1103
  <proof prover="4"><result status="valid" time="0.01" steps="40"/></proof>
1104 1105
  </goal>
  <goal name="VC gauss_jordan.29" expl="loop invariant preservation" proved="true">
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Raphael Rieu-Helft committed
1106
  <proof prover="2"><result status="valid" time="0.80"/></proof>
1107 1108
  </goal>
  <goal name="VC gauss_jordan.30" expl="loop invariant preservation" proved="true">
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Raphael Rieu-Helft committed
1109
  <proof prover="4"><result status="valid" time="0.02" steps="52"/></proof>
1110 1111
  </goal>
  <goal name="VC gauss_jordan.31" expl="loop invariant preservation" proved="true">
1112
  <proof prover="0"><result status="valid" time="0.21"/></proof>
1113 1114
  </goal>
  <goal name="VC gauss_jordan.32" expl="out of loop bounds" proved="true">
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Raphael Rieu-Helft committed
1115
  <proof prover="4"><result status="valid" time="0.02" steps="37"/></proof>
1116 1117 1118 1119 1120
  </goal>
  <goal name="VC gauss_jordan.33" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC gauss_jordan.34" expl="index in array bounds" proved="true">
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Raphael Rieu-Helft committed
1121 1122
  <proof prover="2"><result status="valid" time="0.68"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="43"/></proof>
1123 1124
  </goal>
  <goal name="VC gauss_jordan.35" expl="precondition" proved="true">
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Raphael Rieu-Helft committed
1125
  <proof prover="4"><result status="valid" time="0.02" steps="45"/></proof>
1126 1127 1128
  </goal>
  <goal name="VC gauss_jordan.36" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
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Raphael Rieu-Helft committed
1129
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="8"/></proof>
1130 1131 1132 1133
  </goal>
  <goal name="VC gauss_jordan.37" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
   <goal name="VC gauss_jordan.37.0" expl="assertion" proved="true">
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MARCHE Claude committed
1134
   <proof prover="0"><result status="valid" time="0.13"/></proof>
1135 1136 1137 1138 1139 1140 1141 1142
   </goal>
   <goal name="VC gauss_jordan.37.1" expl="VC for gauss_jordan" proved="true">
   <proof prover="2"><result status="valid" time="0.03"/></proof>
   </goal>
   <goal name="VC gauss_jordan.37.2" expl="VC for gauss_jordan" proved="true">
   <proof prover="2"><result status="valid" time="0.13"/></proof>
   </goal>
   <goal name="VC gauss_jordan.37.3" expl="VC for gauss_jordan" proved="true">
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Raphael Rieu-Helft committed
1143
   <proof prover="4"><result status="valid" time="0.13" steps="430"/></proof>
1144 1145
   </goal>
   <goal name="VC gauss_jordan.37.4" expl="VC for gauss_jordan" proved="true">
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Raphael Rieu-Helft committed
1146
   <proof prover="0"><result status="valid" time="0.30"/></proof>
1147 1148 1149 1150 1151
   </goal>
  </transf>
  </goal>
  <goal name="VC gauss_jordan.38" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
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Raphael Rieu-Helft committed
1152
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="38"/></proof>
1153 1154
  </goal>
  <goal name="VC gauss_jordan.39" expl="loop invariant preservation" proved="true">
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Raphael Rieu-Helft committed
1155
  <proof prover="2"><result status="valid" time="0.83"/></proof>
1156 1157
  </goal>
  <goal name="VC gauss_jordan.40" expl="loop invariant preservation" proved="true">
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Raphael Rieu-Helft committed
1158
  <proof prover="4"><result status="valid" time="0.03" steps="50"/></proof>
1159 1160
  </goal>
  <goal name="VC gauss_jordan.41" expl="loop invariant preservation" proved="true">
MARCHE Claude's avatar
MARCHE Claude committed
1161
  <proof prover="2"><result status="valid" time="0.41"/></proof>
1162 1163
  </goal>
  <goal name="VC gauss_jordan.42" expl="out of loop bounds" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1164
  <proof prover="4"><result status="valid" time="0.02" steps="35"/></proof>
1165 1166 1167 1168 1169 1170
  </goal>
  <goal name="VC gauss_jordan.43" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC gauss_jordan.44" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
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Raphael Rieu-Helft committed
1171
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="8"/></proof>
1172 1173 1174
  </goal>
  <goal name="VC gauss_jordan.45" expl="assertion" proved="true">
  <transf name="split_vc" proved="true" >
1175
   <goal name="VC gauss_jordan.45.0" expl="assertion" proved="true">
1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191
   <proof prover="2"><result status="valid" time="0.04"/></proof>
   </goal>
   <goal name="VC gauss_jordan.45.1" expl="VC for gauss_jordan" proved="true">
   <transf name="revert" proved="true" arg1="H">
    <goal name="VC gauss_jordan.45.1.0" expl="VC for gauss_jordan" proved="true">
    <transf name="split_vc" proved="true" >
     <goal name="VC gauss_jordan.45.1.0.0" expl="VC for gauss_jordan" proved="true">
     <proof prover="2"><result status="valid" time="0.04"/></proof>
     </goal>
    </transf>
    </goal>
   </transf>
   </goal>
   <goal name="VC gauss_jordan.45.2" expl="VC for gauss_jordan" proved="true">
   <proof prover="2"><result status="valid" time="0.03"/></proof>
   </goal>
1192 1193 1194 1195 1196 1197
   <goal name="VC gauss_jordan.45.3" expl="VC for gauss_jordan" proved="true">
   <proof prover="1"><result status="valid" time="0.12"/></proof>
   </goal>
   <goal name="VC gauss_jordan.45.4" expl="VC for gauss_jordan" proved="true">
   <proof prover="1"><result status="valid" time="0.14"/></proof>
   </goal>
1198 1199 1200
  </transf>
  </goal>
  <goal name="VC gauss_jordan.46" expl="loop invariant preservation" proved="true">
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Raphael Rieu-Helft committed
1201
  <proof prover="4"><result status="valid" time="0.02" steps="24"/></proof>
1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220
  </goal>
  <goal name="VC gauss_jordan.47" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.14"/></proof>
