why3session.xml 132 KB
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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">
<why3session shape_version="4">
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<prover id="0" name="Alt-Ergo" version="1.30" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="1" name="CVC4" version="1.4" timelimit="1" steplimit="0" memlimit="1000"/>
<prover id="2" name="Z3" version="4.5.0" timelimit="1" steplimit="0" memlimit="1000"/>
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<prover id="3" name="Eprover" version="1.9.1-001" timelimit="10" steplimit="0" memlimit="2000"/>
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<file name="../lineardecision.mlw">
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<theory name="LinearEquationsCoeffs" proved="true" sum="488b407c1df82858497b5d843f9fa9de">
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 <goal name="VC czero" expl="VC for czero" proved="true">
 <proof prover="2"><result status="valid" time="0.02"/></proof>
 </goal>
 <goal name="VC cone" expl="VC for cone" proved="true">
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 <transf name="split_goal_wp" proved="true" >
 </transf>
 </goal>
</theory>
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<theory name="LinearEquationsDecision" proved="true" sum="72dd8642cd1bc02f1cd8dfc941d10a2d">
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 <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 valid_eq" expl="VC for valid_eq" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC eq_bound" expl="VC for eq_bound" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC valid_ctx" expl="VC for valid_ctx" proved="true">
 <proof prover="2"><result status="valid" time="0.01"/></proof>
 </goal>
 <goal name="VC ctx_bound" expl="VC for ctx_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_wp" 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="0" timelimit="5" 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="0"><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="0"><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="0"><result status="valid" time="0.00" steps="18"/></proof>
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 </goal>
 <goal name="VC ctx_bound_w" expl="VC for ctx_bound_w" proved="true">
 <transf name="split_goal_wp" 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="0"><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="0"><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_wp" proved="true" >
  <goal name="VC apply_r.0" expl="array creation size" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="6"/></proof>
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  </goal>
  <goal name="VC apply_r.1" expl="index in array bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="14"/></proof>
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  </goal>
  <goal name="VC apply_r.2" expl="index in matrix bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
  <goal name="VC apply_r.3" expl="index in array bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="14"/></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="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="14"/></proof>
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  </goal>
  <goal name="VC apply_r.5" expl="exceptional postcondition" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="4"/></proof>
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  </goal>
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  <goal name="VC apply_r.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
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  </goal>
  <goal name="VC apply_r.7" expl="postcondition" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="8"/></proof>
  </goal>
  <goal name="VC apply_r.8" expl="postcondition" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="7"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC apply_l" expl="VC for apply_l" proved="true">
 <transf name="split_goal_wp" proved="true" >
  <goal name="VC apply_l.0" expl="array creation size" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="6"/></proof>
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  </goal>
  <goal name="VC apply_l.1" expl="index in array bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="14"/></proof>
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  </goal>
  <goal name="VC apply_l.2" expl="index in matrix bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
  <goal name="VC apply_l.3" expl="index in array bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="14"/></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="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="14"/></proof>
