diff --git a/examples/WP_revisited/blocking_semantics5/why3session.xml b/examples/WP_revisited/blocking_semantics5/why3session.xml
index 34ce85c65eec0a724c0ed796545429c12d132578..fdb39f82cc1b73b0ca6391b398c63ddfd8d2a485 100644
--- a/examples/WP_revisited/blocking_semantics5/why3session.xml
+++ b/examples/WP_revisited/blocking_semantics5/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="0" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="1" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC3" version="2.4.1" timelimit="30" steplimit="0" memlimit="1000"/>
 <prover id="7" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="9" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -35,7 +35,7 @@
  <proof prover="12"><result status="valid" time="0.05"/></proof>
  </goal>
  <goal name="steps_non_neg" expl="">
- <proof prover="0" edited="blocking_semantics5_SemOp_steps_non_neg_1.v"><result status="valid" time="0.31"/></proof>
+ <proof prover="1" edited="blocking_semantics5_SemOp_steps_non_neg_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
 </theory>
 <theory name="TestSemantics" sum="86970d496f2db125feae52276a283ee6">
@@ -57,7 +57,7 @@
  <proof prover="9"><result status="valid" time="0.05" steps="107"/></proof>
  </goal>
  <goal name="If42" expl="">
- <proof prover="0" timelimit="6" edited="blocking_semantics5_TestSemantics_If42_1.v"><result status="valid" time="0.81"/></proof>
+ <proof prover="1" timelimit="6" edited="blocking_semantics5_TestSemantics_If42_1.v"><result status="valid" time="0.81"/></proof>
  </goal>
 </theory>
 <theory name="Typing" sum="d41d8cd98f00b204e9800998ecf8427e">
@@ -90,14 +90,14 @@
    <proof prover="9"><result status="valid" time="0.08" steps="143"/></proof>
    </goal>
    <goal name="eval_type_term.1.4" expl="">
-   <proof prover="0" edited="blocking_semantics5_TypingAndSemantics_eval_type_term_1.v"><result status="valid" time="1.50"/></proof>
+   <proof prover="1" edited="blocking_semantics5_TypingAndSemantics_eval_type_term_1.v"><result status="valid" time="1.50"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="type_preservation" expl="">
- <proof prover="0" edited="blocking_semantics5_TypingAndSemantics_type_preservation_1.v"><result status="valid" time="1.52"/></proof>
+ <proof prover="1" edited="blocking_semantics5_TypingAndSemantics_type_preservation_1.v"><result status="valid" time="1.52"/></proof>
  </goal>
 </theory>
 <theory name="FreshVariables" sum="e8d942e6e9d0add73d0d37a3267da968">
@@ -171,7 +171,7 @@
    <proof prover="9"><result status="valid" time="0.30" steps="655"/></proof>
    </goal>
    <goal name="eval_msubst.1.11" expl="">
-   <proof prover="0" edited="blocking_semantics5_FreshVariables_eval_msubst_2.v"><result status="valid" time="0.80"/></proof>
+   <proof prover="1" edited="blocking_semantics5_FreshVariables_eval_msubst_2.v"><result status="valid" time="0.80"/></proof>
    </goal>
    <goal name="eval_msubst.1.12" expl="">
    <proof prover="9"><result status="valid" time="0.30" steps="561"/></proof>
@@ -189,7 +189,7 @@
    <proof prover="9"><result status="valid" time="0.04" steps="12"/></proof>
    </goal>
    <goal name="eval_swap_term.1.2" expl="">
-   <proof prover="0" edited="blocking_semantics5_FreshVariables_eval_swap_term_1.v"><result status="valid" time="0.93"/></proof>
+   <proof prover="1" edited="blocking_semantics5_FreshVariables_eval_swap_term_1.v"><result status="valid" time="0.93"/></proof>
    </goal>
    <goal name="eval_swap_term.1.3" expl="">
    <proof prover="3"><result status="valid" time="0.05"/></proof>
@@ -256,7 +256,7 @@
  </transf>
  </goal>
  <goal name="eval_swap" expl="">
- <proof prover="0" memlimit="4000" edited="blocking_semantics5_FreshVariables_eval_swap_3.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="1" memlimit="4000" edited="blocking_semantics5_FreshVariables_eval_swap_3.v"><result status="valid" time="0.33"/></proof>
  </goal>
  <goal name="eval_term_change_free" expl="">
  <transf name="induction_ty_lex">
@@ -327,7 +327,7 @@
    <proof prover="9"><result status="valid" time="0.07" steps="89"/></proof>
    </goal>
    <goal name="eval_change_free.1.11" expl="">
-   <proof prover="0" edited="blocking_semantics5_FreshVariables_eval_change_free_4.v"><result status="valid" time="1.30"/></proof>
+   <proof prover="1" edited="blocking_semantics5_FreshVariables_eval_change_free_4.v"><result status="valid" time="1.30"/></proof>
    </goal>
    <goal name="eval_change_free.1.12" expl="">
    <proof prover="9"><result status="valid" time="0.18" steps="280"/></proof>
@@ -339,32 +339,32 @@
 </theory>
 <theory name="HoareLogic" sum="23cedd132ddce3b408fd64127096ec7a">
  <goal name="many_steps_seq" expl="">
- <proof prover="0" edited="blocking_semantics5_HoareLogic_many_steps_seq_1.v"><result status="valid" time="0.92"/></proof>
+ <proof prover="1" edited="blocking_semantics5_HoareLogic_many_steps_seq_1.v"><result status="valid" time="0.92"/></proof>
  </goal>
  <goal name="consequence_rule" expl="">
  <proof prover="3"><result status="valid" time="0.24"/></proof>
  </goal>
  <goal name="skip_rule" expl="">
- <proof prover="0" edited="blocking_semantics5_HoareLogic_skip_rule_1.v"><result status="valid" time="0.43"/></proof>
+ <proof prover="1" edited="blocking_semantics5_HoareLogic_skip_rule_1.v"><result status="valid" time="0.43"/></proof>
  </goal>
  <goal name="assign_rule" expl="">
- <proof prover="0" timelimit="12" edited="blocking_semantics5_HoareLogic_assign_rule_1.v"><result status="valid" time="1.12"/></proof>
+ <proof prover="1" timelimit="12" edited="blocking_semantics5_HoareLogic_assign_rule_1.v"><result status="valid" time="1.12"/></proof>
  </goal>
  <goal name="seq_rule" expl="">
  <proof prover="7"><result status="valid" time="0.09"/></proof>
  <proof prover="12"><result status="valid" time="0.06"/></proof>
  </goal>
  <goal name="if_rule" expl="">
- <proof prover="0" edited="blocking_semantics5_HoareLogic_if_rule_1.v"><result status="valid" time="0.94"/></proof>
+ <proof prover="1" edited="blocking_semantics5_HoareLogic_if_rule_1.v"><result status="valid" time="0.94"/></proof>
  </goal>
  <goal name="assert_rule" expl="">
- <proof prover="0" edited="blocking_semantics5_HoareLogic_assert_rule_1.v"><result status="valid" time="0.46"/></proof>
+ <proof prover="1" edited="blocking_semantics5_HoareLogic_assert_rule_1.v"><result status="valid" time="0.46"/></proof>
  </goal>
  <goal name="assert_rule_ext" expl="">
- <proof prover="0" edited="blocking_semantics5_HoareLogic_assert_rule_ext_1.v"><result status="valid" time="0.38"/></proof>
+ <proof prover="1" edited="blocking_semantics5_HoareLogic_assert_rule_ext_1.v"><result status="valid" time="0.38"/></proof>
  </goal>
  <goal name="while_rule" expl="">
- <proof prover="0" edited="blocking_semantics5_HoareLogic_while_rule_1.v"><result status="valid" time="0.46"/></proof>
+ <proof prover="1" edited="blocking_semantics5_HoareLogic_while_rule_1.v"><result status="valid" time="0.46"/></proof>
  </goal>
 </theory>
 <theory name="WP" sum="5cc3a5597ba7d5d9898b25547d8addba">
@@ -379,7 +379,7 @@
    <proof prover="12"><result status="valid" time="0.10"/></proof>
    </goal>
    <goal name="monotonicity.1.2" expl="">
-   <proof prover="0" timelimit="30" edited="blocking_semantics5_WP_monotonicity_1.v"><result status="valid" time="0.80"/></proof>
+   <proof prover="1" timelimit="30" edited="blocking_semantics5_WP_monotonicity_1.v"><result status="valid" time="0.80"/></proof>
    </goal>
    <goal name="monotonicity.1.3" expl="">
    <proof prover="3" timelimit="5"><result status="valid" time="0.14"/></proof>
@@ -392,7 +392,7 @@
    <proof prover="3" timelimit="5"><result status="valid" time="0.09"/></proof>
    </goal>
    <goal name="monotonicity.1.6" expl="">
-   <proof prover="0" edited="blocking_semantics5_WP_monotonicity_3.v"><result status="valid" time="0.40"/></proof>
+   <proof prover="1" edited="blocking_semantics5_WP_monotonicity_3.v"><result status="valid" time="0.40"/></proof>
    </goal>
   </transf>
   </goal>
@@ -410,7 +410,7 @@
    <proof prover="9"><result status="valid" time="0.55" steps="1402"/></proof>
    </goal>
    <goal name="distrib_conj.1.3" expl="">
-   <proof prover="0" edited="blocking_semantics5_WP_distrib_conj_2.v"><result status="valid" time="0.95"/></proof>
+   <proof prover="1" edited="blocking_semantics5_WP_distrib_conj_2.v"><result status="valid" time="0.95"/></proof>
    </goal>
    <goal name="distrib_conj.1.4" expl="">
    <proof prover="9"><result status="valid" time="0.34" steps="959"/></proof>
@@ -421,14 +421,14 @@
    <proof prover="9"><result status="valid" time="0.14" steps="333"/></proof>
    </goal>
    <goal name="distrib_conj.1.6" expl="">
-   <proof prover="0" edited="blocking_semantics5_WP_distrib_conj_3.v"><result status="valid" time="0.63"/></proof>
+   <proof prover="1" edited="blocking_semantics5_WP_distrib_conj_3.v"><result status="valid" time="0.63"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="wp_preserved_by_reduction" expl="">
- <proof prover="0" memlimit="4000" edited="blocking_semantics5_WP_wp_preserved_by_reduction_4.v"><result status="valid" time="1.76"/></proof>
+ <proof prover="1" memlimit="4000" edited="blocking_semantics5_WP_wp_preserved_by_reduction_4.v"><result status="valid" time="1.76"/></proof>
  </goal>
  <goal name="progress" expl="">
  <transf name="induction_ty_lex">
@@ -441,27 +441,27 @@
    <proof prover="12"><result status="valid" time="0.00"/></proof>
    </goal>
    <goal name="progress.1.2" expl="">
-   <proof prover="0" edited="blocking_semantics5_WP_progress_1.v"><result status="valid" time="0.39"/></proof>
+   <proof prover="1" edited="blocking_semantics5_WP_progress_1.v"><result status="valid" time="0.39"/></proof>
    </goal>
    <goal name="progress.1.3" expl="">
-   <proof prover="0" edited="blocking_semantics5_WP_progress_2.v"><result status="valid" time="0.83"/></proof>
+   <proof prover="1" edited="blocking_semantics5_WP_progress_2.v"><result status="valid" time="0.83"/></proof>
    </goal>
    <goal name="progress.1.4" expl="">
-   <proof prover="0" edited="blocking_semantics5_WP_progress_3.v"><result status="valid" time="0.35"/></proof>
+   <proof prover="1" edited="blocking_semantics5_WP_progress_3.v"><result status="valid" time="0.35"/></proof>
    </goal>
    <goal name="progress.1.5" expl="">
    <proof prover="3" timelimit="5"><result status="valid" time="0.45"/></proof>
    <proof prover="11"><result status="valid" time="0.20"/></proof>
    </goal>
    <goal name="progress.1.6" expl="">
-   <proof prover="0" edited="blocking_semantics5_WP_progress_5.v"><result status="valid" time="0.39"/></proof>
+   <proof prover="1" edited="blocking_semantics5_WP_progress_5.v"><result status="valid" time="0.39"/></proof>
    </goal>
   </transf>
   </goal>
  </transf>
  </goal>
  <goal name="wp_soundness" expl="">
- <proof prover="0" timelimit="30" edited="blocking_semantics5_WP_wp_soundness_1.v"><result status="valid" time="0.44"/></proof>
+ <proof prover="1" timelimit="30" edited="blocking_semantics5_WP_wp_soundness_1.v"><result status="valid" time="0.44"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/WP_revisited/imp_n/why3session.xml b/examples/WP_revisited/imp_n/why3session.xml
index 13107566d22cd8da55368e601bdef187d1f92def..db9f05dfd83453ebf36d50923ea58fed6a8a0383 100644
--- a/examples/WP_revisited/imp_n/why3session.xml
+++ b/examples/WP_revisited/imp_n/why3session.xml
@@ -2,8 +2,8 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="3" steplimit="0" memlimit="0"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="3" steplimit="0" memlimit="0"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="3" steplimit="0" memlimit="0"/>
 <prover id="5" name="Z3" version="3.2" timelimit="3" steplimit="0" memlimit="0"/>
 <prover id="6" name="Alt-Ergo" version="0.99.1" timelimit="3" steplimit="0" memlimit="0"/>
 <prover id="7" name="Z3" version="4.3.2" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -33,34 +33,34 @@
  <proof prover="7"><result status="valid" time="0.08"/></proof>
  </goal>
  <goal name="progress" expl="">
- <proof prover="2" edited="imp_n_Imp_progress_1.v"><result status="valid" time="0.31"/></proof>
+ <proof prover="0" edited="imp_n_Imp_progress_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
  <goal name="steps_non_neg" expl="">
- <proof prover="2" edited="imp_n_Imp_steps_non_neg_1.v"><result status="valid" time="0.30"/></proof>
+ <proof prover="0" edited="imp_n_Imp_steps_non_neg_1.v"><result status="valid" time="0.30"/></proof>
  </goal>
  <goal name="many_steps_seq" expl="">
- <proof prover="2" edited="imp_n_Imp_many_steps_seq_1.v"><result status="valid" time="0.36"/></proof>
+ <proof prover="0" edited="imp_n_Imp_many_steps_seq_1.v"><result status="valid" time="0.36"/></proof>
  </goal>
  <goal name="eval_subst_expr" expl="">
- <proof prover="2" edited="imp_n_Imp_eval_subst_expr_1.v"><result status="valid" time="0.34"/></proof>
+ <proof prover="0" edited="imp_n_Imp_eval_subst_expr_1.v"><result status="valid" time="0.34"/></proof>
  </goal>
  <goal name="eval_subst" expl="">
- <proof prover="2" edited="imp_n_Imp_eval_subst_1.v"><result status="valid" time="0.35"/></proof>
+ <proof prover="0" edited="imp_n_Imp_eval_subst_1.v"><result status="valid" time="0.35"/></proof>
  </goal>
  <goal name="skip_rule" expl="">
  <proof prover="6"><result status="valid" time="0.04" steps="113"/></proof>
  </goal>
  <goal name="assign_rule" expl="">
- <proof prover="2" edited="imp_n_Imp_assign_rule_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="0" edited="imp_n_Imp_assign_rule_1.v"><result status="valid" time="0.33"/></proof>
  </goal>
  <goal name="seq_rule" expl="">
- <proof prover="2" edited="imp_n_Imp_seq_rule_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="0" edited="imp_n_Imp_seq_rule_1.v"><result status="valid" time="0.33"/></proof>
  </goal>
  <goal name="if_rule" expl="">
- <proof prover="2" edited="imp_n_Imp_if_rule_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="0" edited="imp_n_Imp_if_rule_1.v"><result status="valid" time="0.33"/></proof>
  </goal>
  <goal name="while_rule" expl="">
- <proof prover="2" edited="imp_n_Imp_while_rule_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="0" edited="imp_n_Imp_while_rule_1.v"><result status="valid" time="0.33"/></proof>
  </goal>
  <goal name="consequence_rule" expl="">
  <proof prover="1"><result status="valid" time="0.05"/></proof>
diff --git a/examples/WP_revisited/wp2/why3session.xml b/examples/WP_revisited/wp2/why3session.xml
index f6a7f0fcfe2560cd583a5749bdee49654c79fdd2..3c64e3445cb3bb3d43a641056354d2a39f57212b 100644
--- a/examples/WP_revisited/wp2/why3session.xml
+++ b/examples/WP_revisited/wp2/why3session.xml
@@ -2,26 +2,26 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="3" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="3" steplimit="0" memlimit="0"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="5" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="7" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="4000"/>
 <file name="../wp2.mlw" expanded="true">
 <theory name="Imp" sum="4d6ec4c3ea3a39365f84600c953b8179">
  <goal name="eval_subst_term" expl="">
- <proof prover="1" timelimit="5" edited="wp2_Imp_eval_subst_term_1.v"><result status="valid" time="0.30"/></proof>
+ <proof prover="0" timelimit="5" edited="wp2_Imp_eval_subst_term_1.v"><result status="valid" time="0.30"/></proof>
  </goal>
  <goal name="eval_term_change_free" expl="">
- <proof prover="1" timelimit="5" edited="wp2_Imp_eval_term_change_free_1.v"><result status="valid" time="0.31"/></proof>
+ <proof prover="0" timelimit="5" edited="wp2_Imp_eval_term_change_free_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
  <goal name="eval_subst" expl="">
- <proof prover="1" timelimit="5" edited="wp2_Imp_eval_subst_1.v"><result status="valid" time="0.37"/></proof>
+ <proof prover="0" timelimit="5" edited="wp2_Imp_eval_subst_1.v"><result status="valid" time="0.37"/></proof>
  </goal>
  <goal name="eval_swap" expl="">
  <proof prover="2" timelimit="3"><result status="valid" time="0.02"/></proof>
  </goal>
  <goal name="eval_change_free" expl="">
- <proof prover="1" timelimit="5" edited="wp2_Imp_eval_change_free_1.v"><result status="valid" time="0.34"/></proof>
+ <proof prover="0" timelimit="5" edited="wp2_Imp_eval_change_free_1.v"><result status="valid" time="0.34"/></proof>
  </goal>
  <goal name="check_skip" expl="">
  <proof prover="2"><result status="valid" time="0.02"/></proof>
@@ -29,10 +29,10 @@
  <proof prover="7" memlimit="0"><result status="valid" time="0.01" steps="1"/></proof>
  </goal>
  <goal name="steps_non_neg" expl="">
- <proof prover="1" edited="wp2_Imp_steps_non_neg_1.v"><result status="valid" time="0.36"/></proof>
+ <proof prover="0" edited="wp2_Imp_steps_non_neg_1.v"><result status="valid" time="0.36"/></proof>
  </goal>
  <goal name="many_steps_seq" expl="">
- <proof prover="1" edited="wp2_Imp_many_steps_seq_1.v"><result status="valid" time="0.41"/></proof>
+ <proof prover="0" edited="wp2_Imp_many_steps_seq_1.v"><result status="valid" time="0.41"/></proof>
  </goal>
 </theory>
 <theory name="TestSemantics" sum="ea9fb18b1935c25df0ce7f228aabf76f">
@@ -49,14 +49,14 @@
  <proof prover="7" memlimit="1000"><result status="valid" time="0.02" steps="12"/></proof>
  </goal>
  <goal name="Test55" expl="">
- <proof prover="1" timelimit="5" memlimit="1000" edited="wp2_TestSemantics_Test55_1.v"><result status="valid" time="0.31"/></proof>
+ <proof prover="0" timelimit="5" memlimit="1000" edited="wp2_TestSemantics_Test55_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
  <goal name="Ass42" expl="">
  <proof prover="2" memlimit="1000"><result status="valid" time="0.04"/></proof>
  <proof prover="7" memlimit="1000"><result status="valid" time="0.06" steps="100"/></proof>
  </goal>
  <goal name="If42" expl="">
- <proof prover="1" timelimit="5" memlimit="1000" edited="wp2_TestSemantics_If42_1.v"><result status="valid" time="1.00"/></proof>
+ <proof prover="0" timelimit="5" memlimit="1000" edited="wp2_TestSemantics_If42_1.v"><result status="valid" time="1.00"/></proof>
  </goal>
 </theory>
 <theory name="HoareLogic" sum="ac7395abbc54f2eaf2a4731bbadf3a7c">
@@ -64,28 +64,28 @@
  <proof prover="2" memlimit="1000"><result status="valid" time="0.32"/></proof>
  </goal>
  <goal name="skip_rule" expl="">
- <proof prover="1" edited="wp2_HoareLogic_skip_rule_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="0" edited="wp2_HoareLogic_skip_rule_1.v"><result status="valid" time="0.33"/></proof>
  </goal>
  <goal name="assign_rule" expl="">
- <proof prover="1" edited="wp2_HoareLogic_assign_rule_1.v"><result status="valid" time="0.40"/></proof>
+ <proof prover="0" edited="wp2_HoareLogic_assign_rule_1.v"><result status="valid" time="0.40"/></proof>