  </goal>
  <goal name="VC gauss_jordan.48" expl="loop invariant preservation" proved="true">
  <transf name="introduce_premises" proved="true" >
   <goal name="VC gauss_jordan.48.0" expl="loop invariant preservation" proved="true">
   <proof prover="2"><result status="valid" time="0.02"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC gauss_jordan.49" expl="loop invariant preservation" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC gauss_jordan.50" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC gauss_jordan.51" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
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Raphael Rieu-Helft committed
1221
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="20"/></proof>
1222 1223 1224 1225 1226
  </goal>
  <goal name="VC gauss_jordan.52" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC gauss_jordan.53" expl="index in array bounds" proved="true">
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Raphael Rieu-Helft committed
1227
  <proof prover="4"><result status="valid" time="0.02" steps="27"/></proof>
1228 1229 1230 1231 1232
  </goal>
  <goal name="VC gauss_jordan.54" expl="index in array bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.08"/></proof>
  </goal>
  <goal name="VC gauss_jordan.55" expl="index in array bounds" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1233 1234
  <proof prover="2"><result status="valid" time="0.41"/></proof>
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="34"/></proof>
1235 1236 1237 1238 1239 1240
  </goal>
  <goal name="VC gauss_jordan.56" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC gauss_jordan.57" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
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Raphael Rieu-Helft committed
1241
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="21"/></proof>
1242 1243 1244
  </goal>
  <goal name="VC gauss_jordan.58" expl="out of loop bounds" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
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Raphael Rieu-Helft committed
1245
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="12"/></proof>
1246 1247 1248 1249
  </goal>
 </transf>
 </goal>
 <goal name="VC to_list" expl="VC for to_list" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1250
 <proof prover="2"><result status="valid" time="0.28"/></proof>
1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276
 </goal>
 <goal name="VC linear_decision" expl="VC for linear_decision" proved="true">
 <transf name="split_goal_right" proved="true" >
  <goal name="VC linear_decision.0" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC linear_decision.1" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC linear_decision.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC linear_decision.3" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC linear_decision.4" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC linear_decision.5" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC linear_decision.6" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC linear_decision.7" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.06"/></proof>
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Raphael Rieu-Helft committed
1277
  <proof prover="4" memlimit="2000"><result status="valid" time="0.01" steps="74"/></proof>
1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291
  </goal>
  <goal name="VC linear_decision.8" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC linear_decision.9" expl="integer overflow" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC linear_decision.10" expl="array creation size" proved="true">
  <proof prover="2"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="VC linear_decision.11" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC linear_decision.12" expl="integer overflow" proved="true">
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Raphael Rieu-Helft committed
1292
  <proof prover="4"><result status="valid" time="0.04" steps="159"/></proof>
1293 1294
  </goal>
  <goal name="VC linear_decision.13" expl="index in array bounds" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1295
  <proof prover="4"><result status="valid" time="0.02" steps="182"/></proof>
1296 1297
  </goal>
  <goal name="VC linear_decision.14" expl="index in array bounds" proved="true">
Raphael Rieu-Helft's avatar
Raphael Rieu-Helft committed
1298
  <proof prover="4"><result status="valid" time="0.02" steps="182"/></proof>
1299 1300 1301 1302 1303 1304 1305 1306 1307
  </goal>
  <goal name="VC linear_decision.15" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="VC linear_decision.16" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.36"/></proof>
  </goal>
  <goal name="VC linear_decision.17" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04"/></proof>
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Raphael Rieu-Helft committed
1308
  <proof prover="4"><result status="valid" time="0.01" steps="29"/></proof>
1309 1310
  </goal>
  <goal name="VC linear_decision.18" expl="precondition" proved="true">
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Raphael Rieu-Helft committed
1311
  <proof prover="4"><result status="valid" time="0.02" steps="70"/></proof>
1312 1313
  </goal>
  <goal name="VC linear_decision.19" expl="variant decrease" proved="true">
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Raphael Rieu-Helft committed
1314
  <proof prover="2"><result status="valid" time="0.39"/></proof>
1315 1316 1317
  </goal>
  <goal name="VC linear_decision.20" expl="precondition" proved="true">
  <proof prover="2"><result status="valid" time="0.04"/></proof>
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Raphael Rieu-Helft committed
1318
  <proof prover="4"><result status="valid" time="0.02" steps="29"/></proof>
1319 1320
  </goal>
  <goal name="VC linear_decision.21" expl="precondition" proved="true">
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Raphael Rieu-Helft committed
1321
  <proof prover="4"><result status="valid" time="0.02" steps="70"/></proof>
1322 1323 1324
  </goal>
  <goal name="VC linear_decision.22" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
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Raphael Rieu-Helft committed
1325
  <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
1326 1327 1328
  </goal>
  <goal name="VC linear_decision.23" exp