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  </goal>
  <goal name="VC apply_l.5" expl="exceptional postcondition" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="4"/></proof>
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  </goal>
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  <goal name="VC apply_l.6" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
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  </goal>
  <goal name="VC apply_l.7" expl="postcondition" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="8"/></proof>
  </goal>
  <goal name="VC apply_l.8" expl="postcondition" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="7"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC sprod" expl="VC for sprod" proved="true">
 <transf name="split_goal_wp" proved="true" >
  <goal name="VC sprod.0" expl="index in array bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="8"/></proof>
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  </goal>
  <goal name="VC sprod.1" expl="index in array bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="8"/></proof>
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  </goal>
  <goal name="VC sprod.2" expl="exceptional postcondition" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="4"/></proof>
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  </goal>
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  <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>
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 </transf>
 </goal>
 <goal name="VC m_append" expl="VC for m_append" proved="true">
 <transf name="split_goal_wp" proved="true" >
  <goal name="VC m_append.0" expl="precondition" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="7"/></proof>
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  </goal>
  <goal name="VC m_append.1" expl="loop invariant init" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="8"/></proof>
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  </goal>
  <goal name="VC m_append.2" expl="loop invariant init" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="8"/></proof>
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  </goal>
  <goal name="VC m_append.3" expl="loop invariant init" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="19"/></proof>
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  </goal>
  <goal name="VC m_append.4" expl="loop invariant init" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="17"/></proof>
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  </goal>
  <goal name="VC m_append.5" expl="loop invariant init" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="13"/></proof>
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  </goal>
  <goal name="VC m_append.6" expl="index in matrix bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="18"/></proof>
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  </goal>
  <goal name="VC m_append.7" expl="index in matrix bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="18"/></proof>
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  </goal>
  <goal name="VC m_append.8" expl="loop invariant preservation" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="28"/></proof>
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  </goal>
  <goal name="VC m_append.9" expl="loop invariant preservation" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="25"/></proof>
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  </goal>
  <goal name="VC m_append.10" expl="loop invariant preservation" proved="true">
193
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="24"/></proof>
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  </goal>
  <goal name="VC m_append.11" expl="index in array bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="15"/></proof>
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  </goal>
  <goal name="VC m_append.12" expl="index in matrix bounds" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="16"/></proof>
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  </goal>
  <goal name="VC m_append.13" expl="loop invariant preservation" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="43"/></proof>
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  </goal>
  <goal name="VC m_append.14" expl="loop invariant preservation" proved="true">
205
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="23"/></proof>
206 207
  </goal>
  <goal name="VC m_append.15" expl="out of loop bounds" proved="true">
208
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="17"/></proof>
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  </goal>
  <goal name="VC m_append.16" expl="postcondition" proved="true">
211