  </goal>
  <goal name="seq_rule" expl="">
  <proof prover="5" timelimit="3"><result status="valid" time="0.07"/></proof>
  </goal>
  <goal name="if_rule" expl="">
- <proof prover="1" edited="wp2_HoareLogic_if_rule_1.v"><result status="valid" time="0.48"/></proof>
+ <proof prover="0" edited="wp2_HoareLogic_if_rule_1.v"><result status="valid" time="0.48"/></proof>
  </goal>
  <goal name="assert_rule" expl="">
- <proof prover="1" edited="wp2_HoareLogic_assert_rule_1.v"><result status="valid" time="0.40"/></proof>
+ <proof prover="0" edited="wp2_HoareLogic_assert_rule_1.v"><result status="valid" time="0.40"/></proof>
  </goal>
  <goal name="assert_rule_ext" expl="">
- <proof prover="1" edited="wp2_HoareLogic_assert_rule_ext_1.v"><result status="valid" time="0.40"/></proof>
+ <proof prover="0" edited="wp2_HoareLogic_assert_rule_ext_1.v"><result status="valid" time="0.40"/></proof>
  </goal>
  <goal name="while_rule" expl="">
- <proof prover="1" edited="wp2_HoareLogic_while_rule_1.v"><result status="valid" time="0.52"/></proof>
+ <proof prover="0" edited="wp2_HoareLogic_while_rule_1.v"><result status="valid" time="0.52"/></proof>
  </goal>
  <goal name="while_rule_ext" expl="">
- <proof prover="1" edited="wp2_HoareLogic_while_rule_ext_1.v"><result status="valid" time="0.54"/></proof>
+ <proof prover="0" edited="wp2_HoareLogic_while_rule_ext_1.v"><result status="valid" time="0.54"/></proof>
  </goal>
 </theory>
 <theory name="WP" sum="ac7e95b3f1136de0ba1a9054f4091dbf">
@@ -107,7 +107,7 @@
   <proof prover="7" timelimit="3" memlimit="0"><result status="valid" time="0.06" steps="94"/></proof>
   </goal>
   <goal name="WP_parameter compute_writes.2" expl="postcondition">
-  <proof prover="1" edited="wp2_WP_WP_WP_parameter_compute_writes_1.v"><result status="valid" time="0.38"/></proof>
+  <proof prover="0" edited="wp2_WP_WP_WP_parameter_compute_writes_1.v"><result status="valid" time="0.38"/></proof>
   </goal>
   <goal name="WP_parameter compute_writes.3" expl="variant decrease">
   <proof prover="7"><result status="valid" time="0.04" steps="42"/></proof>
@@ -125,16 +125,16 @@
   <proof prover="7"><result status="valid" time="0.04" steps="48"/></proof>
   </goal>
   <goal name="WP_parameter compute_writes.8" expl="postcondition">
-  <proof prover="1" edited="wp2_WP_WP_WP_parameter_compute_writes_3.v"><result status="valid" time="0.30"/></proof>
+  <proof prover="0" edited="wp2_WP_WP_WP_parameter_compute_writes_3.v"><result status="valid" time="0.46"/></proof>
   </goal>
   <goal name="WP_parameter compute_writes.9" expl="variant decrease">
   <proof prover="7"><result status="valid" time="0.04" steps="47"/></proof>
   </goal>
   <goal name="WP_parameter compute_writes.10" expl="postcondition">
-  <proof prover="1" edited="wp2_WP_WP_WP_parameter_compute_writes_4.v"><result status="valid" time="0.33"/></proof>
+  <proof prover="0" edited="wp2_WP_WP_WP_parameter_compute_writes_4.v"><result status="valid" time="0.33"/></proof>
   </goal>
   <goal name="WP_parameter compute_writes.11" expl="postcondition">
-  <proof prover="1" edited="wp2_WP_WP_WP_parameter_compute_writes_2.v"><result status="valid" time="0.34"/></proof>
+  <proof prover="0" edited="wp2_WP_WP_WP_parameter_compute_writes_2.v"><result status="valid" time="0.34"/></proof>
   </goal>
  </transf>
  </goal>
@@ -168,7 +168,7 @@
   <proof prover="7"><result status="valid" time="0.04" steps="49"/></proof>
   </goal>
   <goal name="WP_parameter wp.8" expl="postcondition">
-  <proof prover="1" edited="wp2_WP_WP_WP_parameter_wp_1.v"><result status="valid" time="0.32"/></proof>
+  <proof prover="0" edited="wp2_WP_WP_WP_parameter_wp_1.v"><result status="valid" time="0.32"/></proof>
   </goal>
   <goal name="WP_parameter wp.9" expl="postcondition">
   <proof prover="2" timelimit="3"><result status="valid" time="0.04"/></proof>
@@ -179,7 +179,7 @@
   <proof prover="7"><result status="valid" time="0.04" steps="47"/></proof>
   </goal>
   <goal name="WP_parameter wp.11" expl="postcondition">
-  <proof prover="1" timelimit="5" edited="wp2_WP_WP_WP_parameter_wp_2.v"><result status="valid" time="0.87"/></proof>
+  <proof prover="0" timelimit="5" edited="wp2_WP_WP_WP_parameter_wp_2.v"><result status="valid" time="0.87"/></proof>
   </goal>
  </transf>
  </goal>
diff --git a/examples/bellman_ford/why3session.xml b/examples/bellman_ford/why3session.xml
index 7bd6c96a91efb8124a03f2bc50653b18e829e2fb..379c96a1e8063bc073ab41b34bc1d87fb64e75f9 100644
--- a/examples/bellman_ford/why3session.xml
+++ b/examples/bellman_ford/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="15" steplimit="0" memlimit="0"/>
 <prover id="4" name="Spass" version="3.7" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Z3" version="3.2" timelimit="15" steplimit="0" memlimit="0"/>
@@ -17,30 +17,30 @@
  <proof prover="8" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="5"/></proof>
  </goal>
  <goal name="path_in_vertices" expl="">
- <proof prover="1" timelimit="10" memlimit="0" edited="bf_Graph_path_in_vertices_2.v"><result status="valid" time="0.35"/></proof>
+ <proof prover="0" timelimit="10" memlimit="0" edited="bf_Graph_path_in_vertices_2.v"><result status="valid" time="0.35"/></proof>
  </goal>
  <goal name="long_path_decomposition_pigeon1" expl="">
- <proof prover="1" timelimit="8" edited="bellman_ford_Graph_long_path_decomposition_pigeon1_1.v"><result status="valid" time="0.72"/></proof>
+ <proof prover="0" timelimit="8" edited="bellman_ford_Graph_long_path_decomposition_pigeon1_1.v"><result status="valid" time="0.90"/></proof>
  </goal>
  <goal name="long_path_decomposition_pigeon2" expl="">
  <proof prover="8"><result status="valid" time="0.06" steps="42"/></proof>
  </goal>
  <goal name="long_path_decomposition_pigeon3" expl="">
- <proof prover="1" timelimit="7" edited="bellman_ford_Graph_long_path_decomposition_pigeon3_1.v"><result status="valid" time="1.07"/></proof>
+ <proof prover="0" timelimit="7" edited="bellman_ford_Graph_long_path_decomposition_pigeon3_1.v"><result status="valid" time="1.07"/></proof>
  </goal>
  <goal name="long_path_decomposition" expl="">
- <proof prover="1" edited="bellman_ford_Graph_long_path_decomposition_1.v"><result status="valid" time="0.86"/></proof>
+ <proof prover="0" edited="bellman_ford_Graph_long_path_decomposition_1.v"><result status="valid" time="0.86"/></proof>
  </goal>
  <goal name="simple_path" expl="">
- <proof prover="1" timelimit="10" memlimit="0" edited="bf_Graph_simple_path_1.v"><result status="valid" time="1.23"/></proof>
+ <proof prover="0" timelimit="10" memlimit="0" edited="bf_Graph_simple_path_1.v"><result status="valid" time="1.23"/></proof>
  </goal>
  <goal name="key_lemma_1" expl="">
- <proof prover="1" timelimit="10" memlimit="0" edited="bf_Graph_key_lemma_1_1.v"><result status="valid" time="1.69"/></proof>
+ <proof prover="0" timelimit="10" memlimit="0" edited="bf_Graph_key_lemma_1_1.v"><result status="valid" time="1.69"/></proof>
  </goal>
 </theory>
 <theory name="BellmanFord" sum="540e790f09b5437cdfcd7396da7c836f" expanded="true">
  <goal name="key_lemma_2" expl="">
- <proof prover="1" memlimit="4000" edited="bf_WP_BellmanFord_key_lemma_2_1.v"><result status="valid" time="3.34"/></proof>
+ <proof prover="0" memlimit="4000" edited="bf_WP_BellmanFord_key_lemma_2_1.v"><result status="valid" time="2.76"/></proof>
  </goal>
  <goal name="WP_parameter relax" expl="VC for relax">
  <transf name="split_goal_wp">
@@ -49,7 +49,7 @@
    <goal name="WP_parameter relax.1.1" expl="postcondition">
    <transf name="split_goal_wp">
     <goal name="WP_parameter relax.1.1.1" expl="postcondition">
-    <proof prover="1" timelimit="10" memlimit="0" edited="bf_WP_BellmanFord_WP_parameter_relax_7.v"><result status="valid" time="1.00"/></proof>
+    <proof prover="0" timelimit="10" memlimit="0" edited="bf_WP_BellmanFord_WP_parameter_relax_7.v"><result status="valid" time="1.00"/></proof>
     </goal>
     <goal name="WP_parameter relax.1.1.2" expl="postcondition">
     <proof prover="2"><result status="valid" time="0.22"/></proof>
@@ -130,7 +130,7 @@
   <proof prover="8" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="12"/></proof>
   </goal>
   <goal name="WP_parameter bellman_ford.4" expl="exceptional postcondition">
-  <proof prover="1" edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_20.v"><result status="valid" time="1.25"/></proof>
+  <proof prover="0" edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_20.v"><result status="valid" time="1.25"/></proof>
   </goal>
   <goal name="WP_parameter bellman_ford.5" expl="loop invariant preservation">
   <proof prover="8"><result status="valid" time="0.96" steps="676"/></proof>
@@ -238,23 +238,23 @@
        <ip_library name="Unit"/>
        <ip_qualid name="unit"/>
       </ts_pos>
-      <ts_pos name="&apos;mark" arity="0" id="68"
+      <ts_pos name="&#39;mark" arity="0" id="68"
        ip_theory="Mark">
        <ip_library name="why3"/>
        <ip_library name="Mark"/>
-       <ip_qualid name="&apos;mark"/>
+       <ip_qualid name="&#39;mark"/>
       </ts_pos>
-      <ts_pos name="ref" arity="1" id="5105"
+      <ts_pos name="ref" arity="1" id="5118"
        ip_theory="Ref">
        <ip_library name="ref"/>
        <ip_qualid name="ref"/>
       </ts_pos>
-      <ts_pos name="t" arity="1" id="5255"
+      <ts_pos name="t" arity="1" id="5268"
        ip_theory="Impset">
        <ip_library name="impset"/>
        <ip_qualid name="t"/>
       </ts_pos>
-      <ts_pos name="distmap" arity="0" id="5347"
+      <ts_pos name="distmap" arity="0" id="5360"
        ip_theory="BellmanFord">
        <ip_qualid name="distmap"/>
       </ts_pos>
@@ -299,154 +299,154 @@
        <ip_library name="int"/>
        <ip_qualid name="infix *"/>
       </ls_pos>
-      <ls_pos name="add" id="2369"
+      <ls_pos name="add" id="2382"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="add"/>
       </ls_pos>
-      <ls_pos name="lt" id="2388"
+      <ls_pos name="lt" id="2401"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="lt"/>
       </ls_pos>
-      <ls_pos name="le" id="2407"
+      <ls_pos name="le" id="2420"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="le"/>
       </ls_pos>
-      <ls_pos name="mem" id="2492"
+      <ls_pos name="mem" id="2505"
        ip_theory="Mem">
        <ip_library name="list"/>
        <ip_qualid name="mem"/>
       </ls_pos>
-      <ls_pos name="mem" id="2819"
+      <ls_pos name="mem" id="2832"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="mem"/>
       </ls_pos>
-      <ls_pos name="infix ==" id="2822"
+      <ls_pos name="infix ==" id="2835"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="infix =="/>
       </ls_pos>
-      <ls_pos name="subset" id="2840"
+      <ls_pos name="subset" id="2853"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset"/>
       </ls_pos>
-      <ls_pos name="empty" id="2861"
+      <ls_pos name="empty" id="2874"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="empty"/>
       </ls_pos>
-      <ls_pos name="is_empty" id="2863"
+      <ls_pos name="is_empty" id="2876"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="is_empty"/>
       </ls_pos>
-      <ls_pos name="add" id="2873"
+      <ls_pos name="add" id="2886"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="add"/>
       </ls_pos>
-      <ls_pos name="singleton" id="2879"
+      <ls_pos name="singleton" id="2892"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="singleton"/>
       </ls_pos>
-      <ls_pos name="remove" id="2884"
+      <ls_pos name="remove" id="2897"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="remove"/>
       </ls_pos>
-      <ls_pos name="union" id="2902"
+      <ls_pos name="union" id="2915"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="union"/>
       </ls_pos>
-      <ls_pos name="inter" id="2909"
+      <ls_pos name="inter" id="2922"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="inter"/>
       </ls_pos>
-      <ls_pos name="diff" id="2916"
+      <ls_pos name="diff" id="2929"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="diff"/>
       </ls_pos>
-      <ls_pos name="choose" id="2928"
+      <ls_pos name="choose" id="2941"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="choose"/>
       </ls_pos>
-      <ls_pos name="cardinal" id="2932"
+      <ls_pos name="cardinal" id="2945"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal"/>
       </ls_pos>
-      <ls_pos name="get" id="3142"
+      <ls_pos name="get" id="3155"
        ip_theory="Map">
        <ip_library name="map"/>
        <ip_qualid name="get"/>
       </ls_pos>
-      <ls_pos name="set" id="3145"
+      <ls_pos name="set" id="3158"
        ip_theory="Map">
        <ip_library name="map"/>
        <ip_qualid name="set"/>
       </ls_pos>
-      <ls_pos name="mixfix [&lt;-]" id="3165"
+      <ls_pos name="mixfix [&lt;-]" id="3178"
        ip_theory="Map">
        <ip_library name="map"/>
        <ip_qualid name="mixfix [&lt;-]"/>
       </ls_pos>
-      <ls_pos name="const" id="3197"
+      <ls_pos name="const" id="3210"
        ip_theory="Const">
        <ip_library name="map"/>
        <ip_qualid name="const"/>
       </ls_pos>
-      <ls_pos name="infix ++" id="3865"
+      <ls_pos name="infix ++" id="3878"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="infix ++"/>
       </ls_pos>
-      <ls_pos name="vertices" id="4535"
+      <ls_pos name="vertices" id="4548"
        ip_theory="Graph">
        <ip_qualid name="vertices"/>
       </ls_pos>
-      <ls_pos name="edges" id="4536"
+      <ls_pos name="edges" id="4549"
        ip_theory="Graph">
        <ip_qualid name="edges"/>
       </ls_pos>
-      <ls_pos name="s" id="4551" ip_theory="Graph">
+      <ls_pos name="s" id="4564" ip_theory="Graph">
        <ip_qualid name="s"/>
       </ls_pos>
-      <ls_pos name="weight" id="4805"
+      <ls_pos name="weight" id="4818"
        ip_theory="Graph">
        <ip_qualid name="weight"/>
       </ls_pos>
-      <ls_pos name="pigeon_set" id="4942"
+      <ls_pos name="pigeon_set" id="4955"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="pigeon_set"/>
       </ls_pos>
-      <ls_pos name="negative_cycle" id="5080"
+      <ls_pos name="negative_cycle" id="5093"
        ip_theory="Graph">
        <ip_qualid name="negative_cycle"/>
       </ls_pos>
-      <ls_pos name="prefix !" id="5111"
+      <ls_pos name="prefix !" id="5124"
        ip_theory="Ref">
        <ip_library name="ref"/>
        <ip_qualid name="prefix !"/>
       </ls_pos>
-      <ls_pos name="initialize_single_source" id="5348"
+      <ls_pos name="initialize_single_source" id="5361"
        ip_theory="BellmanFord">
        <ip_qualid name="initialize_single_source"/>
       </ls_pos>
-      <ls_pos name="inv1" id="5354"
+      <ls_pos name="inv1" id="5367"
        ip_theory="BellmanFord">
        <ip_qualid name="inv1"/>
       </ls_pos>
-      <ls_pos name="inv2" id="5410"
+      <ls_pos name="inv2" id="5423"
        ip_theory="BellmanFord">
        <ip_qualid name="inv2"/>
       </ls_pos>
@@ -554,271 +554,271 @@
        <ip_library name="int"/>
        <ip_qualid name="CompatOrderMult"/>
       </pr_pos>
-      <pr_pos name="Refl" id="2416"
+      <pr_pos name="Refl" id="2429"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="Refl"/>
       </pr_pos>
-      <pr_pos name="Trans" id="2419"
+      <pr_pos name="Trans" id="2432"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="Trans"/>
       </pr_pos>
-      <pr_pos name="Antisymm" id="2426"
+      <pr_pos name="Antisymm" id="2439"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="Antisymm"/>
       </pr_pos>
-      <pr_pos name="Total" id="2431"
+      <pr_pos name="Total" id="2444"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="Total"/>
       </pr_pos>
-      <pr_pos name="Length_nonnegative" id="2485"
+      <pr_pos name="Length_nonnegative" id="2498"
        ip_theory="Length">
        <ip_library name="list"/>
        <ip_qualid name="Length_nonnegative"/>
       </pr_pos>
-      <pr_pos name="Length_nil" id="2488"
+      <pr_pos name="Length_nil" id="2501"
        ip_theory="Length">
        <ip_library name="list"/>
        <ip_qualid name="Length_nil"/>
       </pr_pos>
-      <pr_pos name="extensionality" id="2833"
+      <pr_pos name="extensionality" id="2846"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="extensionality"/>
       </pr_pos>
-      <pr_pos name="subset_refl" id="2851"
+      <pr_pos name="subset_refl" id="2864"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset_refl"/>
       </pr_pos>
-      <pr_pos name="subset_trans" id="2854"
+      <pr_pos name="subset_trans" id="2867"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset_trans"/>
       </pr_pos>
-      <pr_pos name="empty_def1" id="2870"
+      <pr_pos name="empty_def1" id="2883"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="empty_def1"/>
       </pr_pos>
-      <pr_pos name="mem_empty" id="2871"
+      <pr_pos name="mem_empty" id="2884"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="mem_empty"/>
       </pr_pos>
-      <pr_pos name="add_remove" id="2890"
+      <pr_pos name="add_remove" id="2903"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="add_remove"/>
       </pr_pos>
-      <pr_pos name="remove_add" id="2894"
+      <pr_pos name="remove_add" id="2907"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="remove_add"/>
       </pr_pos>
-      <pr_pos name="subset_remove" id="2898"
+      <pr_pos name="subset_remove" id="2911"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset_remove"/>
       </pr_pos>
-      <pr_pos name="union_def1" id="2903"
+      <pr_pos name="union_def1" id="2916"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="union_def1"/>
       </pr_pos>
-      <pr_pos name="inter_def1" id="2910"
+      <pr_pos name="inter_def1" id="2923"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="inter_def1"/>
       </pr_pos>
-      <pr_pos name="subset_diff" id="2923"
+      <pr_pos name="subset_diff" id="2936"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset_diff"/>
       </pr_pos>
-      <pr_pos name="choose_def" id="2929"
+      <pr_pos name="choose_def" id="2942"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="choose_def"/>
       </pr_pos>
-      <pr_pos name="cardinal_nonneg" id="2934"
+      <pr_pos name="cardinal_nonneg" id="2947"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal_nonneg"/>
       </pr_pos>
-      <pr_pos name="cardinal_empty" id="2937"
+      <pr_pos name="cardinal_empty" id="2950"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal_empty"/>
       </pr_pos>
-      <pr_pos name="cardinal_add" id="2940"
+      <pr_pos name="cardinal_add" id="2953"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal_add"/>
       </pr_pos>