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="10"/></proof>
212 213
  </goal>
  <goal name="VC m_append.17" expl="postcondition" proved="true">
214
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="11"/></proof>
215 216
  </goal>
  <goal name="VC m_append.18" expl="postcondition" proved="true">
217
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="17"/></proof>
218 219
  </goal>
  <goal name="VC m_append.19" expl="postcondition" proved="true">
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  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="16"/></proof>
221 222
  </goal>
  <goal name="VC m_append.20" expl="out of loop bounds" proved="true">
223
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="8"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC v_append" expl="VC for v_append" proved="true">
 <transf name="split_goal_wp" proved="true" >
  <goal name="VC v_append.0" expl="array creation size" proved="true">
230
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="5"/></proof>
231 232
  </goal>
  <goal name="VC v_append.1" expl="loop invariant init" proved="true">
233
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="6"/></proof>
234 235
  </goal>
  <goal name="VC v_append.2" expl="loop invariant init" proved="true">
236
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="8"/></proof>
237 238
  </goal>
  <goal name="VC v_append.3" expl="index in array bounds" proved="true">
239
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="10"/></proof>
240 241
  </goal>
  <goal name="VC v_append.4" expl="index in array bounds" proved="true">
242
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="10"/></proof>
243 244
  </goal>
  <goal name="VC v_append.5" expl="loop invariant preservation" proved="true">
245
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="31"/></proof>
246 247
  </goal>
  <goal name="VC v_append.6" expl="loop invariant preservation" proved="true">
248
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="25"/></proof>
249 250
  </goal>
  <goal name="VC v_append.7" expl="postcondition" proved="true">
251
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.01" steps="8"/></proof>
252 253
  </goal>
  <goal name="VC v_append.8" expl="postcondition" proved="true">
254
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="14"/></proof>
255 256
  </goal>
  <goal name="VC v_append.9" expl="postcondition" proved="true">
257
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="9"/></proof>
258 259
  </goal>
  <goal name="VC v_append.10" expl="out of loop bounds" proved="true">
260
  <proof prover="0" timelimit="5" memlimit="2000"><result status="valid" time="0.00" steps="8"/></proof>
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  </goal>
 </transf>
 </goal>
 <goal name="VC infix ==" expl="VC for infix ==" proved="true">
 <transf name="split_goal_wp" 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="loop invariant init" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC infix ==.2" expl="index in array bounds" 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="loop invariant preservation" proved="true">
279
  <proof prover="0"><result status="valid" time="0.01" steps="10"/></proof>
280 281
  </goal>
  <goal name="VC infix ==.5" expl="loop invariant preservation" proved="true">
282
  <proof prover="0"><result status="valid" time="0.02" steps="15"/></proof>
283 284 285 286 287 288
  </goal>
  <goal name="VC infix ==.6" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC infix ==.7" expl="postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
289 290 291 292
  </goal>
 </transf>
 </goal>
 <goal name="VC max_var" expl="VC for max_var" proved="true">
293
 <proof prover="0"><result status="valid" time="0.04" steps="199"/></proof>
294 295 296 297 298
 </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">
299
 <proof prover="0"><result status="valid" time="0.04" steps="146"/></proof>
300 301 302
 </goal>
 <goal name="VC opp_expr" expl="VC for opp_expr" proved="true">
 <transf name="split_goal_wp" proved="true" >
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  <goal name="VC opp_expr.0" expl="assertion" proved="true">
  <transf name="split_goal_wp" proved="true" >
   <goal name="VC opp_expr.0.0" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="7"/></proof>
   </goal>
   <goal name="VC opp_expr.0.1" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.01" steps="7"/></proof>
   </goal>
   <goal name="VC opp_expr.0.2" expl="assertion" proved="true">
312
   <proof prover="3"><result status="valid" time="2.46"/></proof>
313 314 315 316 317
   </goal>
   <goal name="VC opp_expr.0.3" expl="assertion" proved="true">
   <proof prover="0"><result status="valid" time="0.02" steps="7"/></proof>
   </goal>
  </transf>