-      <pr_pos name="cardinal_remove" id="2945"
+      <pr_pos name="cardinal_remove" id="2958"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal_remove"/>
       </pr_pos>
-      <pr_pos name="cardinal_subset" id="2950"
+      <pr_pos name="cardinal_subset" id="2963"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal_subset"/>
       </pr_pos>
-      <pr_pos name="subset_eq" id="2955"
+      <pr_pos name="subset_eq" id="2968"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset_eq"/>
       </pr_pos>
-      <pr_pos name="cardinal1" id="2960"
+      <pr_pos name="cardinal1" id="2973"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal1"/>
       </pr_pos>
-      <pr_pos name="Select_eq" id="3178"
+      <pr_pos name="Select_eq" id="3191"
        ip_theory="Map">
        <ip_library name="map"/>
        <ip_qualid name="Select_eq"/>
       </pr_pos>
-      <pr_pos name="Select_neq" id="3187"
+      <pr_pos name="Select_neq" id="3200"
        ip_theory="Map">
        <ip_library name="map"/>
        <ip_qualid name="Select_neq"/>
       </pr_pos>
-      <pr_pos name="Const" id="3199"
+      <pr_pos name="Const" id="3212"
        ip_theory="Const">
        <ip_library name="map"/>
        <ip_qualid name="Const"/>
       </pr_pos>
-      <pr_pos name="Append_assoc" id="3882"
+      <pr_pos name="Append_assoc" id="3895"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="Append_assoc"/>
       </pr_pos>
-      <pr_pos name="Append_l_nil" id="3889"
+      <pr_pos name="Append_l_nil" id="3902"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="Append_l_nil"/>
       </pr_pos>
-      <pr_pos name="Append_length" id="3892"
+      <pr_pos name="Append_length" id="3905"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="Append_length"/>
       </pr_pos>
-      <pr_pos name="mem_append" id="3897"
+      <pr_pos name="mem_append" id="3910"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="mem_append"/>
       </pr_pos>
-      <pr_pos name="mem_decomp" id="3904"
+      <pr_pos name="mem_decomp" id="3917"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="mem_decomp"/>
       </pr_pos>
-      <pr_pos name="edges_def" id="4546"
+      <pr_pos name="edges_def" id="4559"
        ip_theory="Graph">
        <ip_qualid name="edges_def"/>
       </pr_pos>
-      <pr_pos name="s_in_graph" id="4552"
+      <pr_pos name="s_in_graph" id="4565"
        ip_theory="Graph">
        <ip_qualid name="s_in_graph"/>
       </pr_pos>
-      <pr_pos name="vertices_cardinal_pos" id="4553"
+      <pr_pos name="vertices_cardinal_pos" id="4566"
        ip_theory="Graph">
        <ip_qualid name="vertices_cardinal_pos"/>
       </pr_pos>
-      <pr_pos name="path_right_extension" id="4758"
+      <pr_pos name="path_right_extension" id="4771"
        ip_theory="Graph">
        <ip_qualid name="path_right_extension"/>
       </pr_pos>
-      <pr_pos name="path_right_inversion" id="4767"
+      <pr_pos name="path_right_inversion" id="4780"
        ip_theory="Graph">
        <ip_qualid name="path_right_inversion"/>
       </pr_pos>
-      <pr_pos name="path_trans" id="4778"
+      <pr_pos name="path_trans" id="4791"
        ip_theory="Graph">
        <ip_qualid name="path_trans"/>
       </pr_pos>
-      <pr_pos name="empty_path" id="4789"
+      <pr_pos name="empty_path" id="4802"
        ip_theory="Graph">
        <ip_qualid name="empty_path"/>
       </pr_pos>
-      <pr_pos name="path_decomposition" id="4794"
+      <pr_pos name="path_decomposition" id="4807"
        ip_theory="Graph">
        <ip_qualid name="path_decomposition"/>
       </pr_pos>
-      <pr_pos name="path_weight_right_extension" id="4837"
+      <pr_pos name="path_weight_right_extension" id="4850"
        ip_theory="Graph">
        <ip_qualid name="path_weight_right_extension"/>
       </pr_pos>
-      <pr_pos name="path_weight_decomposition" id="4844"
+      <pr_pos name="path_weight_decomposition" id="4857"
        ip_theory="Graph">
        <ip_qualid name="path_weight_decomposition"/>
       </pr_pos>
-      <pr_pos name="path_in_vertices" id="4853"
+      <pr_pos name="path_in_vertices" id="4866"
        ip_theory="Graph">
        <ip_qualid name="path_in_vertices"/>
       </pr_pos>
-      <pr_pos name="Induction" id="4959"
+      <pr_pos name="Induction" id="4972"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="FsetInduction"/>
        <ip_qualid name="Induction"/>
       </pr_pos>
-      <pr_pos name="corner" id="4968"
+      <pr_pos name="corner" id="4981"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="corner"/>
       </pr_pos>
-      <pr_pos name="pigeon_0" id="4985"
+      <pr_pos name="pigeon_0" id="4998"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="pigeon_0"/>
       </pr_pos>
-      <pr_pos name="pigeon_1" id="4986"
+      <pr_pos name="pigeon_1" id="4999"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="pigeon_1"/>
       </pr_pos>
-      <pr_pos name="pigeon_2" id="4991"
+      <pr_pos name="pigeon_2" id="5004"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="pigeon_2"/>
       </pr_pos>
-      <pr_pos name="pigeonhole" id="4994"
+      <pr_pos name="pigeonhole" id="5007"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="pigeonhole"/>
       </pr_pos>
-      <pr_pos name="long_path_decomposition_pigeon1" id="5009"
+      <pr_pos name="long_path_decomposition_pigeon1" id="5022"
        ip_theory="Graph">
        <ip_qualid name="long_path_decomposition_pigeon1"/>
       </pr_pos>
-      <pr_pos name="long_path_decomposition_pigeon2" id="5016"
+      <pr_pos name="long_path_decomposition_pigeon2" id="5029"
        ip_theory="Graph">
        <ip_qualid name="long_path_decomposition_pigeon2"/>
       </pr_pos>
-      <pr_pos name="long_path_decomposition_pigeon3" id="5031"
+      <pr_pos name="long_path_decomposition_pigeon3" id="5044"
        ip_theory="Graph">
        <ip_qualid name="long_path_decomposition_pigeon3"/>
       </pr_pos>
-      <pr_pos name="long_path_decomposition" id="5056"
+      <pr_pos name="long_path_decomposition" id="5069"
        ip_theory="Graph">
        <ip_qualid name="long_path_decomposition"/>
       </pr_pos>
-      <pr_pos name="simple_path" id="5073"
+      <pr_pos name="simple_path" id="5086"
        ip_theory="Graph">
        <ip_qualid name="simple_path"/>
       </pr_pos>
-      <pr_pos name="key_lemma_1" id="5091"
+      <pr_pos name="key_lemma_1" id="5104"
        ip_theory="Graph">
        <ip_qualid name="key_lemma_1"/>
       </pr_pos>
-      <pr_pos name="key_lemma_2" id="5429"
+      <pr_pos name="key_lemma_2" id="5442"
        ip_theory="BellmanFord">
        <ip_qualid name="key_lemma_2"/>
       </pr_pos>
@@ -847,100 +847,100 @@
        <meta_arg_ls id="1621"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2369"/>
+       <meta_arg_ls id="2382"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2388"/>
+       <meta_arg_ls id="2401"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2407"/>
+       <meta_arg_ls id="2420"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2492"/>
+       <meta_arg_ls id="2505"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2819"/>
+       <meta_arg_ls id="2832"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2822"/>
+       <meta_arg_ls id="2835"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2840"/>
+       <meta_arg_ls id="2853"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2861"/>
+       <meta_arg_ls id="2874"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2863"/>
+       <meta_arg_ls id="2876"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2873"/>
+       <meta_arg_ls id="2886"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2879"/>
+       <meta_arg_ls id="2892"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2884"/>
+       <meta_arg_ls id="2897"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2902"/>
+       <meta_arg_ls id="2915"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2909"/>
+       <meta_arg_ls id="2922"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2916"/>
+       <meta_arg_ls id="2929"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2928"/>
+       <meta_arg_ls id="2941"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2932"/>
+       <meta_arg_ls id="2945"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3142"/>
+       <meta_arg_ls id="3155"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3145"/>
+       <meta_arg_ls id="3158"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3165"/>
+       <meta_arg_ls id="3178"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3197"/>
+       <meta_arg_ls id="3210"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3865"/>
+       <meta_arg_ls id="3878"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4535"/>
+       <meta_arg_ls id="4548"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4536"/>
+       <meta_arg_ls id="4549"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4551"/>
+       <meta_arg_ls id="4564"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4805"/>
+       <meta_arg_ls id="4818"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4942"/>
+       <meta_arg_ls id="4955"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5080"/>
+       <meta_arg_ls id="5093"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5111"/>
+       <meta_arg_ls id="5124"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5348"/>
+       <meta_arg_ls id="5361"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5354"/>
+       <meta_arg_ls id="5367"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5410"/>
+       <meta_arg_ls id="5423"/>
       </meta>
       <meta name="remove_prop">
        <meta_arg_pr id="1622"/>
@@ -1000,175 +1000,175 @@
        <meta_arg_pr id="1726"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2416"/>
+       <meta_arg_pr id="2429"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2419"/>
+       <meta_arg_pr id="2432"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2426"/>
+       <meta_arg_pr id="2439"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2431"/>
+       <meta_arg_pr id="2444"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2485"/>
+       <meta_arg_pr id="2498"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2488"/>
+       <meta_arg_pr id="2501"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2833"/>
+       <meta_arg_pr id="2846"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2851"/>
+       <meta_arg_pr id="2864"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2854"/>
+       <meta_arg_pr id="2867"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2870"/>
+       <meta_arg_pr id="2883"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2871"/>
+       <meta_arg_pr id="2884"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2890"/>
+       <meta_arg_pr id="2903"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2894"/>
+       <meta_arg_pr id="2907"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2898"/>
+       <meta_arg_pr id="2911"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2903"/>
+       <meta_arg_pr id="2916"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2910"/>
+       <meta_arg_pr id="2923"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2923"/>
+       <meta_arg_pr id="2936"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2929"/>
+       <meta_arg_pr id="2942"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2934"/>
+       <meta_arg_pr id="2947"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2937"/>
+       <meta_arg_pr id="2950"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2940"/>
+       <meta_arg_pr id="2953"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2945"/>
+       <meta_arg_pr id="2958"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2950"/>
+       <meta_arg_pr id="2963"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2955"/>
+       <meta_arg_pr id="2968"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2960"/>
+       <meta_arg_pr id="2973"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3178"/>
+       <meta_arg_pr id="3191"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3187"/>
+       <meta_arg_pr id="3200"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3199"/>
+       <meta_arg_pr id="3212"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3882"/>
+       <meta_arg_pr id="3895"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3889"/>
+       <meta_arg_pr id="3902"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3892"/>
+       <meta_arg_pr id="3905"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3897"/>
+       <meta_arg_pr id="3910"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3904"/>
+       <meta_arg_pr id="3917"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4546"/>
+       <meta_arg_pr id="4559"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4552"/>
+       <meta_arg_pr id="4565"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4553"/>
+       <meta_arg_pr id="4566"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4758"/>
+       <meta_arg_pr id="4771"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4767"/>
+       <meta_arg_pr id="4780"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4778"/>
+       <meta_arg_pr id="4791"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4789"/>
+       <meta_arg_pr id="4802"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4794"/>
+       <meta_arg_pr id="4807"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4837"/>
+       <meta_arg_pr id="4850"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4844"/>
+       <meta_arg_pr id="4857"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4853"/>
+       <meta_arg_pr id="4866"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4959"/>
+       <meta_arg_pr id="4972"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4968"/>
+       <meta_arg_pr id="4981"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4985"/>
+       <meta_arg_pr id="4998"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4986"/>
+       <meta_arg_pr id="4999"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4991"/>
+       <meta_arg_pr id="5004"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4994"/>
+       <meta_arg_pr id="5007"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5009"/>
+       <meta_arg_pr id="5022"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5016"/>
+       <meta_arg_pr id="5029"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5031"/>
+       <meta_arg_pr id="5044"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5056"/>
+       <meta_arg_pr id="5069"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5073"/>
+       <meta_arg_pr id="5086"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5091"/>
+       <meta_arg_pr id="5104"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5429"/>
+       <meta_arg_pr id="5442"/>
       </meta>
       <meta name="remove_type">
        <meta_arg_ts id="2"/>
@@ -1183,13 +1183,13 @@
        <meta_arg_ts id="68"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5105"/>
+       <meta_arg_ts id="5118"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5255"/>
+       <meta_arg_ts id="5268"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5347"/>
+       <meta_arg_ts id="5360"/>
       </meta>
       <goal name="WP_parameter bellman_ford.14.2.1.3" expl="VC for bellman_ford">
       <transf name="eliminate_builtin">
@@ -1228,23 +1228,23 @@
        <ip_library name="Unit"/>
        <ip_qualid name="unit"/>
       </ts_pos>
-      <ts_pos name="&apos;mark" arity="0" id="68"
+      <ts_pos name="&#39;mark" arity="0" id="68"
        ip_theory="Mark">
        <ip_library name="why3"/>
        <ip_library name="Mark"/>
-       <ip_qualid name="&apos;mark"/>
+       <ip_qualid name="&#39;mark"/>
       </ts_pos>
-      <ts_pos name="ref" arity="1" id="5105"
+      <ts_pos name="ref" arity="1" id="5118"
        ip_theory="Ref">
        <ip_library name="ref"/>
        <ip_qualid name="ref"/>
       </ts_pos>
-      <ts_pos name="t" arity="1" id="5255"
+      <ts_pos name="t" arity="1" id="5268"
        ip_theory="Impset">
        <ip_library name="impset"/>
        <ip_qualid name="t"/>
       </ts_pos>
-      <ts_pos name="distmap" arity="0" id="5347"
+      <ts_pos name="distmap" arity="0" id="5360"
        ip_theory="BellmanFord">
        <ip_qualid name="distmap"/>
       </ts_pos>
@@ -1289,154 +1289,154 @@
        <ip_library name="int"/>
        <ip_qualid name="infix *"/>
       </ls_pos>
-      <ls_pos name="add" id="2369"
+      <ls_pos name="add" id="2382"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="add"/>
       </ls_pos>
-      <ls_pos name="lt" id="2388"
+      <ls_pos name="lt" id="2401"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="lt"/>
       </ls_pos>
-      <ls_pos name="le" id="2407"
+      <ls_pos name="le" id="2420"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="le"/>
       </ls_pos>
-      <ls_pos name="mem" id="2492"
+      <ls_pos name="mem" id="2505"
        ip_theory="Mem">
        <ip_library name="list"/>
        <ip_qualid name="mem"/>
       </ls_pos>
-      <ls_pos name="mem" id="2819"
+      <ls_pos name="mem" id="2832"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="mem"/>
       </ls_pos>
-      <ls_pos name="infix ==" id="2822"
+      <ls_pos name="infix ==" id="2835"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="infix =="/>
       </ls_pos>
-      <ls_pos name="subset" id="2840"
+      <ls_pos name="subset" id="2853"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset"/>
       </ls_pos>
-      <ls_pos name="empty" id="2861"
+      <ls_pos name="empty" id="2874"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="empty"/>
       </ls_pos>
-      <ls_pos name="is_empty" id="2863"
+      <ls_pos name="is_empty" id="2876"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="is_empty"/>
       </ls_pos>
-      <ls_pos name="add" id="2873"
+      <ls_pos name="add" id="2886"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="add"/>
       </ls_pos>
-      <ls_pos name="singleton" id="2879"
+      <ls_pos name="singleton" id="2892"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="singleton"/>
       </ls_pos>
-      <ls_pos name="remove" id="2884"
+      <ls_pos name="remove" id="2897"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="remove"/>
       </ls_pos>
-      <ls_pos name="union" id="2902"
+      <ls_pos name="union" id="2915"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="union"/>
       </ls_pos>
-      <ls_pos name="inter" id="2909"
+      <ls_pos name="inter" id="2922"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="inter"/>
       </ls_pos>
-      <ls_pos name="diff" id="2916"
+      <ls_pos name="diff" id="2929"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="diff"/>
       </ls_pos>
-      <ls_pos name="choose" id="2928"
+      <ls_pos name="choose" id="2941"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="choose"/>
       </ls_pos>
-      <ls_pos name="cardinal" id="2932"
+      <ls_pos name="cardinal" id="2945"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal"/>
       </ls_pos>
-      <ls_pos name="get" id="3142"
+      <ls_pos name="get" id="3155"
        ip_theory="Map">
        <ip_library name="map"/>
        <ip_qualid name="get"/>
       </ls_pos>
-      <ls_pos name="set" id="3145"
+      <ls_pos name="set" id="3158"
        ip_theory="Map">
        <ip_library name="map"/>
        <ip_qualid name="set"/>
       </ls_pos>
-      <ls_pos name="mixfix [&lt;-]" id="3165"
+      <ls_pos name="mixfix [&lt;-]" id="3178"
        ip_theory="Map">
        <ip_library name="map"/>
        <ip_qualid name="mixfix [&lt;-]"/>
       </ls_pos>
-      <ls_pos name="const" id="3197"
+      <ls_pos name="const" id="3210"
        ip_theory="Const">
        <ip_library name="map"/>
        <ip_qualid name="const"/>
       </ls_pos>
-      <ls_pos name="infix ++" id="3865"
+      <ls_pos name="infix ++" id="3878"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="infix ++"/>
       </ls_pos>
-      <ls_pos name="vertices" id="4535"
+      <ls_pos name="vertices" id="4548"
        ip_theory="Graph">
        <ip_qualid name="vertices"/>
       </ls_pos>
-      <ls_pos name="edges" id="4536"
+      <ls_pos name="edges" id="4549"
        ip_theory="Graph">
        <ip_qualid name="edges"/>
       </ls_pos>
-      <ls_pos name="s" id="4551" ip_theory="Graph">
+      <ls_pos name="s" id="4564" ip_theory="Graph">
        <ip_qualid name="s"/>
       </ls_pos>
-      <ls_pos name="weight" id="4805"
+      <ls_pos name="weight" id="4818"
        ip_theory="Graph">
        <ip_qualid name="weight"/>
       </ls_pos>
-      <ls_pos name="pigeon_set" id="4942"
+      <ls_pos name="pigeon_set" id="4955"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="pigeon_set"/>
       </ls_pos>
-      <ls_pos name="negative_cycle" id="5080"
+      <ls_pos name="negative_cycle" id="5093"
        ip_theory="Graph">
        <ip_qualid name="negative_cycle"/>
       </ls_pos>
-      <ls_pos name="prefix !" id="5111"
+      <ls_pos name="prefix !" id="5124"
        ip_theory="Ref">
        <ip_library name="ref"/>
        <ip_qualid name="prefix !"/>
       </ls_pos>
-      <ls_pos name="initialize_single_source" id="5348"
+      <ls_pos name="initialize_single_source" id="5361"
        ip_theory="BellmanFord">
        <ip_qualid name="initialize_single_source"/>
       </ls_pos>
-      <ls_pos name="inv1" id="5354"
+      <ls_pos name="inv1" id="5367"
        ip_theory="BellmanFord">
        <ip_qualid name="inv1"/>
       </ls_pos>
-      <ls_pos name="inv2" id="5410"
+      <ls_pos name="inv2" id="5423"
        ip_theory="BellmanFord">
        <ip_qualid name="inv2"/>
       </ls_pos>
@@ -1544,271 +1544,271 @@
        <ip_library name="int"/>
        <ip_qualid name="CompatOrderMult"/>
       </pr_pos>
-      <pr_pos name="Refl" id="2416"
+      <pr_pos name="Refl" id="2429"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="Refl"/>
       </pr_pos>
-      <pr_pos name="Trans" id="2419"
+      <pr_pos name="Trans" id="2432"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="Trans"/>
       </pr_pos>
-      <pr_pos name="Antisymm" id="2426"
+      <pr_pos name="Antisymm" id="2439"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="Antisymm"/>
       </pr_pos>
-      <pr_pos name="Total" id="2431"
+      <pr_pos name="Total" id="2444"
        ip_theory="IntInf">
        <ip_library name="int"/>
        <ip_qualid name="Total"/>
       </pr_pos>
-      <pr_pos name="Length_nonnegative" id="2485"
+      <pr_pos name="Length_nonnegative" id="2498"
        ip_theory="Length">
        <ip_library name="list"/>
        <ip_qualid name="Length_nonnegative"/>
       </pr_pos>
-      <pr_pos name="Length_nil" id="2488"
+      <pr_pos name="Length_nil" id="2501"
        ip_theory="Length">
        <ip_library name="list"/>
        <ip_qualid name="Length_nil"/>
       </pr_pos>
-      <pr_pos name="extensionality" id="2833"
+      <pr_pos name="extensionality" id="2846"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="extensionality"/>
       </pr_pos>
-      <pr_pos name="subset_refl" id="2851"
+      <pr_pos name="subset_refl" id="2864"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset_refl"/>
       </pr_pos>
-      <pr_pos name="subset_trans" id="2854"
+      <pr_pos name="subset_trans" id="2867"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset_trans"/>
       </pr_pos>
-      <pr_pos name="empty_def1" id="2870"
+      <pr_pos name="empty_def1" id="2883"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="empty_def1"/>
       </pr_pos>
-      <pr_pos name="mem_empty" id="2871"
+      <pr_pos name="mem_empty" id="2884"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="mem_empty"/>
       </pr_pos>
-      <pr_pos name="add_remove" id="2890"
+      <pr_pos name="add_remove" id="2903"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="add_remove"/>
       </pr_pos>
-      <pr_pos name="remove_add" id="2894"
+      <pr_pos name="remove_add" id="2907"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="remove_add"/>
       </pr_pos>
-      <pr_pos name="subset_remove" id="2898"
+      <pr_pos name="subset_remove" id="2911"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset_remove"/>
       </pr_pos>
-      <pr_pos name="union_def1" id="2903"
+      <pr_pos name="union_def1" id="2916"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="union_def1"/>
       </pr_pos>
-      <pr_pos name="inter_def1" id="2910"
+      <pr_pos name="inter_def1" id="2923"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="inter_def1"/>
       </pr_pos>
-      <pr_pos name="subset_diff" id="2923"
+      <pr_pos name="subset_diff" id="2936"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset_diff"/>
       </pr_pos>
-      <pr_pos name="choose_def" id="2929"
+      <pr_pos name="choose_def" id="2942"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="choose_def"/>
       </pr_pos>
-      <pr_pos name="cardinal_nonneg" id="2934"
+      <pr_pos name="cardinal_nonneg" id="2947"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal_nonneg"/>
       </pr_pos>
-      <pr_pos name="cardinal_empty" id="2937"
+      <pr_pos name="cardinal_empty" id="2950"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal_empty"/>
       </pr_pos>
-      <pr_pos name="cardinal_add" id="2940"
+      <pr_pos name="cardinal_add" id="2953"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal_add"/>
       </pr_pos>
-      <pr_pos name="cardinal_remove" id="2945"
+      <pr_pos name="cardinal_remove" id="2958"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal_remove"/>
       </pr_pos>
-      <pr_pos name="cardinal_subset" id="2950"
+      <pr_pos name="cardinal_subset" id="2963"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal_subset"/>
       </pr_pos>
-      <pr_pos name="subset_eq" id="2955"
+      <pr_pos name="subset_eq" id="2968"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="subset_eq"/>
       </pr_pos>
-      <pr_pos name="cardinal1" id="2960"
+      <pr_pos name="cardinal1" id="2973"
        ip_theory="Fset">
        <ip_library name="set"/>
        <ip_qualid name="cardinal1"/>
       </pr_pos>
-      <pr_pos name="Select_eq" id="3178"
+      <pr_pos name="Select_eq" id="3191"
        ip_theory="Map">
        <ip_library name="map"/>
        <ip_qualid name="Select_eq"/>
       </pr_pos>
-      <pr_pos name="Select_neq" id="3187"
+      <pr_pos name="Select_neq" id="3200"
        ip_theory="Map">
        <ip_library name="map"/>
        <ip_qualid name="Select_neq"/>
       </pr_pos>
-      <pr_pos name="Const" id="3199"
+      <pr_pos name="Const" id="3212"
        ip_theory="Const">
        <ip_library name="map"/>
        <ip_qualid name="Const"/>
       </pr_pos>
-      <pr_pos name="Append_assoc" id="3882"
+      <pr_pos name="Append_assoc" id="3895"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="Append_assoc"/>
       </pr_pos>
-      <pr_pos name="Append_l_nil" id="3889"
+      <pr_pos name="Append_l_nil" id="3902"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="Append_l_nil"/>
       </pr_pos>
-      <pr_pos name="Append_length" id="3892"
+      <pr_pos name="Append_length" id="3905"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="Append_length"/>
       </pr_pos>
-      <pr_pos name="mem_append" id="3897"
+      <pr_pos name="mem_append" id="3910"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="mem_append"/>
       </pr_pos>
-      <pr_pos name="mem_decomp" id="3904"
+      <pr_pos name="mem_decomp" id="3917"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="mem_decomp"/>
       </pr_pos>
-      <pr_pos name="edges_def" id="4546"
+      <pr_pos name="edges_def" id="4559"
        ip_theory="Graph">
        <ip_qualid name="edges_def"/>
       </pr_pos>
-      <pr_pos name="s_in_graph" id="4552"
+      <pr_pos name="s_in_graph" id="4565"
        ip_theory="Graph">
        <ip_qualid name="s_in_graph"/>
       </pr_pos>
-      <pr_pos name="vertices_cardinal_pos" id="4553"
+      <pr_pos name="vertices_cardinal_pos" id="4566"
        ip_theory="Graph">
        <ip_qualid name="vertices_cardinal_pos"/>
       </pr_pos>
-      <pr_pos name="path_right_extension" id="4758"
+      <pr_pos name="path_right_extension" id="4771"
        ip_theory="Graph">
        <ip_qualid name="path_right_extension"/>
       </pr_pos>
-      <pr_pos name="path_right_inversion" id="4767"
+      <pr_pos name="path_right_inversion" id="4780"
        ip_theory="Graph">
        <ip_qualid name="path_right_inversion"/>
       </pr_pos>
-      <pr_pos name="path_trans" id="4778"
+      <pr_pos name="path_trans" id="4791"
        ip_theory="Graph">
        <ip_qualid name="path_trans"/>
       </pr_pos>
-      <pr_pos name="empty_path" id="4789"
+      <pr_pos name="empty_path" id="4802"
        ip_theory="Graph">
        <ip_qualid name="empty_path"/>
       </pr_pos>
-      <pr_pos name="path_decomposition" id="4794"
+      <pr_pos name="path_decomposition" id="4807"
        ip_theory="Graph">
        <ip_qualid name="path_decomposition"/>
       </pr_pos>
-      <pr_pos name="path_weight_right_extension" id="4837"
+      <pr_pos name="path_weight_right_extension" id="4850"
        ip_theory="Graph">
        <ip_qualid name="path_weight_right_extension"/>
       </pr_pos>
-      <pr_pos name="path_weight_decomposition" id="4844"
+      <pr_pos name="path_weight_decomposition" id="4857"
        ip_theory="Graph">
        <ip_qualid name="path_weight_decomposition"/>
       </pr_pos>
-      <pr_pos name="path_in_vertices" id="4853"
+      <pr_pos name="path_in_vertices" id="4866"
        ip_theory="Graph">
        <ip_qualid name="path_in_vertices"/>
       </pr_pos>
-      <pr_pos name="Induction" id="4959"
+      <pr_pos name="Induction" id="4972"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="FsetInduction"/>
        <ip_qualid name="Induction"/>
       </pr_pos>
-      <pr_pos name="corner" id="4968"
+      <pr_pos name="corner" id="4981"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="corner"/>
       </pr_pos>
-      <pr_pos name="pigeon_0" id="4985"
+      <pr_pos name="pigeon_0" id="4998"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="pigeon_0"/>
       </pr_pos>
-      <pr_pos name="pigeon_1" id="4986"
+      <pr_pos name="pigeon_1" id="4999"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="pigeon_1"/>
       </pr_pos>
-      <pr_pos name="pigeon_2" id="4991"
+      <pr_pos name="pigeon_2" id="5004"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="pigeon_2"/>
       </pr_pos>
-      <pr_pos name="pigeonhole" id="4994"
+      <pr_pos name="pigeonhole" id="5007"
        ip_theory="Graph">
        <ip_qualid name="Pigeonhole"/>
        <ip_qualid name="pigeonhole"/>
       </pr_pos>
-      <pr_pos name="long_path_decomposition_pigeon1" id="5009"
+      <pr_pos name="long_path_decomposition_pigeon1" id="5022"
        ip_theory="Graph">
        <ip_qualid name="long_path_decomposition_pigeon1"/>
       </pr_pos>
-      <pr_pos name="long_path_decomposition_pigeon2" id="5016"
+      <pr_pos name="long_path_decomposition_pigeon2" id="5029"
        ip_theory="Graph">
        <ip_qualid name="long_path_decomposition_pigeon2"/>
       </pr_pos>
-      <pr_pos name="long_path_decomposition_pigeon3" id="5031"
+      <pr_pos name="long_path_decomposition_pigeon3" id="5044"
        ip_theory="Graph">
        <ip_qualid name="long_path_decomposition_pigeon3"/>
       </pr_pos>
-      <pr_pos name="long_path_decomposition" id="5056"
+      <pr_pos name="long_path_decomposition" id="5069"
        ip_theory="Graph">
        <ip_qualid name="long_path_decomposition"/>
       </pr_pos>
-      <pr_pos name="simple_path" id="5073"
+      <pr_pos name="simple_path" id="5086"
        ip_theory="Graph">
        <ip_qualid name="simple_path"/>
       </pr_pos>
-      <pr_pos name="key_lemma_1" id="5091"
+      <pr_pos name="key_lemma_1" id="5104"
        ip_theory="Graph">
        <ip_qualid name="key_lemma_1"/>
       </pr_pos>
-      <pr_pos name="key_lemma_2" id="5429"
+      <pr_pos name="key_lemma_2" id="5442"
        ip_theory="BellmanFord">
        <ip_qualid name="key_lemma_2"/>
       </pr_pos>
@@ -1837,100 +1837,100 @@
        <meta_arg_ls id="1621"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2369"/>
+       <meta_arg_ls id="2382"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2388"/>
+       <meta_arg_ls id="2401"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2407"/>
+       <meta_arg_ls id="2420"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2492"/>
+       <meta_arg_ls id="2505"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2819"/>
+       <meta_arg_ls id="2832"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2822"/>
+       <meta_arg_ls id="2835"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2840"/>
+       <meta_arg_ls id="2853"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2861"/>
+       <meta_arg_ls id="2874"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2863"/>
+       <meta_arg_ls id="2876"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2873"/>
+       <meta_arg_ls id="2886"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2879"/>
+       <meta_arg_ls id="2892"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2884"/>
+       <meta_arg_ls id="2897"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2902"/>
+       <meta_arg_ls id="2915"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2909"/>
+       <meta_arg_ls id="2922"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2916"/>
+       <meta_arg_ls id="2929"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2928"/>
+       <meta_arg_ls id="2941"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2932"/>
+       <meta_arg_ls id="2945"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3142"/>
+       <meta_arg_ls id="3155"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3145"/>
+       <meta_arg_ls id="3158"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3165"/>
+       <meta_arg_ls id="3178"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3197"/>
+       <meta_arg_ls id="3210"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3865"/>
+       <meta_arg_ls id="3878"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4535"/>
+       <meta_arg_ls id="4548"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4536"/>
+       <meta_arg_ls id="4549"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4551"/>
+       <meta_arg_ls id="4564"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4805"/>
+       <meta_arg_ls id="4818"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4942"/>
+       <meta_arg_ls id="4955"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5080"/>
+       <meta_arg_ls id="5093"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5111"/>
+       <meta_arg_ls id="5124"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5348"/>
+       <meta_arg_ls id="5361"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5354"/>
+       <meta_arg_ls id="5367"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5410"/>
+       <meta_arg_ls id="5423"/>
       </meta>
       <meta name="remove_prop">
        <meta_arg_pr id="1622"/>
@@ -1990,175 +1990,175 @@
        <meta_arg_pr id="1726"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2416"/>
+       <meta_arg_pr id="2429"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2419"/>
+       <meta_arg_pr id="2432"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2426"/>
+       <meta_arg_pr id="2439"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2431"/>
+       <meta_arg_pr id="2444"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2485"/>
+       <meta_arg_pr id="2498"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2488"/>
+       <meta_arg_pr id="2501"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2833"/>
+       <meta_arg_pr id="2846"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2851"/>
+       <meta_arg_pr id="2864"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2854"/>
+       <meta_arg_pr id="2867"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2870"/>
+       <meta_arg_pr id="2883"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2871"/>
+       <meta_arg_pr id="2884"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2890"/>
+       <meta_arg_pr id="2903"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2894"/>
+       <meta_arg_pr id="2907"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2898"/>
+       <meta_arg_pr id="2911"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2903"/>
+       <meta_arg_pr id="2916"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2910"/>
+       <meta_arg_pr id="2923"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2923"/>
+       <meta_arg_pr id="2936"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2929"/>
+       <meta_arg_pr id="2942"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2934"/>
+       <meta_arg_pr id="2947"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2937"/>
+       <meta_arg_pr id="2950"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2940"/>
+       <meta_arg_pr id="2953"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2945"/>
+       <meta_arg_pr id="2958"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2950"/>