318 319 320 321
  </goal>
  <goal name="VC opp_expr.1" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
322 323
  <goal name="VC opp_expr.2" expl="variant decrease" proved="true">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
324 325
  </goal>
  <goal name="VC opp_expr.3" expl="assertion" proved="true">
326 327 328
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="VC opp_expr.4" expl="assertion" proved="true">
329
  <transf name="split_goal_wp" proved="true" >
330
   <goal name="VC opp_expr.4.0" expl="assertion" proved="true">
331 332
   <proof prover="0"><result status="valid" time="0.01" steps="7"/></proof>
   </goal>
333
   <goal name="VC opp_expr.4.1" expl="assertion" proved="true">
334 335
   <proof prover="2"><result status="valid" time="0.02"/></proof>
   </goal>
336
   <goal name="VC opp_expr.4.2" expl="assertion" proved="true">
337 338
   <proof prover="2"><result status="valid" time="0.02"/></proof>
   </goal>
339
   <goal name="VC opp_expr.4.3" expl="assertion" proved="true">
340 341
   <proof prover="0"><result status="valid" time="0.02" steps="7"/></proof>
   </goal>
342
   <goal name="VC opp_expr.4.4" expl="VC for opp_expr" proved="true">
343 344 345 346
   <proof prover="2"><result status="valid" time="0.02"/></proof>
   </goal>
  </transf>
  </goal>
347
  <goal name="VC opp_expr.5" expl="postcondition" proved="true">
348
  <transf name="split_goal_wp" proved="true" >
349
   <goal name="VC opp_expr.5.0" expl="postcondition" proved="true">
350 351
   <proof prover="0"><result status="valid" time="0.01" steps="12"/></proof>
   </goal>
352
   <goal name="VC opp_expr.5.1" expl="postcondition" proved="true">
353
   <transf name="compute_in_goal" proved="true" >
354 355
    <goal name="VC opp_expr.5.1.0" expl="postcondition" proved="true">
    <proof prover="3"><result status="valid" time="0.07"/></proof>
356 357 358
    </goal>
   </transf>
   </goal>
359
   <goal name="VC opp_expr.5.2" expl="postcondition" proved="true">
360 361
   <proof prover="0"><result status="valid" time="0.02" steps="8"/></proof>
   </goal>
362 363
  </transf>
  </goal>
364
  <goal name="VC opp_expr.6" expl="postcondition" proved="true">
365 366 367 368
  <proof prover="0"><result status="valid" time="0.02" steps="113"/></proof>
  </goal>
  <goal name="VC opp_expr.7" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="83"/></proof>
369 370 371
  </goal>
 </transf>
 </goal>
372
 <goal name="VC norm_eq_aux" expl="VC for norm_eq_aux" proved="true">
373
 <transf name="split_goal_wp" proved="true" >
374
  <goal name="VC norm_eq_aux.0" expl="postcondition" proved="true">
375
  <proof prover="0"><result status="valid" time="0.01" steps="22"/></proof>
376
  </goal>
377
  <goal name="VC norm_eq_aux.1" expl="postcondition" proved="true">
378
  <proof prover="0"><result status="valid" time="0.01" steps="8"/></proof>
379
  </goal>
380
  <goal name="VC norm_eq_aux.2" expl="exceptional postcondition" proved="true">
381 382
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
383 384 385
  <goal name="VC norm_eq_aux.3" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="7"/></proof>
  </goal>
386
  <goal name="VC norm_eq_aux.4" expl="postcondition" proved="true">
387
  <proof prover="0"><result status="valid" time="0.02" steps="12"/></proof>
388
  </goal>
389
  <goal name="VC norm_eq_aux.5" expl="variant decrease" proved="true">
390
  <proof prover="2"><result status="valid" time="0.02"/></proof>
391
  </goal>
392
  <goal name="VC norm_eq_aux.6" expl="variant decrease" proved="true">
393
  <proof prover="2"><result status="valid" time="0.02"/></proof>
394
  </goal>
395
  <goal name="VC norm_eq_aux.7" expl="postcondition" proved="true">
396
  <proof prover="0"><result status="valid" time="0.02" steps="23"/></proof>
397
  </goal>
398
  <goal name="VC norm_eq_aux.8" expl="postcondition" proved="true">
399
  <proof prover="0"><result status="valid" time="0.02" steps="33"/></proof>
400
  </goal>
401
  <goal name="VC norm_eq_aux.9" expl="exceptional postcondition" proved="true">
402
  <proof prover="2"><result status="valid" time="0.01"/></proof>
403
  </goal>
404
  <goal name="VC norm_eq_aux.10" expl="exceptional postcondition" proved="true">
405
  <proof prover="2"><result status="valid" time="0.02"/></proof>
406
  </goal>
407 408 409 410 411
 </transf>
 </goal>
 <goal name="VC norm_eq" expl="VC for norm_eq" proved="true">
 <transf name="split_goal_wp" proved="true" >
  <goal name="VC norm_eq.0" expl="assertion" proved="true">
412
  <proof prover="0"><result status="valid" time="0.02" steps="27"/></proof>
413
  </goal>
414
  <goal name="VC norm_eq.1" expl="assertion" proved="true">
415 416
  <proof prover="3"><result status="valid" time="0.03"/></proof>
  </goal>
417
  <goal name="VC norm_eq.2" expl="assertion" proved="true">