+       <meta_arg_pr id="2963"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2955"/>
+       <meta_arg_pr id="2968"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2960"/>
+       <meta_arg_pr id="2973"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3178"/>
+       <meta_arg_pr id="3191"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3187"/>
+       <meta_arg_pr id="3200"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3199"/>
+       <meta_arg_pr id="3212"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3882"/>
+       <meta_arg_pr id="3895"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3889"/>
+       <meta_arg_pr id="3902"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3892"/>
+       <meta_arg_pr id="3905"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3897"/>
+       <meta_arg_pr id="3910"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="3904"/>
+       <meta_arg_pr id="3917"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4546"/>
+       <meta_arg_pr id="4559"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4552"/>
+       <meta_arg_pr id="4565"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4553"/>
+       <meta_arg_pr id="4566"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4758"/>
+       <meta_arg_pr id="4771"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4767"/>
+       <meta_arg_pr id="4780"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4778"/>
+       <meta_arg_pr id="4791"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4789"/>
+       <meta_arg_pr id="4802"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4794"/>
+       <meta_arg_pr id="4807"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4837"/>
+       <meta_arg_pr id="4850"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4844"/>
+       <meta_arg_pr id="4857"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4853"/>
+       <meta_arg_pr id="4866"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4959"/>
+       <meta_arg_pr id="4972"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4968"/>
+       <meta_arg_pr id="4981"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4985"/>
+       <meta_arg_pr id="4998"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4986"/>
+       <meta_arg_pr id="4999"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4991"/>
+       <meta_arg_pr id="5004"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4994"/>
+       <meta_arg_pr id="5007"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5009"/>
+       <meta_arg_pr id="5022"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5016"/>
+       <meta_arg_pr id="5029"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5031"/>
+       <meta_arg_pr id="5044"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5056"/>
+       <meta_arg_pr id="5069"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5073"/>
+       <meta_arg_pr id="5086"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5091"/>
+       <meta_arg_pr id="5104"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5429"/>
+       <meta_arg_pr id="5442"/>
       </meta>
       <meta name="remove_type">
        <meta_arg_ts id="2"/>
@@ -2173,13 +2173,13 @@
        <meta_arg_ts id="68"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5105"/>
+       <meta_arg_ts id="5118"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5255"/>
+       <meta_arg_ts id="5268"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5347"/>
+       <meta_arg_ts id="5360"/>
       </meta>
       <goal name="WP_parameter bellman_ford.14.2.1.5" expl="VC for bellman_ford">
       <transf name="eliminate_builtin">
@@ -2217,7 +2217,7 @@
     <proof prover="8"><result status="valid" time="0.16" steps="222"/></proof>
     </goal>
     <goal name="WP_parameter bellman_ford.17.1.2" expl="loop invariant preservation">
-    <proof prover="1" timelimit="30" edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_17.v"><result status="valid" time="1.57"/></proof>
+    <proof prover="0" timelimit="30" edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_17.v"><result status="valid" time="1.57"/></proof>
     </goal>
     <goal name="WP_parameter bellman_ford.17.1.3" expl="loop invariant preservation">
     <proof prover="2" timelimit="5" memlimit="1000"><result status="valid" time="0.04"/></proof>
@@ -2225,7 +2225,7 @@
     <proof prover="8"><result status="valid" time="0.07" steps="43"/></proof>
     </goal>
     <goal name="WP_parameter bellman_ford.17.1.4" expl="loop invariant preservation">
-    <proof prover="1" timelimit="30" edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_18.v"><result status="valid" time="1.16"/></proof>
+    <proof prover="0" timelimit="30" edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_18.v"><result status="valid" time="1.16"/></proof>
     </goal>
     <goal name="WP_parameter bellman_ford.17.1.5" expl="loop invariant preservation">
     <proof prover="8" timelimit="15"><result status="valid" time="0.04" steps="32"/></proof>
@@ -2244,7 +2244,7 @@
   <proof prover="8"><result status="valid" time="0.02" steps="13"/></proof>
   </goal>
   <goal name="WP_parameter bellman_ford.21" expl="exceptional postcondition">
-  <proof prover="1" edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_15.v"><result status="valid" time="1.44"/></proof>
+  <proof prover="0" edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_15.v"><result status="valid" time="1.44"/></proof>
   </goal>
   <goal name="WP_parameter bellman_ford.22" expl="loop invariant preservation">
   <transf name="split_goal_wp">
@@ -2270,7 +2270,7 @@
    <proof prover="8" timelimit="15" memlimit="0"><result status="valid" time="0.11" steps="69"/></proof>
    </goal>
    <goal name="WP_parameter bellman_ford.25.2" expl="postcondition">
-   <proof prover="1" edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_19.v"><result status="valid" time="0.84"/></proof>
+   <proof prover="0" edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_19.v"><result status="valid" time="0.84"/></proof>
    </goal>
    <goal name="WP_parameter bellman_ford.25.3" expl="postcondition">
    <proof prover="2"><result status="valid" time="0.14"/></proof>
diff --git a/examples/bitvectors/bitvector/why3session.xml b/examples/bitvectors/bitvector/why3session.xml
index 9602cb36083c4e17a1ef16d88214cce43dc18ad9..3393b9e18ab44d538b709bb90f9707d6849eb834 100644
--- a/examples/bitvectors/bitvector/why3session.xml
+++ b/examples/bitvectors/bitvector/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="0" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="1" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="6" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -31,16 +31,16 @@
  <proof prover="6"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="to_nat_of_zero2" expl="">
- <proof prover="0" edited="bitvector_BitVector_to_nat_of_zero2_1.v"><result status="valid" time="0.31"/></proof>
+ <proof prover="1" edited="bitvector_BitVector_to_nat_of_zero2_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
  <goal name="to_nat_of_zero" expl="">
- <proof prover="0" timelimit="30" edited="bitvector_BitVector_to_nat_of_zero_1.v"><result status="valid" time="1.01"/></proof>
+ <proof prover="1" timelimit="30" edited="bitvector_BitVector_to_nat_of_zero_1.v"><result status="valid" time="1.01"/></proof>
  </goal>
  <goal name="to_nat_of_one" expl="">
- <proof prover="0" edited="bitvector_BitVector_to_nat_of_one_1.v"><result status="valid" time="0.96"/></proof>
+ <proof prover="1" edited="bitvector_BitVector_to_nat_of_one_1.v"><result status="valid" time="0.96"/></proof>
  </goal>
  <goal name="to_nat_sub_footprint" expl="">
- <proof prover="0" timelimit="7" edited="bitvector_BitVector_to_nat_sub_footprint_1.v"><result status="valid" time="1.22"/></proof>
+ <proof prover="1" timelimit="7" edited="bitvector_BitVector_to_nat_sub_footprint_1.v"><result status="valid" time="1.48"/></proof>
  </goal>
  <goal name="nth_from_int_low_even" expl="">
  <proof prover="2"><result status="valid" time="0.02" steps="68"/></proof>
@@ -72,7 +72,7 @@
  <proof prover="3"><result status="valid" time="0.11"/></proof>
  </goal>
  <goal name="nth_from_int2c_plus_pow2" expl="">
- <proof prover="0" timelimit="10" edited="bitvector_BitVector_nth_from_int2c_plus_pow2_1.v"><result status="valid" time="0.51"/></proof>
+ <proof prover="1" timelimit="10" edited="bitvector_BitVector_nth_from_int2c_plus_pow2_1.v"><result status="valid" time="0.75"/></proof>
  <proof prover="2"><result status="valid" time="0.33" steps="94"/></proof>
  </goal>
 </theory>
diff --git a/examples/bitvectors/double/why3session.xml b/examples/bitvectors/double/why3session.xml
index dcc32eb4f93d2faf4855fbb2994b0ec1130eaf89..9f8c6dd2e6ed168230083a8939d850420526781a 100644
--- a/examples/bitvectors/double/why3session.xml
+++ b/examples/bitvectors/double/why3session.xml
@@ -4,8 +4,8 @@
 <why3session shape_version="4">
 <prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="30" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Coq" version="8.7.1" timelimit="30" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../double.why" expanded="true">
 <theory name="BV_double" sum="d41d8cd98f00b204e9800998ecf8427e">
@@ -28,7 +28,7 @@
  </goal>
  <goal name="exp_one" expl="" expanded="true">
  <proof prover="0" timelimit="30"><result status="valid" time="2.23" steps="668"/></proof>
- <proof prover="2" edited="double_TestDouble_exp_one_1.v"><result status="valid" time="0.38"/></proof>
+ <proof prover="4" edited="double_TestDouble_exp_one_1.v"><result status="valid" time="0.38"/></proof>
  </goal>
  <goal name="mantissa_one" expl="">
  <proof prover="0"><result status="valid" time="0.09" steps="87"/></proof>
diff --git a/examples/bitvectors/double_of_int/why3session.xml b/examples/bitvectors/double_of_int/why3session.xml
index b3aad3024184791b598ef380d8358b5b60680565..866694b58d3f6a289ba20250615ce6c5b0e61bb7 100644
--- a/examples/bitvectors/double_of_int/why3session.xml
+++ b/examples/bitvectors/double_of_int/why3session.xml
@@ -5,8 +5,8 @@
 <prover id="0" name="Gappa" version="1.3.0" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="3" name="Coq" version="8.6.1" timelimit="60" steplimit="0" memlimit="1000"/>
 <prover id="4" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="5" name="Coq" version="8.7.1" timelimit="60" steplimit="0" memlimit="1000"/>
 <prover id="6" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="8" name="Z3" version="4.3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../double_of_int.why" expanded="true">
@@ -86,7 +86,7 @@
  <proof prover="8"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="exp_const" expl="">
- <proof prover="3" timelimit="30" edited="double_of_int_DoubleOfInt_exp_const_1.v"><result status="valid" time="0.80"/></proof>
+ <proof prover="5" timelimit="30" edited="double_of_int_DoubleOfInt_exp_const_1.v"><result status="valid" time="0.80"/></proof>
  </goal>
  <goal name="to_nat_mantissa_1" expl="">
  <proof prover="1"><result status="valid" time="0.05" steps="91"/></proof>
@@ -162,10 +162,10 @@
  <proof prover="8"><result status="valid" time="0.12"/></proof>
  </goal>
  <goal name="from_int2c_to_nat_sub_pos" expl="">
- <proof prover="3" edited="double_of_int_DoubleOfInt_from_int2c_to_nat_sub_pos_1.v"><result status="valid" time="1.76"/></proof>
+ <proof prover="5" edited="double_of_int_DoubleOfInt_from_int2c_to_nat_sub_pos_1.v"><result status="valid" time="1.76"/></proof>
  </goal>
  <goal name="lemma1_pos" expl="">
- <proof prover="3" timelimit="6" edited="double_of_int_DoubleOfInt_lemma1_pos_1.v"><result status="valid" time="1.39"/></proof>
+ <proof prover="5" timelimit="6" edited="double_of_int_DoubleOfInt_lemma1_pos_1.v"><result status="valid" time="1.39"/></proof>
  </goal>
  <goal name="jpxorx_neg" expl="">
  <proof prover="2"><result status="valid" time="0.07"/></proof>
@@ -174,10 +174,10 @@
  <proof prover="8"><result status="valid" time="0.19"/></proof>
  </goal>
  <goal name="from_int2c_to_nat_sub_neg" expl="">
- <proof prover="3" timelimit="5" edited="double_of_int_DoubleOfInt_from_int2c_to_nat_sub_neg_1.v"><result status="valid" time="1.74"/></proof>
+ <proof prover="5" timelimit="5" edited="double_of_int_DoubleOfInt_from_int2c_to_nat_sub_neg_1.v"><result status="valid" time="1.74"/></proof>
  </goal>
  <goal name="lemma1_neg" expl="">
- <proof prover="3" timelimit="10" edited="double_of_int_DoubleOfInt_lemma1_neg_1.v"><result status="valid" time="0.52"/></proof>
+ <proof prover="5" timelimit="10" edited="double_of_int_DoubleOfInt_lemma1_neg_1.v"><result status="valid" time="0.52"/></proof>
  </goal>
  <goal name="lemma1" expl="">
  <proof prover="1"><result status="valid" time="0.06" steps="95"/></proof>
@@ -190,7 +190,7 @@
  <proof prover="4" timelimit="10"><result status="valid" time="1.98"/></proof>
  </goal>
  <goal name="to_nat_bv32_bv64_aux" expl="">
- <proof prover="3" timelimit="5" edited="double_of_int_DoubleOfInt_to_nat_bv32_bv64_aux_1.v"><result status="valid" time="1.74"/></proof>
+ <proof prover="5" timelimit="5" edited="double_of_int_DoubleOfInt_to_nat_bv32_bv64_aux_1.v"><result status="valid" time="1.74"/></proof>
  </goal>
  <goal name="to_nat_bv32_bv64" expl="">
  <proof prover="1"><result status="valid" time="0.06" steps="90"/></proof>
@@ -213,7 +213,7 @@
  <proof prover="8"><result status="valid" time="0.88"/></proof>
  </goal>
  <goal name="lemma2" expl="">
- <proof prover="3" edited="double_of_int_DoubleOfInt_lemma2_1.v"><result status="valid" time="23.13"/></proof>
+ <proof prover="5" edited="double_of_int_DoubleOfInt_lemma2_1.v"><result status="valid" time="18.61"/></proof>
  </goal>
  <goal name="nth_var4" expl="">
  <proof prover="1"><result status="valid" time="1.14" steps="148"/></proof>
@@ -267,7 +267,7 @@
  <proof prover="8"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="var_value0" expl="">
- <proof prover="3" timelimit="30" edited="double_of_int_DoubleOfInt_var_value0_1.v"><result status="valid" time="3.14"/></proof>
+ <proof prover="5" timelimit="30" edited="double_of_int_DoubleOfInt_var_value0_1.v"><result status="valid" time="3.14"/></proof>
  </goal>
  <goal name="from_int_sum" expl="">
  <proof prover="1"><result status="valid" time="0.05" steps="92"/></proof>
diff --git a/examples/bitvectors/power2/why3session.xml b/examples/bitvectors/power2/why3session.xml
index 4c492251dab4f8d8567bec8f8babdea8edb2e354..f829eeddde1beb2fe9a1cacbc12a998cc829fcca 100644
--- a/examples/bitvectors/power2/why3session.xml
+++ b/examples/bitvectors/power2/why3session.xml
@@ -3,9 +3,9 @@
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
 <prover id="0" name="Gappa" version="1.3.0" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="6" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="9" name="Z3" version="4.3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="10" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -18,10 +18,10 @@
  <proof prover="10"><result status="valid" time="0.00" steps="3"/></proof>
  </goal>
  <goal name="Power_sum" expl="">
- <proof prover="1" edited="power2_Pow2int_Power_sum_1.v"><result status="valid" time="0.61"/></proof>
+ <proof prover="4" edited="power2_Pow2int_Power_sum_1.v"><result status="valid" time="0.61"/></proof>
  </goal>
  <goal name="pow2pos" expl="">
- <proof prover="1" edited="power2_Pow2int_pow2pos_1.v"><result status="valid" time="0.49"/></proof>
+ <proof prover="4" edited="power2_Pow2int_pow2pos_1.v"><result status="valid" time="0.74"/></proof>
  </goal>
  <goal name="pow2_0" expl="">
  <proof prover="0"><result status="valid" time="0.00"/></proof>
@@ -431,7 +431,7 @@
  <proof prover="10"><result status="valid" time="0.24" steps="99"/></proof>
  </goal>
  <goal name="Mod_pow2_gen" expl="">
- <proof prover="1" edited="power2_Pow2int_Mod_pow2_gen_1.v"><result status="valid" time="0.86"/></proof>
+ <proof prover="4" edited="power2_Pow2int_Mod_pow2_gen_1.v"><result status="valid" time="0.86"/></proof>
  </goal>
 </theory>
 <theory name="Pow2real" sum="129a1971aba7e377549f155f30711f18" expanded="true">
@@ -467,25 +467,25 @@
  <proof prover="10"><result status="valid" time="0.00" steps="5"/></proof>
  </goal>
  <goal name="Power_non_null_aux" expl="">
- <proof prover="1" edited="power2_Pow2real_Power_non_null_aux_1.v"><result status="valid" time="0.65"/></proof>
+ <proof prover="4" edited="power2_Pow2real_Power_non_null_aux_1.v"><result status="valid" time="0.65"/></proof>
  </goal>
  <goal name="Power_neg_aux" expl="">
- <proof prover="1" edited="power2_Pow2real_Power_neg_aux_1.v"><result status="valid" time="0.68"/></proof>
+ <proof prover="4" edited="power2_Pow2real_Power_neg_aux_1.v"><result status="valid" time="0.68"/></proof>
  </goal>
  <goal name="Power_non_null" expl="">
- <proof prover="1" edited="power2_Pow2real_Power_non_null_1.v"><result status="valid" time="0.64"/></proof>
+ <proof prover="4" edited="power2_Pow2real_Power_non_null_1.v"><result status="valid" time="0.81"/></proof>
  </goal>
  <goal name="Power_neg" expl="">
  <proof prover="10"><result status="valid" time="0.02" steps="42"/></proof>
  </goal>
  <goal name="Power_sum_aux" expl="">
- <proof prover="1" edited="power2_Pow2real_Power_sum_aux_1.v"><result status="valid" time="0.62"/></proof>
+ <proof prover="4" edited="power2_Pow2real_Power_sum_aux_1.v"><result status="valid" time="0.62"/></proof>
  </goal>
  <goal name="Power_sum" expl="">
- <proof prover="1" edited="power2_Pow2real_Power_sum_1.v"><result status="valid" time="0.62"/></proof>
+ <proof prover="4" edited="power2_Pow2real_Power_sum_1.v"><result status="valid" time="0.80"/></proof>
  </goal>
  <goal name="Pow2_int_real" expl="">
- <proof prover="1" edited="power2_Pow2real_Pow2_int_real_1.v"><result status="valid" time="0.51"/></proof>
+ <proof prover="4" edited="power2_Pow2real_Pow2_int_real_1.v"><result status="valid" time="0.51"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/bresenham/why3session.xml b/examples/bresenham/why3session.xml
index 67fd3f4dc9e2e1dea9c60a1c2d40d61eecee48ae..4e6d02532bba86875d39aa15d3d25c2124596b28 100644
--- a/examples/bresenham/why3session.xml
+++ b/examples/bresenham/why3session.xml
@@ -2,15 +2,15 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="10" steplimit="0" memlimit="0"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="4" name="Alt-Ergo" version="0.95.2" timelimit="30" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="6" name="Z3" version="4.3.2" timelimit="10" steplimit="0" memlimit="0"/>
 <file name="../bresenham.mlw" expanded="true">
 <theory name="M" sum="3da6ad55dc32260aace6cf777010522a" expanded="true">
  <goal name="closest" expl="" expanded="true">
- <proof prover="2" edited="bresenham_M_closest_1.v"><result status="valid" time="0.54"/></proof>