418
  <transf name="split_goal_wp" proved="true" >
419
   <goal name="VC norm_eq.2.0" expl="assertion" proved="true">
420
   <proof prover="0"><result status="valid" time="0.02" steps="48"/></proof>
421
   </goal>
422
   <goal name="VC norm_eq.2.1" expl="VC for norm_eq" proved="true">
423
   <proof prover="0"><result status="valid" time="0.03" steps="24"/></proof>
424
   </goal>
425
   <goal name="VC norm_eq.2.2" expl="VC for norm_eq" proved="true">
426 427
   <proof prover="1"><result status="valid" time="0.05"/></proof>
   </goal>
428
   <goal name="VC norm_eq.2.3" expl="VC for norm_eq" proved="true">
429
   <proof prover="0"><result status="valid" time="0.02" steps="30"/></proof>
430
   </goal>
431
   <goal name="VC norm_eq.2.4" expl="VC for norm_eq" proved="true">
432
   <proof prover="0"><result status="valid" time="0.02" steps="17"/></proof>
433
   </goal>
434 435
   <goal name="VC norm_eq.2.5" expl="VC for norm_eq" proved="true">
   <proof prover="0"><result status="valid" time="0.02" steps="12"/></proof>
436 437
   </goal>
  </transf>
438
  </goal>
439
  <goal name="VC norm_eq.3" expl="postcondition" proved="true">
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440 441
  <transf name="split_goal_wp" proved="true" >
   <goal name="VC norm_eq.3.0" expl="postcondition" proved="true">
442
   <proof prover="0"><result status="valid" time="0.02" steps="18"/></proof>
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443 444
   </goal>
   <goal name="VC norm_eq.3.1" expl="postcondition" proved="true">
445
   <proof prover="3"><result status="valid" time="0.34"/></proof>
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446 447
   </goal>
  </transf>
448
  </goal>
449
  <goal name="VC norm_eq.4" expl="postcondition" proved="true">
450
  <proof prover="0"><result status="valid" time="0.02" steps="25"/></proof>
451
  </goal>
452
  <goal name="VC norm_eq.5" expl="exceptional postcondition" proved="true">
453
  <proof prover="2"><result status="valid" time="0.02"/></proof>
454 455 456
  </goal>
 </transf>
 </goal>
457 458 459 460 461 462 463 464 465
 <goal name="VC interp_ctx_impl" expl="VC for interp_ctx_impl" proved="true">
 <transf name="split_goal_wp" 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">
466
  <proof prover="3"><result status="valid" time="0.55"/></proof>
467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485
  </goal>
 </transf>
 </goal>
 <goal name="VC interp_ctx_valid" expl="VC for interp_ctx_valid" proved="true">
 <transf name="split_goal_wp" 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">
 <proof prover="0"><result status="valid" time="0.02" steps="108"/></proof>
 </goal>
 <goal name="VC interp_ctx_wl" expl="VC for interp_ctx_wl" proved="true">
 <proof prover="0"><result status="valid" time="0.02" steps="87"/></proof>
 </goal>
486 487
 <goal name="VC mul_expr" expl="VC for mul_expr" proved="true">
 <transf name="split_goal_wp" proved="true" >
488
  <goal name="VC mul_expr.0" expl="postcondition" proved="true">
489
  <proof prover="3"><result status="valid" time="0.07"/></proof>
490
  </goal>
491 492
  <goal name="VC mul_expr.1" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="8"/></proof>
493 494
  </goal>
  <goal name="VC mul_expr.2" expl="postcondition" proved="true">
495
  <proof prover="0"><result status="valid" time="0.01" steps="14"/></proof>
496 497
  </goal>
  <goal name="VC mul_expr.3" expl="postcondition" proved="true">
498
  <proof prover="0"><result status="valid" time="0.02" steps="9"/></proof>
499 500
  </goal>
  <goal name="VC mul_expr.4" expl="exceptional postcondition" proved="true">
501 502 503 504 505 506 507 508 509
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="VC mul_expr.5" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="16"/></proof>
  </goal>
  <goal name="VC mul_expr.6" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="VC mul_expr.7" expl="exceptional postcondition" proved="true">
510 511
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
512 513 514 515 516
  <goal name="VC mul_expr.8" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="32"/></proof>
  </goal>
  <goal name="VC mul_expr.9" expl="variant decrease" proved="true">
  <proof prover="0"><result status="valid" time="0.01" steps="35"/></proof>
517
  </goal>
518 519
  <goal name="VC mul_expr.10" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="18"/></proof>
520
  </goal>
521 522
  <goal name="VC mul_expr.11" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="48"/></proof>
523
  </goal>
524
  <goal name="VC mul_expr.12" expl="exceptional postcondition" proved="true">
525 526
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
527
  <goal name="VC mul_expr.13" expl="exceptional postcondition" proved="true">
528