+ <proof prover="0" edited="bresenham_M_closest_1.v"><result status="valid" time="0.54"/></proof>
  </goal>
  <goal name="WP_parameter bresenham" expl="VC for bresenham" expanded="true">
  <transf name="split_goal_wp" expanded="true">
diff --git a/examples/bts/12934/why3session.xml b/examples/bts/12934/why3session.xml
index fb2b916eeba8d94bc538d8e75ce9038ce9b21a8d..9e7edc628c071b62cf5539cae23116dcc970c125 100644
--- a/examples/bts/12934/why3session.xml
+++ b/examples/bts/12934/why3session.xml
@@ -2,11 +2,11 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <file name="../12934.why" expanded="true">
 <theory name="BTS12934" sum="e32351513bba9a37f680056dd466bcee" expanded="true">
  <goal name="t" expl="" expanded="true">
- <proof prover="1" edited="12934_BTS12934_t_1.v"><result status="valid" time="0.29"/></proof>
+ <proof prover="0" edited="12934_BTS12934_t_1.v"><result status="valid" time="0.29"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/bts/13849/why3session.xml b/examples/bts/13849/why3session.xml
index a1305390601d5c84de841303cda3ffc3aedef9ae..93d9a55dc3373c8e132e62d15733dac8fcfb8d9d 100644
--- a/examples/bts/13849/why3session.xml
+++ b/examples/bts/13849/why3session.xml
@@ -2,11 +2,11 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <file name="../13849.why" expanded="true">
 <theory name="T" sum="fe6d0a97ed129807ad9b025e583a359d" expanded="true">
  <goal name="x" expl="" expanded="true">
- <proof prover="1" edited="13849_T_x_2.v"><result status="valid" time="0.29"/></proof>
+ <proof prover="0" edited="13849_T_x_2.v"><result status="valid" time="0.29"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/bts/13854/why3session.xml b/examples/bts/13854/why3session.xml
index 14b8d1fe5d512dc0d7b17b5e344cd9715a2f3288..94bc48dda16fcc02fed5638f14419f8fc374899c 100644
--- a/examples/bts/13854/why3session.xml
+++ b/examples/bts/13854/why3session.xml
@@ -2,14 +2,14 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="0"/>
 <file name="../13854.why">
 <theory name="T" sum="e0ed6fa44df780ea63fc8d3dbdece469" expanded="true">
  <goal name="g" expl="" expanded="true">
- <proof prover="1" edited="13854_T_g_1.v"><result status="valid" time="0.29"/></proof>
+ <proof prover="0" edited="13854_T_g_1.v"><result status="valid" time="0.29"/></proof>
  </goal>
  <goal name="x" expl="" expanded="true">
- <proof prover="1" edited="13854_T_x_1.v"><result status="valid" time="0.30"/></proof>
+ <proof prover="0" edited="13854_T_x_1.v"><result status="valid" time="0.30"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/check-builtin/real/why3session.xml b/examples/check-builtin/real/why3session.xml
index 4fa884d76053d4f8816d8783976a0f5a02024e9e..9e4bb11794a5edbba88c0d66ef6970e22a18e7bc 100644
--- a/examples/check-builtin/real/why3session.xml
+++ b/examples/check-builtin/real/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="7" name="Yices" version="1.0.38" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="8" name="Z3" version="3.2" timelimit="3" steplimit="0" memlimit="0"/>
@@ -135,13 +135,13 @@
  <proof prover="14"><result status="valid" time="0.17"/></proof>
  </goal>
  <goal name="Tan_pi_4" expl="" expanded="true">
- <proof prover="1" edited="real_TrigonometryTest_Tan_pi_4_1.v"><result status="valid" time="0.39"/></proof>
+ <proof prover="0" edited="real_TrigonometryTest_Tan_pi_4_1.v"><result status="valid" time="0.39"/></proof>
  </goal>
  <goal name="Tan_pi_3" expl="" expanded="true">
- <proof prover="1" edited="real_TrigonometryTest_Tan_pi_3_1.v"><result status="valid" time="0.43"/></proof>
+ <proof prover="0" edited="real_TrigonometryTest_Tan_pi_3_1.v"><result status="valid" time="0.43"/></proof>
  </goal>
  <goal name="Atan_1" expl="" expanded="true">
- <proof prover="1" edited="real_TrigonometryTest_Atan_1_1.v"><result status="valid" time="0.41"/></proof>
+ <proof prover="0" edited="real_TrigonometryTest_Atan_1_1.v"><result status="valid" time="0.41"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/decrease1/why3session.xml b/examples/decrease1/why3session.xml
index 623883e295a208922a7b8046fd9d91f150f8667c..a7d705d25d5a6beb182ed5c60cf5a144ef94250c 100644
--- a/examples/decrease1/why3session.xml
+++ b/examples/decrease1/why3session.xml
@@ -2,9 +2,9 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="1" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="3" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="4" name="Z3" version="2.19" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="5" name="CVC3" version="2.2" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="6" name="Z3" version="4.3.1" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -16,7 +16,7 @@
 <file name="../decrease1.mlw" expanded="true">
 <theory name="Decrease1" sum="095ceb3b0449b764d13399f91bda1ab7" expanded="true">
  <goal name="decrease1_induction" expl="" expanded="true">
- <proof prover="3" edited="decrease1_Decrease1_decrease1_induction_2.v"><result status="valid" time="0.40"/></proof>
+ <proof prover="0" edited="decrease1_Decrease1_decrease1_induction_2.v"><result status="valid" time="0.40"/></proof>
  </goal>
  <goal name="WP_parameter search" expl="VC for search" expanded="true">
  <transf name="split_goal_wp" expanded="true">
diff --git a/examples/dfa_example/why3session.xml b/examples/dfa_example/why3session.xml
index 8cb1a6194796dc62ecc2534c8ee63f0e32d16e70..cfa68298b31d457ea8844ba1cb477f9170af2e6e 100644
--- a/examples/dfa_example/why3session.xml
+++ b/examples/dfa_example/why3session.xml
@@ -2,15 +2,15 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="8" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="8" steplimit="0" memlimit="1000"/>
 <prover id="4" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="4000"/>
 <prover id="7" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="8" name="Z3" version="4.4.0" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../dfa_example.mlw" expanded="true">
 <theory name="DfaExample" sum="609db869d4cfe35076ba1a796f8c66a9" expanded="true">
  <goal name="nil_notin_r1" expl="">
- <proof prover="2" edited="dfa_example_DfaExample_nil_notin_r1_1.v"><result status="valid" time="0.26"/></proof>
+ <proof prover="0" edited="dfa_example_DfaExample_nil_notin_r1_1.v"><result status="valid" time="0.26"/></proof>
  <proof prover="4"><result status="valid" time="0.10"/></proof>
  <proof prover="7" memlimit="4000"><result status="valid" time="0.08" steps="140"/></proof>
  </goal>
diff --git a/examples/dijkstra/why3session.xml b/examples/dijkstra/why3session.xml
index 9638f9e4a6acaaccde3069ca5a32e0b5a4529d54..b8e6042b86cca25d22895c1fe48ab0c9c5c80f7e 100644
--- a/examples/dijkstra/why3session.xml
+++ b/examples/dijkstra/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="0" name="Coq" version="8.6.1" timelimit="30" steplimit="0" memlimit="1000"/>
+<prover id="1" name="Coq" version="8.7.1" timelimit="30" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC4" version="1.4" timelimit="6" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -40,7 +40,7 @@
  <proof prover="8"><result status="valid" time="0.02" steps="9"/></proof>
  </goal>
  <goal name="Path_shortest_path" expl="">
- <proof prover="0" timelimit="5" edited="dijkstra_DijkstraShortestPath_Path_shortest_path_1.v"><result status="valid" time="0.65"/></proof>
+ <proof prover="1" timelimit="5" edited="dijkstra_DijkstraShortestPath_Path_shortest_path_1.v"><result status="valid" time="0.88"/></proof>
  </goal>
  <goal name="Main_lemma" expl="">
  <proof prover="3" timelimit="5"><result status="valid" time="0.08"/></proof>
@@ -149,7 +149,7 @@
     <proof prover="8"><result status="valid" time="0.12" steps="156"/></proof>
     </goal>
     <goal name="WP_parameter shortest_path_code.12.1.7" expl="VC for shortest_path_code">
-    <proof prover="0" edited="dijkstra_DijkstraShortestPath_WP_parameter_shortest_path_code_2.v"><result status="valid" time="7.97"/></proof>
+    <proof prover="1" edited="dijkstra_DijkstraShortestPath_WP_parameter_shortest_path_code_2.v"><result status="valid" time="7.97"/></proof>
     </goal>
    </transf>
    </goal>
@@ -184,7 +184,7 @@
   <proof prover="5"><result status="valid" time="0.17"/></proof>
   </goal>
   <goal name="WP_parameter shortest_path_code.17" expl="loop invariant preservation">
-  <proof prover="0" edited="dijkstra_DijkstraShortestPath_WP_parameter_shortest_path_code_3.v"><result status="valid" time="4.38"/></proof>
+  <proof prover="1" edited="dijkstra_DijkstraShortestPath_WP_parameter_shortest_path_code_3.v"><result status="valid" time="4.38"/></proof>
   </goal>
   <goal name="WP_parameter shortest_path_code.18" expl="loop variant decrease">
   <proof prover="8"><result status="valid" time="0.07" steps="73"/></proof>
diff --git a/examples/double_wp/compiler/why3session.xml b/examples/double_wp/compiler/why3session.xml
index 27c084207faf7d08544b715e8fd2cd3f0cb4a5c6..585072a20c48054887840036042f81ca1ac575e4 100644
--- a/examples/double_wp/compiler/why3session.xml
+++ b/examples/double_wp/compiler/why3session.xml
@@ -6,9 +6,9 @@
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="Eprover" version="1.8-001" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Alt-Ergo" version="1.00.prv" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="6" name="Z3" version="4.3.2" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="7" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../compiler.mlw" expanded="true">
 <theory name="Compile_aexpr" sum="411273fbd1fd074bd85d168f5a46d8fc" expanded="true">
  <goal name="WP_parameter compile_aexpr" expl="VC for compile_aexpr">
@@ -714,72 +714,72 @@
     <ip_library name="Tuple2"/>
     <ip_qualid name="tuple2"/>
    </ts_pos>
-   <ts_pos name="state" arity="0" id="4871"
+   <ts_pos name="state" arity="0" id="4884"
     ip_theory="State">
     <ip_library name="state"/>
     <ip_qualid name="state"/>
    </ts_pos>
-   <ts_pos name="com" arity="0" id="4885"
+   <ts_pos name="com" arity="0" id="4898"
     ip_theory="Imp">
     <ip_library name="imp"/>
     <ip_qualid name="com"/>
    </ts_pos>
-   <ts_pos name="pos" arity="0" id="5149"
+   <ts_pos name="pos" arity="0" id="5162"
     ip_theory="Vm">
     <ip_library name="vm"/>
     <ip_qualid name="pos"/>
    </ts_pos>
-   <ts_pos name="stack" arity="0" id="5150"
+   <ts_pos name="stack" arity="0" id="5163"
     ip_theory="Vm">
     <ip_library name="vm"/>
     <ip_qualid name="stack"/>
    </ts_pos>
-   <ts_pos name="ofs" arity="0" id="5153"
+   <ts_pos name="ofs" arity="0" id="5166"
     ip_theory="Vm">
     <ip_library name="vm"/>
     <ip_qualid name="ofs"/>
    </ts_pos>
-   <ts_pos name="code" arity="0" id="5167"
+   <ts_pos name="code" arity="0" id="5180"
     ip_theory="Vm">
     <ip_library name="vm"/>
     <ip_qualid name="code"/>
    </ts_pos>
-   <ts_pos name="pred" arity="0" id="5555"
+   <ts_pos name="pred" arity="0" id="5568"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="pred"/>
    </ts_pos>
-   <ts_pos name="rel" arity="0" id="5556"
+   <ts_pos name="rel" arity="0" id="5569"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="rel"/>
    </ts_pos>
-   <ts_pos name="pre" arity="1" id="5557"
+   <ts_pos name="pre" arity="1" id="5570"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="pre"/>
    </ts_pos>
-   <ts_pos name="post" arity="1" id="5558"
+   <ts_pos name="post" arity="1" id="5571"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="post"/>
    </ts_pos>
-   <ts_pos name="wp_trans" arity="1" id="5565"
+   <ts_pos name="wp_trans" arity="1" id="5578"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="wp_trans"/>
    </ts_pos>
-   <ts_pos name="wp" arity="1" id="5566"
+   <ts_pos name="wp" arity="1" id="5579"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="wp"/>
    </ts_pos>
-   <ts_pos name="binop" arity="0" id="6259"
+   <ts_pos name="binop" arity="0" id="6272"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="binop"/>
    </ts_pos>
-   <ts_pos name="cond" arity="0" id="6639"
+   <ts_pos name="cond" arity="0" id="6652"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="cond"/>
@@ -851,216 +851,216 @@
     <ip_library name="int"/>
     <ip_qualid name="mod"/>
    </ls_pos>
-   <ls_pos name="mem" id="2786"
+   <ls_pos name="mem" id="2799"
     ip_theory="Mem">
     <ip_library name="list"/>
     <ip_qualid name="mem"/>
    </ls_pos>
-   <ls_pos name="orb" id="3872"
+   <ls_pos name="orb" id="3885"
     ip_theory="Bool">
     <ip_library name="bool"/>
     <ip_qualid name="orb"/>
    </ls_pos>
-   <ls_pos name="xorb" id="3886"
+   <ls_pos name="xorb" id="3899"
     ip_theory="Bool">
     <ip_library name="bool"/>
     <ip_qualid name="xorb"/>
    </ls_pos>
-   <ls_pos name="implb" id="3895"
+   <ls_pos name="implb" id="3908"
     ip_theory="Bool">
     <ip_library name="bool"/>
     <ip_qualid name="implb"/>
    </ls_pos>
-   <ls_pos name="get" id="4831"
+   <ls_pos name="get" id="4844"
     ip_theory="State">
     <ip_library name="state"/>
     <ip_qualid name="get"/>
    </ls_pos>
-   <ls_pos name="set" id="4832"
+   <ls_pos name="set" id="4845"
     ip_theory="State">
     <ip_library name="state"/>
     <ip_qualid name="set"/>
    </ls_pos>
-   <ls_pos name="ceval" id="4984"
+   <ls_pos name="ceval" id="4997"
     ip_theory="Imp">
     <ip_library name="imp"/>
     <ip_qualid name="ceval"/>
    </ls_pos>
-   <ls_pos name="ihalt" id="5249"
+   <ls_pos name="ihalt" id="5262"
     ip_theory="Vm">
     <ip_library name="vm"/>
     <ip_qualid name="ihalt"/>
    </ls_pos>
-   <ls_pos name="vm_terminates" id="5500"
+   <ls_pos name="vm_terminates" id="5513"
     ip_theory="Vm">
     <ip_library name="vm"/>
     <ip_qualid name="vm_terminates"/>
    </ls_pos>
-   <ls_pos name="fst" id="5520"
+   <ls_pos name="fst" id="5533"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="fst"/>
    </ls_pos>
-   <ls_pos name="snd" id="5539"
+   <ls_pos name="snd" id="5552"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="snd"/>
    </ls_pos>
-   <ls_pos name="wp_correctness" id="5618"
+   <ls_pos name="wp_correctness" id="5631"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="wp_correctness"/>
    </ls_pos>
-   <ls_pos name="seq_wp" id="5644"
+   <ls_pos name="seq_wp" id="5657"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="seq_wp"/>
    </ls_pos>
-   <ls_pos name="fork_wp" id="5733"
+   <ls_pos name="fork_wp" id="5746"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="fork_wp"/>
    </ls_pos>
-   <ls_pos name="towp_wp" id="5793"
+   <ls_pos name="towp_wp" id="5806"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="towp_wp"/>
    </ls_pos>
-   <ls_pos name="acc" id="5904"
+   <ls_pos name="acc" id="5917"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="acc"/>
    </ls_pos>
-   <ls_pos name="loop_progress" id="5918"
+   <ls_pos name="loop_progress" id="5931"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="loop_progress"/>
    </ls_pos>
-   <ls_pos name="forget_old" id="5954"
+   <ls_pos name="forget_old" id="5967"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="forget_old"/>
    </ls_pos>
-   <ls_pos name="ifun_post" id="6004"
+   <ls_pos name="ifun_post" id="6017"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="ifun_post"/>
    </ls_pos>
-   <ls_pos name="iconst_post" id="6057"
+   <ls_pos name="iconst_post" id="6070"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="iconst_post"/>
    </ls_pos>
-   <ls_pos name="iconst_fun" id="6091"
+   <ls_pos name="iconst_fun" id="6104"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="iconst_fun"/>
    </ls_pos>
-   <ls_pos name="ivar_post" id="6158"
+   <ls_pos name="ivar_post" id="6171"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="ivar_post"/>
    </ls_pos>
-   <ls_pos name="ivar_fun" id="6192"
+   <ls_pos name="ivar_fun" id="6205"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="ivar_fun"/>
    </ls_pos>
-   <ls_pos name="ibinop_pre" id="6260"
+   <ls_pos name="ibinop_pre" id="6273"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="ibinop_pre"/>
    </ls_pos>
-   <ls_pos name="ibinop_post" id="6293"
+   <ls_pos name="ibinop_post" id="6306"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="ibinop_post"/>
    </ls_pos>
-   <ls_pos name="ibinop_fun" id="6335"
+   <ls_pos name="ibinop_fun" id="6348"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="ibinop_fun"/>
    </ls_pos>
-   <ls_pos name="plus" id="6434"
+   <ls_pos name="plus" id="6447"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="plus"/>
    </ls_pos>
-   <ls_pos name="sub" id="6447"
+   <ls_pos name="sub" id="6460"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="sub"/>
    </ls_pos>
-   <ls_pos name="mul" id="6460"
+   <ls_pos name="mul" id="6473"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="mul"/>
    </ls_pos>
-   <ls_pos name="inil_post" id="6506"
+   <ls_pos name="inil_post" id="6519"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="inil_post"/>
    </ls_pos>
-   <ls_pos name="ibranch_post" id="6538"
+   <ls_pos name="ibranch_post" id="6551"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="ibranch_post"/>
    </ls_pos>
-   <ls_pos name="ibranch_fun" id="6572"
+   <ls_pos name="ibranch_fun" id="6585"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="ibranch_fun"/>
    </ls_pos>
-   <ls_pos name="icjump_post" id="6640"
+   <ls_pos name="icjump_post" id="6653"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="icjump_post"/>
    </ls_pos>
-   <ls_pos name="icjump_fun" id="6687"
+   <ls_pos name="icjump_fun" id="6700"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="icjump_fun"/>
    </ls_pos>
-   <ls_pos name="beq" id="6794"
+   <ls_pos name="beq" id="6807"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="beq"/>
    </ls_pos>
-   <ls_pos name="bne" id="6807"
+   <ls_pos name="bne" id="6820"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="bne"/>
    </ls_pos>
-   <ls_pos name="ble" id="6820"
+   <ls_pos name="ble" id="6833"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="ble"/>
    </ls_pos>
-   <ls_pos name="bgt" id="6833"
+   <ls_pos name="bgt" id="6846"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="bgt"/>
    </ls_pos>
-   <ls_pos name="isetvar_pre" id="6902"
+   <ls_pos name="isetvar_pre" id="6915"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="isetvar_pre"/>
    </ls_pos>
-   <ls_pos name="isetvar_post" id="6931"
+   <ls_pos name="isetvar_post" id="6944"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="isetvar_post"/>
    </ls_pos>
-   <ls_pos name="isetvar_fun" id="6969"
+   <ls_pos name="isetvar_fun" id="6982"
     ip_theory="VM_instr_spec">
     <ip_library name="specs"/>
     <ip_qualid name="isetvar_fun"/>
    </ls_pos>
-   <ls_pos name="aexpr_post" id="7046"
+   <ls_pos name="aexpr_post" id="7059"
     ip_theory="Compile_aexpr">
     <ip_qualid name="aexpr_post"/>
    </ls_pos>
-   <ls_pos name="exec_cond" id="8773"
+   <ls_pos name="exec_cond" id="8786"
     ip_theory="Compile_bexpr">
     <ip_qualid name="exec_cond"/>
    </ls_pos>
@@ -1253,92 +1253,92 @@
     <ip_library name="int"/>
     <ip_qualid name="Mod_mult"/>
    </pr_pos>
-   <pr_pos name="Length_nonnegative" id="2779"
+   <pr_pos name="Length_nonnegative" id="2792"
     ip_theory="Length">
     <ip_library name="list"/>
     <ip_qualid name="Length_nonnegative"/>
    </pr_pos>
-   <pr_pos name="Length_nil" id="2782"
+   <pr_pos name="Length_nil" id="2795"
     ip_theory="Length">
     <ip_library name="list"/>
     <ip_qualid name="Length_nil"/>
    </pr_pos>
-   <pr_pos name="Append_assoc" id="4176"
+   <pr_pos name="Append_assoc" id="4189"
     ip_theory="Append">
     <ip_library name="list"/>
     <ip_qualid name="Append_assoc"/>
    </pr_pos>
-   <pr_pos name="Append_l_nil" id="4183"
+   <pr_pos name="Append_l_nil" id="4196"
     ip_theory="Append">
     <ip_library name="list"/>
     <ip_qualid name="Append_l_nil"/>
    </pr_pos>
-   <pr_pos name="Append_length" id="4186"
+   <pr_pos name="Append_length" id="4199"
     ip_theory="Append">
     <ip_library name="list"/>
     <ip_qualid name="Append_length"/>
    </pr_pos>
-   <pr_pos name="mem_append" id="4191"
+   <pr_pos name="mem_append" id="4204"
     ip_theory="Append">
     <ip_library name="list"/>
     <ip_qualid name="mem_append"/>
    </pr_pos>
-   <pr_pos name="mem_decomp" id="4198"
+   <pr_pos name="mem_decomp" id="4211"
     ip_theory="Append">
     <ip_library name="list"/>
     <ip_qualid name="mem_decomp"/>
    </pr_pos>
-   <pr_pos name="Select_eq" id="4857"
+   <pr_pos name="Select_eq" id="4870"
     ip_theory="State">
     <ip_library name="state"/>
     <ip_qualid name="Select_eq"/>
    </pr_pos>
-   <pr_pos name="Select_neq" id="4863"
+   <pr_pos name="Select_neq" id="4876"
     ip_theory="State">
     <ip_library name="state"/>
     <ip_qualid name="Select_neq"/>
    </pr_pos>
-   <pr_pos name="ceval_deterministic_aux" id="5073"
+   <pr_pos name="ceval_deterministic_aux" id="5086"
     ip_theory="Imp">
     <ip_library name="imp"/>
     <ip_qualid name="ceval_deterministic_aux"/>
    </pr_pos>
-   <pr_pos name="ceval_deterministic" id="5082"
+   <pr_pos name="ceval_deterministic" id="5095"
     ip_theory="Imp">
     <ip_library name="imp"/>
     <ip_qualid name="ceval_deterministic"/>
    </pr_pos>
-   <pr_pos name="codeseq_at_app_right" id="5179"
+   <pr_pos name="codeseq_at_app_right" id="5192"
     ip_theory="Vm">
     <ip_library name="vm"/>
     <ip_qualid name="codeseq_at_app_right"/>
    </pr_pos>
-   <pr_pos name="codeseq_at_app_left" id="5188"
+   <pr_pos name="codeseq_at_app_left" id="5201"
     ip_theory="Vm">
     <ip_library name="vm"/>
     <ip_qualid name="codeseq_at_app_left"/>
    </pr_pos>
-   <pr_pos name="transition_star_one" id="5484"
+   <pr_pos name="transition_star_one" id="5497"
     ip_theory="Vm">
     <ip_library name="vm"/>
     <ip_qualid name="transition_star_one"/>
    </pr_pos>
-   <pr_pos name="transition_star_transitive" id="5491"
+   <pr_pos name="transition_star_transitive" id="5504"
     ip_theory="Vm">
     <ip_library name="vm"/>
     <ip_qualid name="transition_star_transitive"/>
    </pr_pos>
-   <pr_pos name="seq_wp_lemma" id="5680"
+   <pr_pos name="seq_wp_lemma" id="5693"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="seq_wp_lemma"/>
    </pr_pos>
-   <pr_pos name="fork_wp_lemma" id="5764"
+   <pr_pos name="fork_wp_lemma" id="5777"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="fork_wp_lemma"/>
    </pr_pos>
-   <pr_pos name="towp_wp_lemma" id="5828"
+   <pr_pos name="towp_wp_lemma" id="5841"
     ip_theory="Compiler_logic">
     <ip_library name="logic"/>
     <ip_qualid name="towp_wp_lemma"/>
@@ -1383,85 +1383,82 @@
     <meta_arg_ls id="2151"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="2786"/>
+    <meta_arg_ls id="2799"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="3872"/>
+    <meta_arg_ls id="3885"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="3886"/>
+    <meta_arg_ls id="3899"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="3895"/>
+    <meta_arg_ls id="3908"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="4831"/>
+    <meta_arg_ls id="4844"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="4832"/>
+    <meta_arg_ls id="4845"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="4984"/>
+    <meta_arg_ls id="4997"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5249"/>
+    <meta_arg_ls id="5262"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5500"/>
+    <meta_arg_ls id="5513"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5520"/>
+    <meta_arg_ls id="5533"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5539"/>
+    <meta_arg_ls id="5552"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5618"/>
+    <meta_arg_ls id="5631"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5644"/>
+    <meta_arg_ls id="5657"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5733"/>
+    <meta_arg_ls id="5746"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5793"/>
+    <meta_arg_ls id="5806"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5904"/>
+    <meta_arg_ls id="5917"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5918"/>
+    <meta_arg_ls id="5931"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="5954"/>
+    <meta_arg_ls id="5967"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6004"/>
+    <meta_arg_ls id="6017"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6057"/>
+    <meta_arg_ls id="6070"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6091"/>
+    <meta_arg_ls id="6104"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6158"/>
+    <meta_arg_ls id="6171"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6192"/>
+    <meta_arg_ls id="6205"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6260"/>
+    <meta_arg_ls id="6273"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6293"/>
+    <meta_arg_ls id="6306"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6335"/>
-   </meta>
-   <meta name="remove_logic">
-    <meta_arg_ls id="6434"/>
+    <meta_arg_ls id="6348"/>
    </meta>
    <meta name="remove_logic">
     <meta_arg_ls id="6447"/>
@@ -1470,22 +1467,22 @@
     <meta_arg_ls id="6460"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6506"/>
+    <meta_arg_ls id="6473"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6538"/>
+    <meta_arg_ls id="6519"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6572"/>
+    <meta_arg_ls id="6551"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6640"/>
+    <meta_arg_ls id="6585"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6687"/>
+    <meta_arg_ls id="6653"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6794"/>
+    <meta_arg_ls id="6700"/>
    </meta>
    <meta name="remove_logic">
     <meta_arg_ls id="6807"/>
@@ -1497,19 +1494,22 @@
     <meta_arg_ls id="6833"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6902"/>
+    <meta_arg_ls id="6846"/>
+   </meta>
+   <meta name="remove_logic">
+    <meta_arg_ls id="6915"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6931"/>
+    <meta_arg_ls id="6944"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="6969"/>
+    <meta_arg_ls id="6982"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="7046"/>
+    <meta_arg_ls id="7059"/>
    </meta>
    <meta name="remove_logic">
-    <meta_arg_ls id="8773"/>
+    <meta_arg_ls id="8786"/>
    </meta>
    <meta name="remove_prop">
     <meta_arg_pr id="1911"/>
@@ -1620,58 +1620,58 @@
     <meta_arg_pr id="2214"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2779"/>
+    <meta_arg_pr id="2792"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2782"/>
+    <meta_arg_pr id="2795"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="4176"/>
+    <meta_arg_pr id="4189"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="4183"/>
+    <meta_arg_pr id="4196"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="4186"/>
+    <meta_arg_pr id="4199"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="4191"/>
+    <meta_arg_pr id="4204"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="4198"/>
+    <meta_arg_pr id="4211"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="4857"/>
+    <meta_arg_pr id="4870"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="4863"/>
+    <meta_arg_pr id="4876"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="5073"/>
+    <meta_arg_pr id="5086"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="5082"/>
+    <meta_arg_pr id="5095"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="5179"/>
+    <meta_arg_pr id="5192"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="5188"/>
+    <meta_arg_pr id="5201"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="5484"/>
+    <meta_arg_pr id="5497"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="5491"/>
+    <meta_arg_pr id="5504"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="5680"/>
+    <meta_arg_pr id="5693"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="5764"/>
+    <meta_arg_pr id="5777"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="5828"/>
+    <meta_arg_pr id="5841"/>
    </meta>
    <meta name="remove_type">
     <meta_arg_ts id="2"/>
@@ -1686,46 +1686,46 @@
     <meta_arg_ts id="1453"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="4871"/>
+    <meta_arg_ts id="4884"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="4885"/>
+    <meta_arg_ts id="4898"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="5149"/>
+    <meta_arg_ts id="5162"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="5150"/>
+    <meta_arg_ts id="5163"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="5153"/>
+    <meta_arg_ts id="5166"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="5167"/>
+    <meta_arg_ts id="5180"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="5555"/>
+    <meta_arg_ts id="5568"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="5556"/>
+    <meta_arg_ts id="5569"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="5557"/>
+    <meta_arg_ts id="5570"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="5558"/>
+    <meta_arg_ts id="5571"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="5565"/>
+    <meta_arg_ts id="5578"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="5566"/>
+    <meta_arg_ts id="5579"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="6259"/>
+    <meta_arg_ts id="6272"/>
    </meta>
    <meta name="remove_type">
-    <meta_arg_ts id="6639"/>
+    <meta_arg_ts id="6652"/>
    </meta>
    <goal name="WP_parameter compile_bexpr_natural.2" expl="postcondition">
    <transf name="eliminate_builtin">
@@ -2068,68 +2068,68 @@
        <ip_library name="Unit"/>
        <ip_qualid name="unit"/>
       </ts_pos>
-      <ts_pos name="&apos;mark" arity="0" id="68"
+      <ts_pos name="&#39;mark" arity="0" id="68"
        ip_theory="Mark">
        <ip_library name="why3"/>
        <ip_library name="Mark"/>
-       <ip_qualid name="&apos;mark"/>
+       <ip_qualid name="&#39;mark"/>
       </ts_pos>
-      <ts_pos name="state" arity="0" id="4871"
+      <ts_pos name="state" arity="0" id="4884"
        ip_theory="State">
        <ip_library name="state"/>
        <ip_qualid name="state"/>
       </ts_pos>
-      <ts_pos name="pos" arity="0" id="5149"
+      <ts_pos name="pos" arity="0" id="5162"
        ip_theory="Vm">
        <ip_library name="vm"/>
        <ip_qualid name="pos"/>
       </ts_pos>
-      <ts_pos name="stack" arity="0" id="5150"
+      <ts_pos name="stack" arity="0" id="5163"
        ip_theory="Vm">
        <ip_library name="vm"/>
        <ip_qualid name="stack"/>
       </ts_pos>
-      <ts_pos name="ofs" arity="0" id="5153"
+      <ts_pos name="ofs" arity="0" id="5166"
        ip_theory="Vm">
        <ip_library name="vm"/>
        <ip_qualid name="ofs"/>
       </ts_pos>
-      <ts_pos name="code" arity="0" id="5167"
+      <ts_pos name="code" arity="0" id="5180"
        ip_theory="Vm">
        <ip_library name="vm"/>
        <ip_qualid name="code"/>
       </ts_pos>
-      <ts_pos name="pred" arity="0" id="5555"
+      <ts_pos name="pred" arity="0" id="5568"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="pred"/>
       </ts_pos>
-      <ts_pos name="rel" arity="0" id="5556"
+      <ts_pos name="rel" arity="0" id="5569"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="rel"/>
       </ts_pos>
-      <ts_pos name="pre" arity="1" id="5557"
+      <ts_pos name="pre" arity="1" id="5570"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="pre"/>
       </ts_pos>
-      <ts_pos name="post" arity="1" id="5558"
+      <ts_pos name="post" arity="1" id="5571"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="post"/>
       </ts_pos>
-      <ts_pos name="wp_trans" arity="1" id="5565"
+      <ts_pos name="wp_trans" arity="1" id="5578"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="wp_trans"/>
       </ts_pos>
-      <ts_pos name="binop" arity="0" id="6259"
+      <ts_pos name="binop" arity="0" id="6272"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="binop"/>
       </ts_pos>
-      <ts_pos name="cond" arity="0" id="6639"
+      <ts_pos name="cond" arity="0" id="6652"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="cond"/>
@@ -2201,224 +2201,224 @@
        <ip_library name="int"/>
        <ip_qualid name="mod"/>
       </ls_pos>
-      <ls_pos name="mem" id="2786"
+      <ls_pos name="mem" id="2799"
        ip_theory="Mem">
        <ip_library name="list"/>
        <ip_qualid name="mem"/>
       </ls_pos>
-      <ls_pos name="orb" id="3872"
+      <ls_pos name="orb" id="3885"
        ip_theory="Bool">
        <ip_library name="bool"/>
        <ip_qualid name="orb"/>
       </ls_pos>
-      <ls_pos name="xorb" id="3886"
+      <ls_pos name="xorb" id="3899"
        ip_theory="Bool">
        <ip_library name="bool"/>
        <ip_qualid name="xorb"/>
       </ls_pos>
-      <ls_pos name="implb" id="3895"
+      <ls_pos name="implb" id="3908"
        ip_theory="Bool">
        <ip_library name="bool"/>
        <ip_qualid name="implb"/>
       </ls_pos>
-      <ls_pos name="get" id="4831"
+      <ls_pos name="get" id="4844"
        ip_theory="State">
        <ip_library name="state"/>
        <ip_qualid name="get"/>
       </ls_pos>
-      <ls_pos name="set" id="4832"
+      <ls_pos name="set" id="4845"
        ip_theory="State">
        <ip_library name="state"/>
        <ip_qualid name="set"/>
       </ls_pos>
-      <ls_pos name="ihalt" id="5249"
+      <ls_pos name="ihalt" id="5262"
        ip_theory="Vm">
        <ip_library name="vm"/>
        <ip_qualid name="ihalt"/>
       </ls_pos>
-      <ls_pos name="vm_terminates" id="5500"
+      <ls_pos name="vm_terminates" id="5513"
        ip_theory="Vm">
        <ip_library name="vm"/>
        <ip_qualid name="vm_terminates"/>
       </ls_pos>
-      <ls_pos name="fst" id="5520"
+      <ls_pos name="fst" id="5533"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="fst"/>
       </ls_pos>
-      <ls_pos name="snd" id="5539"
+      <ls_pos name="snd" id="5552"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="snd"/>
       </ls_pos>
-      <ls_pos name="trivial_pre" id="5875"
+      <ls_pos name="trivial_pre" id="5888"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="trivial_pre"/>
       </ls_pos>
-      <ls_pos name="acc" id="5904"
+      <ls_pos name="acc" id="5917"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="acc"/>
       </ls_pos>
-      <ls_pos name="loop_progress" id="5918"
+      <ls_pos name="loop_progress" id="5931"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="loop_progress"/>
       </ls_pos>
-      <ls_pos name="forget_old" id="5954"
+      <ls_pos name="forget_old" id="5967"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="forget_old"/>
       </ls_pos>
-      <ls_pos name="ifun_post" id="6004"
+      <ls_pos name="ifun_post" id="6017"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="ifun_post"/>
       </ls_pos>
-      <ls_pos name="iconst_post" id="6057"
+      <ls_pos name="iconst_post" id="6070"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="iconst_post"/>
       </ls_pos>
-      <ls_pos name="iconst_fun" id="6091"
+      <ls_pos name="iconst_fun" id="6104"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="iconst_fun"/>
       </ls_pos>
-      <ls_pos name="ivar_post" id="6158"
+      <ls_pos name="ivar_post" id="6171"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="ivar_post"/>
       </ls_pos>
-      <ls_pos name="ivar_fun" id="6192"
+      <ls_pos name="ivar_fun" id="6205"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="ivar_fun"/>
       </ls_pos>
-      <ls_pos name="ibinop_pre" id="6260"
+      <ls_pos name="ibinop_pre" id="6273"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="ibinop_pre"/>
       </ls_pos>
-      <ls_pos name="ibinop_post" id="6293"
+      <ls_pos name="ibinop_post" id="6306"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="ibinop_post"/>
       </ls_pos>
-      <ls_pos name="ibinop_fun" id="6335"
+      <ls_pos name="ibinop_fun" id="6348"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="ibinop_fun"/>
       </ls_pos>
-      <ls_pos name="plus" id="6434"
+      <ls_pos name="plus" id="6447"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="plus"/>
       </ls_pos>
-      <ls_pos name="sub" id="6447"
+      <ls_pos name="sub" id="6460"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="sub"/>
       </ls_pos>
-      <ls_pos name="mul" id="6460"
+      <ls_pos name="mul" id="6473"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="mul"/>
       </ls_pos>
-      <ls_pos name="inil_post" id="6506"
+      <ls_pos name="inil_post" id="6519"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="inil_post"/>
       </ls_pos>
-      <ls_pos name="ibranch_post" id="6538"
+      <ls_pos name="ibranch_post" id="6551"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="ibranch_post"/>
       </ls_pos>
-      <ls_pos name="ibranch_fun" id="6572"
+      <ls_pos name="ibranch_fun" id="6585"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="ibranch_fun"/>
       </ls_pos>
-      <ls_pos name="icjump_post" id="6640"
+      <ls_pos name="icjump_post" id="6653"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="icjump_post"/>
       </ls_pos>
-      <ls_pos name="icjump_fun" id="6687"
+      <ls_pos name="icjump_fun" id="6700"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="icjump_fun"/>
       </ls_pos>
-      <ls_pos name="beq" id="6794"
+      <ls_pos name="beq" id="6807"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="beq"/>