  <proof prover="2"><result status="valid" time="0.01"/></proof>
529 530 531 532 533 534
  </goal>
 </transf>
 </goal>
 <goal name="VC add_expr" expl="VC for add_expr" proved="true">
 <transf name="split_goal_wp" proved="true" >
  <goal name="VC add_expr.0" expl="postcondition" proved="true">
535
  <proof prover="3"><result status="valid" time="0.32"/></proof>
536
  </goal>
537 538
  <goal name="VC add_expr.1" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.03" steps="15"/></proof>
539
  </goal>
540 541
  <goal name="VC add_expr.2" expl="exceptional postcondition" proved="true">
  <proof prover="2"><result status="valid" time="0.01"/></proof>
542 543
  </goal>
  <goal name="VC add_expr.3" expl="postcondition" proved="true">
544 545 546 547 548 549 550 551 552 553 554
  <transf name="split_goal_wp" proved="true" >
   <goal name="VC add_expr.3.0" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.32"/></proof>
   </goal>
   <goal name="VC add_expr.3.1" expl="postcondition" proved="true">
   <proof prover="3"><result status="valid" time="0.22"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC add_expr.4" expl="postcondition" proved="true">
  <proof prover="3"><result status="valid" time="0.22"/></proof>
555
  </goal>
556
  <goal name="VC add_expr.5" expl="variant decrease" proved="true">
557 558
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
559
  <goal name="VC add_expr.6" expl="precondition" proved="true">
560 561
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
562
  <goal name="VC add_expr.7" expl="assertion" proved="true">
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563
  <proof prover="0"><result status="valid" time="0.02" steps="53"/></proof>
564
  </goal>
565
  <goal name="VC add_expr.8" expl="postcondition" proved="true">
566
  <proof prover="0"><result status="valid" time="0.31" steps="221"/></proof>
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567
  </goal>
568
  <goal name="VC add_expr.9" expl="variant decrease" proved="true">
569 570
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
571
  <goal name="VC add_expr.10" expl="precondition" proved="true">
572 573
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
574
  <goal name="VC add_expr.11" expl="assertion" proved="true">
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575
  <proof prover="0"><result status="valid" time="0.02" steps="53"/></proof>
576
  </goal>
577
  <goal name="VC add_expr.12" expl="postcondition" proved="true">
578
  <proof prover="0"><result status="valid" time="0.57" steps="414"/></proof>
579
  </goal>
580
  <goal name="VC add_expr.13" expl="exceptional postcondition" proved="true">
581 582
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
583
  <goal name="VC add_expr.14" expl="exceptional postcondition" proved="true">
584 585
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
586
  <goal name="VC add_expr.15" expl="postcondition" proved="true">
587 588
  <proof prover="0"><result status="valid" time="0.02" steps="17"/></proof>
  </goal>
589
  <goal name="VC add_expr.16" expl="exceptional postcondition" proved="true">
590 591
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
592
  <goal name="VC add_expr.17" expl="postcondition" proved="true">
593
  <proof prover="3"><result status="valid" time="0.32"/></proof>
594
  </goal>
595
  <goal name="VC add_expr.18" expl="variant decrease" proved="true">
596 597
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
598
  <goal name="VC add_expr.19" expl="precondition" proved="true">
599 600
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
601 602 603 604 605 606 607
  <goal name="VC add_expr.20" expl="assertion" proved="true">
  <proof prover="0"><result status="valid" time="0.02" steps="50"/></proof>
  </goal>
  <goal name="VC add_expr.21" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.20" steps="209"/></proof>
  </goal>
  <goal name="VC add_expr.22" expl="variant decrease" proved="true">
608 609
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631
  <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">
  <proof prover="0"><result status="valid" time="0.02" steps="50"/></proof>
  </goal>
  <goal name="VC add_expr.25" expl="postcondition" proved="true">
  <proof prover="0"><result status="valid" time="0.35" steps="391"/></proof>
  </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">
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632
  <proof prover="0"><result status="valid" time="0.01" steps="16"/></proof>
633
  </goal>
634
  <goal name="VC add_expr.31" expl="postcondition" proved="true">
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635
  <transf name="split_goal_wp" proved="true" >
636
   <goal name="VC add_expr.31.0" expl="postcondition" proved="true">
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637
   <transf name="split_goal_wp" proved="true" >
638
    <goal name="VC add_expr.31.0.0" expl="postcondition" proved="true">
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639 640
    <proof prover="0"><result status="valid" time="0.02" steps="18"/></proof>
    </goal>
641
    <goal name="VC add_expr.31.0.1" expl="postcondition" proved="true">
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642 643 644 645
    <proof prover="0"><result status="valid" time="0.01" steps="19"/></proof>
    </goal>
   </transf>
   </goal>
646
   <goal name="VC add_expr.31.1" expl="postcondition" proved="true">
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647 648 649 650
   <proof prover="0"><result status="valid" time="0.03" steps="18"/></proof>
   </goal>
  </transf>
  </goal>
651
  <goal name="VC add_expr.32" expl="variant decrease" proved="true">
652 653
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
654
  <goal name="VC add_expr.33" expl="precondition" proved="true">
655 656
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
657
  <goal name="VC add_expr.34" expl="assertion" proved="true">
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658 659
  <proof prover="0"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
660
  <goal name="VC add_expr.35" expl="postcondition" proved="true">
661
  <proof prover="0"><result status="valid" time="0.03" steps="18"/></proof>
662
  </goal>
663
  <goal name="VC add_expr.36" expl="exceptional postcondition" proved="true">
664 665
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
666
  <goal name="VC add_expr.37" expl="exceptional postcondition" proved="true">
667 668
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
669
  <goal name="VC add_expr.38" expl="unreachable point" proved="true">
670 671
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
672
  <goal name="VC add_expr.39" expl="variant decrease" proved="true">
673 674
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
675
  <goal name="VC add_expr.40" expl="variant decrease" proved="true">
676 677
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
678
  <goal name="VC add_expr.41" expl="postcondition" proved="true">
679 680
  <proof prover="0"><result status="valid" time="0.02" steps="11"/></proof>
  </goal>
681
  <goal name="VC add_expr.42" expl="exceptional postcondition" proved="true">
682 683
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
684
  <goal name="VC add_expr.43" expl="exceptional postcondition" proved="true">
685 686
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
687
  <goal name="VC add_expr.44" expl="precondition" proved="true">
688 689
  <proof prover="2"><result status="valid" time="0.02"/></proof>
  </goal>
690
  <goal name="VC add_expr.45" expl="postcondition" proved="true">
691 692
  <proof prover="2"><result status="valid" time="0.03"/></proof>
  </goal>
693
  <goal name="VC add_expr.46" expl="exceptional postcondition" proved="true">
694 695
  <proof prover="2"><result status="valid" time="0.01"/></proof>
  </goal>
696 697 698
 </transf>
 </goal>
 <goal name="VC mul_eq" expl="VC for mul_eq" proved="true">
699
 <proof prover="0"><result status="valid" time="0.01" steps="17"/></proof>
700 701
 </goal>
 <goal name="VC add_eq" expl="VC for add_eq" proved="true">
702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721
 <transf name="split_goal_wp" 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="0.04"/></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>
722 723 724 725 726 727 728 729 730 731 732 733
 </goal>
 <goal name="VC zero_expr" expl="VC for zero_expr" proved="true">
 <transf name="split_goal_wp" 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_wp" proved="true" >
   <goal name="VC zero_expr.2.0" expl="postcondition" proved="true">
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734
   <proof prover="0"><result status="valid" time="0.02" steps="18"/></proof>
735 736
   </goal>
   <goal name="VC zero_expr.2.1" expl="postcondition" proved="true">
737
   <proof prover="3" timelimit="5"><result status="valid" time="0.26"/></proof>
738 739
   </goal>
   <goal name="VC zero_expr.2.2" expl="postcondition" proved="true">
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740 741 742 743 744 745 746 747
   <proof prover="0"><result status="valid" time="0.03" steps="23"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="VC zero_expr.3" expl="postcondition" proved="true">
  <transf name="split_goal_wp" proved="true" >
   <goal name="VC zero_expr.3.0" expl="postcondition" proved="true">
   <proof prover="1"><result status="valid" time="0.06"/></proof>
748 749 750
   </goal>
  </transf>
  </goal>
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Raphael Rieu-Helft committed
751