       </ls_pos>
-      <ls_pos name="bne" id="6807"
+      <ls_pos name="bne" id="6820"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="bne"/>
       </ls_pos>
-      <ls_pos name="ble" id="6820"
+      <ls_pos name="ble" id="6833"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="ble"/>
       </ls_pos>
-      <ls_pos name="bgt" id="6833"
+      <ls_pos name="bgt" id="6846"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="bgt"/>
       </ls_pos>
-      <ls_pos name="isetvar_pre" id="6902"
+      <ls_pos name="isetvar_pre" id="6915"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="isetvar_pre"/>
       </ls_pos>
-      <ls_pos name="isetvar_post" id="6931"
+      <ls_pos name="isetvar_post" id="6944"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="isetvar_post"/>
       </ls_pos>
-      <ls_pos name="isetvar_fun" id="6969"
+      <ls_pos name="isetvar_fun" id="6982"
        ip_theory="VM_instr_spec">
        <ip_library name="specs"/>
        <ip_qualid name="isetvar_fun"/>
       </ls_pos>
-      <ls_pos name="aexpr_post" id="7046"
+      <ls_pos name="aexpr_post" id="7059"
        ip_theory="Compile_aexpr">
        <ip_qualid name="aexpr_post"/>
       </ls_pos>
-      <ls_pos name="bexpr_post" id="8714"
+      <ls_pos name="bexpr_post" id="8727"
        ip_theory="Compile_bexpr">
        <ip_qualid name="bexpr_post"/>
       </ls_pos>
-      <ls_pos name="exec_cond" id="8773"
+      <ls_pos name="exec_cond" id="8786"
        ip_theory="Compile_bexpr">
        <ip_qualid name="exec_cond"/>
       </ls_pos>
-      <ls_pos name="com_pre" id="10622"
+      <ls_pos name="com_pre" id="10635"
        ip_theory="Compile_com">
        <ip_qualid name="com_pre"/>
       </ls_pos>
-      <ls_pos name="com_post" id="10666"
+      <ls_pos name="com_post" id="10679"
        ip_theory="Compile_com">
        <ip_qualid name="com_post"/>
       </ls_pos>
-      <ls_pos name="exec_cond_old" id="10745"
+      <ls_pos name="exec_cond_old" id="10758"
        ip_theory="Compile_com">
        <ip_qualid name="exec_cond_old"/>
       </ls_pos>
-      <ls_pos name="loop_invariant" id="10784"
+      <ls_pos name="loop_invariant" id="10797"
        ip_theory="Compile_com">
        <ip_qualid name="loop_invariant"/>
       </ls_pos>
-      <ls_pos name="loop_post" id="10852"
+      <ls_pos name="loop_post" id="10865"
        ip_theory="Compile_com">
        <ip_qualid name="loop_post"/>
       </ls_pos>
-      <ls_pos name="loop_variant" id="10921"
+      <ls_pos name="loop_variant" id="10934"
        ip_theory="Compile_com">
        <ip_qualid name="loop_variant"/>
       </ls_pos>
@@ -2611,87 +2611,87 @@
        <ip_library name="int"/>
        <ip_qualid name="Mod_mult"/>
       </pr_pos>
-      <pr_pos name="Length_nonnegative" id="2779"
+      <pr_pos name="Length_nonnegative" id="2792"
        ip_theory="Length">
        <ip_library name="list"/>
        <ip_qualid name="Length_nonnegative"/>
       </pr_pos>
-      <pr_pos name="Length_nil" id="2782"
+      <pr_pos name="Length_nil" id="2795"
        ip_theory="Length">
        <ip_library name="list"/>
        <ip_qualid name="Length_nil"/>
       </pr_pos>
-      <pr_pos name="Append_assoc" id="4176"
+      <pr_pos name="Append_assoc" id="4189"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="Append_assoc"/>
       </pr_pos>
-      <pr_pos name="Append_l_nil" id="4183"
+      <pr_pos name="Append_l_nil" id="4196"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="Append_l_nil"/>
       </pr_pos>
-      <pr_pos name="Append_length" id="4186"
+      <pr_pos name="Append_length" id="4199"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="Append_length"/>
       </pr_pos>
-      <pr_pos name="mem_append" id="4191"
+      <pr_pos name="mem_append" id="4204"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="mem_append"/>
       </pr_pos>
-      <pr_pos name="mem_decomp" id="4198"
+      <pr_pos name="mem_decomp" id="4211"
        ip_theory="Append">
        <ip_library name="list"/>
        <ip_qualid name="mem_decomp"/>
       </pr_pos>
-      <pr_pos name="Select_eq" id="4857"
+      <pr_pos name="Select_eq" id="4870"
        ip_theory="State">
        <ip_library name="state"/>
        <ip_qualid name="Select_eq"/>
       </pr_pos>
-      <pr_pos name="Select_neq" id="4863"
+      <pr_pos name="Select_neq" id="4876"
        ip_theory="State">
        <ip_library name="state"/>
        <ip_qualid name="Select_neq"/>
       </pr_pos>
-      <pr_pos name="ceval_deterministic" id="5082"
+      <pr_pos name="ceval_deterministic" id="5095"
        ip_theory="Imp">
        <ip_library name="imp"/>
        <ip_qualid name="ceval_deterministic"/>
       </pr_pos>
-      <pr_pos name="codeseq_at_app_right" id="5179"
+      <pr_pos name="codeseq_at_app_right" id="5192"
        ip_theory="Vm">
        <ip_library name="vm"/>
        <ip_qualid name="codeseq_at_app_right"/>
       </pr_pos>
-      <pr_pos name="codeseq_at_app_left" id="5188"
+      <pr_pos name="codeseq_at_app_left" id="5201"
        ip_theory="Vm">
        <ip_library name="vm"/>
        <ip_qualid name="codeseq_at_app_left"/>
       </pr_pos>
-      <pr_pos name="transition_star_one" id="5484"
+      <pr_pos name="transition_star_one" id="5497"
        ip_theory="Vm">
        <ip_library name="vm"/>
        <ip_qualid name="transition_star_one"/>
       </pr_pos>
-      <pr_pos name="transition_star_transitive" id="5491"
+      <pr_pos name="transition_star_transitive" id="5504"
        ip_theory="Vm">
        <ip_library name="vm"/>
        <ip_qualid name="transition_star_transitive"/>
       </pr_pos>
-      <pr_pos name="seq_wp_lemma" id="5680"
+      <pr_pos name="seq_wp_lemma" id="5693"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="seq_wp_lemma"/>
       </pr_pos>
-      <pr_pos name="fork_wp_lemma" id="5764"
+      <pr_pos name="fork_wp_lemma" id="5777"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="fork_wp_lemma"/>
       </pr_pos>
-      <pr_pos name="towp_wp_lemma" id="5828"
+      <pr_pos name="towp_wp_lemma" id="5841"
        ip_theory="Compiler_logic">
        <ip_library name="logic"/>
        <ip_qualid name="towp_wp_lemma"/>
@@ -2736,73 +2736,70 @@
        <meta_arg_ls id="2151"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="2786"/>
+       <meta_arg_ls id="2799"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3872"/>
+       <meta_arg_ls id="3885"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3886"/>
+       <meta_arg_ls id="3899"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="3895"/>
+       <meta_arg_ls id="3908"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4831"/>
+       <meta_arg_ls id="4844"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="4832"/>
+       <meta_arg_ls id="4845"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5249"/>
+       <meta_arg_ls id="5262"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5500"/>
+       <meta_arg_ls id="5513"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5520"/>
+       <meta_arg_ls id="5533"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5539"/>
+       <meta_arg_ls id="5552"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5875"/>
+       <meta_arg_ls id="5888"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5904"/>
+       <meta_arg_ls id="5917"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5918"/>
+       <meta_arg_ls id="5931"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="5954"/>
+       <meta_arg_ls id="5967"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6004"/>
+       <meta_arg_ls id="6017"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6057"/>
+       <meta_arg_ls id="6070"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6091"/>
+       <meta_arg_ls id="6104"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6158"/>
+       <meta_arg_ls id="6171"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6192"/>
+       <meta_arg_ls id="6205"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6260"/>
+       <meta_arg_ls id="6273"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6293"/>
+       <meta_arg_ls id="6306"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6335"/>
-      </meta>
-      <meta name="remove_logic">
-       <meta_arg_ls id="6434"/>
+       <meta_arg_ls id="6348"/>
       </meta>
       <meta name="remove_logic">
        <meta_arg_ls id="6447"/>
@@ -2811,22 +2808,22 @@
        <meta_arg_ls id="6460"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6506"/>
+       <meta_arg_ls id="6473"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6538"/>
+       <meta_arg_ls id="6519"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6572"/>
+       <meta_arg_ls id="6551"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6640"/>
+       <meta_arg_ls id="6585"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6687"/>
+       <meta_arg_ls id="6653"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6794"/>
+       <meta_arg_ls id="6700"/>
       </meta>
       <meta name="remove_logic">
        <meta_arg_ls id="6807"/>
@@ -2838,40 +2835,43 @@
        <meta_arg_ls id="6833"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6902"/>
+       <meta_arg_ls id="6846"/>
+      </meta>
+      <meta name="remove_logic">
+       <meta_arg_ls id="6915"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6931"/>
+       <meta_arg_ls id="6944"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="6969"/>
+       <meta_arg_ls id="6982"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="7046"/>
+       <meta_arg_ls id="7059"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="8714"/>
+       <meta_arg_ls id="8727"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="8773"/>
+       <meta_arg_ls id="8786"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="10622"/>
+       <meta_arg_ls id="10635"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="10666"/>
+       <meta_arg_ls id="10679"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="10745"/>
+       <meta_arg_ls id="10758"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="10784"/>
+       <meta_arg_ls id="10797"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="10852"/>
+       <meta_arg_ls id="10865"/>
       </meta>
       <meta name="remove_logic">
-       <meta_arg_ls id="10921"/>
+       <meta_arg_ls id="10934"/>
       </meta>
       <meta name="remove_prop">
        <meta_arg_pr id="1911"/>
@@ -2982,55 +2982,55 @@
        <meta_arg_pr id="2214"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2779"/>
+       <meta_arg_pr id="2792"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="2782"/>
+       <meta_arg_pr id="2795"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4176"/>
+       <meta_arg_pr id="4189"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4183"/>
+       <meta_arg_pr id="4196"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4186"/>
+       <meta_arg_pr id="4199"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4191"/>
+       <meta_arg_pr id="4204"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4198"/>
+       <meta_arg_pr id="4211"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4857"/>
+       <meta_arg_pr id="4870"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="4863"/>
+       <meta_arg_pr id="4876"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5082"/>
+       <meta_arg_pr id="5095"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5179"/>
+       <meta_arg_pr id="5192"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5188"/>
+       <meta_arg_pr id="5201"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5484"/>
+       <meta_arg_pr id="5497"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5491"/>
+       <meta_arg_pr id="5504"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5680"/>
+       <meta_arg_pr id="5693"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5764"/>
+       <meta_arg_pr id="5777"/>
       </meta>
       <meta name="remove_prop">
-       <meta_arg_pr id="5828"/>
+       <meta_arg_pr id="5841"/>
       </meta>
       <meta name="remove_type">
        <meta_arg_ts id="2"/>
@@ -3048,40 +3048,40 @@
        <meta_arg_ts id="68"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="4871"/>
+       <meta_arg_ts id="4884"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5149"/>
+       <meta_arg_ts id="5162"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5150"/>
+       <meta_arg_ts id="5163"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5153"/>
+       <meta_arg_ts id="5166"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5167"/>
+       <meta_arg_ts id="5180"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5555"/>
+       <meta_arg_ts id="5568"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5556"/>
+       <meta_arg_ts id="5569"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5557"/>
+       <meta_arg_ts id="5570"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5558"/>
+       <meta_arg_ts id="5571"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="5565"/>
+       <meta_arg_ts id="5578"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="6259"/>
+       <meta_arg_ts id="6272"/>
       </meta>
       <meta name="remove_type">
-       <meta_arg_ts id="6639"/>
+       <meta_arg_ts id="6652"/>
       </meta>
       <goal name="WP_parameter compile_com.45.1.1.6" expl="VC for compile_com">
       <transf name="eliminate_builtin">
@@ -3109,7 +3109,7 @@
   <proof prover="2"><result status="valid" time="0.12" steps="40"/></proof>
   </goal>
   <goal name="WP_parameter compile_com.47" expl="precondition">
-  <proof prover="7" edited="compiler_Compile_com_WP_parameter_compile_com_1.v"><result status="valid" time="1.76"/></proof>
+  <proof prover="4" edited="compiler_Compile_com_WP_parameter_compile_com_1.v"><result status="valid" time="1.76"/></proof>
   </goal>
   <goal name="WP_parameter compile_com.48" expl="precondition">
   <proof prover="2"><result status="valid" time="0.14" steps="40"/></proof>
diff --git a/examples/edit_distance/why3session.xml b/examples/edit_distance/why3session.xml
index 8f826c81c5b7b93a37c33144f4552bc931d6d6b8..361ae67f85b3ef7b12778a5609330bb415bccef1 100644
--- a/examples/edit_distance/why3session.xml
+++ b/examples/edit_distance/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="6" steplimit="0" memlimit="1000"/>
 <prover id="3" name="Z3" version="2.19" timelimit="6" steplimit="0" memlimit="1000"/>
 <prover id="4" name="Z3" version="4.3.1" timelimit="6" steplimit="0" memlimit="1000"/>
@@ -21,10 +21,10 @@
  </transf>
  </goal>
  <goal name="first_last" expl="">
- <proof prover="1" edited="edit_distance_Word_first_last_1.v"><result status="valid" time="0.30"/></proof>
+ <proof prover="0" edited="edit_distance_Word_first_last_1.v"><result status="valid" time="0.30"/></proof>
  </goal>
  <goal name="key_lemma_right" expl="">
- <proof prover="1" edited="edit_distance_Word_key_lemma_right_1.v"><result status="valid" time="0.31"/></proof>
+ <proof prover="0" edited="edit_distance_Word_key_lemma_right_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
  <goal name="dist_symetry" expl="">
  <transf name="induction_pr">
@@ -93,7 +93,7 @@
  </transf>
  </goal>
  <goal name="min_dist_diff" expl="">
- <proof prover="1" edited="edit_distance_Word_min_dist_diff_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="0" edited="edit_distance_Word_min_dist_diff_1.v"><result status="valid" time="0.33"/></proof>
  </goal>
  <goal name="min_dist_eps" expl="">
  <transf name="inline_goal">
@@ -140,7 +140,7 @@
 </theory>
 <theory name="EditDistance" sum="d8e87fc0ce1b354c78e698b47d0dfe31" expanded="true">
  <goal name="suffix_length" expl="">
- <proof prover="1" timelimit="20" edited="edit_distance_WP_EditDistance_suffix_length_1.v"><result status="valid" time="0.41"/></proof>
+ <proof prover="0" timelimit="20" edited="edit_distance_WP_EditDistance_suffix_length_1.v"><result status="valid" time="0.41"/></proof>
  </goal>
  <goal name="WP_parameter distance" expl="VC for distance">
  <transf name="split_goal_wp">
@@ -301,7 +301,7 @@
   <proof prover="9"><result status="valid" time="0.02" steps="18"/></proof>
   </goal>
   <goal name="WP_parameter distance.52" expl="loop invariant preservation">
-  <proof prover="1" timelimit="5" memlimit="1000" edited="edit_distance_WP_EditDistance_WP_parameter_distance_2.v"><result status="valid" time="0.50"/></proof>
+  <proof prover="0" timelimit="5" memlimit="1000" edited="edit_distance_WP_EditDistance_WP_parameter_distance_2.v"><result status="valid" time="0.50"/></proof>
   </goal>
   <goal name="WP_parameter distance.53" expl="loop invariant preservation">
   <proof prover="9"><result status="valid" time="0.02" steps="28"/></proof>
@@ -319,7 +319,7 @@
   <proof prover="9"><result status="valid" time="0.02" steps="20"/></proof>
   </goal>
   <goal name="WP_parameter distance.58" expl="loop invariant preservation">
-  <proof prover="1" timelimit="5" memlimit="1000" edited="edit_distance_WP_EditDistance_WP_parameter_distance_1.v"><result status="valid" time="0.50"/></proof>
+  <proof prover="0" timelimit="5" memlimit="1000" edited="edit_distance_WP_EditDistance_WP_parameter_distance_1.v"><result status="valid" time="0.50"/></proof>
   </goal>
   <goal name="WP_parameter distance.59" expl="loop invariant preservation">
   <proof prover="9"><result status="valid" time="0.02" steps="30"/></proof>
diff --git a/examples/euler001/why3session.xml b/examples/euler001/why3session.xml
index a0dffea1e4b2e67210ec8bfe3b3ce4efa351fc28..84f964b533e1f21eb20068682711e7e88aa4798b 100644
--- a/examples/euler001/why3session.xml
+++ b/examples/euler001/why3session.xml
@@ -2,20 +2,20 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="30" steplimit="0" memlimit="1000"/>
 <prover id="2" name="Z3" version="3.2" timelimit="30" steplimit="0" memlimit="1000"/>
 <prover id="3" name="Alt-Ergo" version="0.95.2" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="4" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="0"/>
 <file name="../euler001.mlw" expanded="true">
 <theory name="DivModHints" sum="6f77cd46f4f6ca514a80124063f6a33c">
  <goal name="mod_div_unique" expl="">
- <proof prover="4" edited="euler001_DivModHints_mod_div_unique_1.v"><result status="valid" time="0.34"/></proof>
+ <proof prover="0" edited="euler001_DivModHints_mod_div_unique_1.v"><result status="valid" time="0.34"/></proof>
  </goal>
  <goal name="mod_succ_1" expl="">
- <proof prover="4" edited="euler001_DivModHints_mod_succ_1_1.v"><result status="valid" time="0.40"/></proof>
+ <proof prover="0" edited="euler001_DivModHints_mod_succ_1_1.v"><result status="valid" time="0.40"/></proof>
  </goal>
  <goal name="mod_succ_2" expl="">
- <proof prover="4" edited="euler001_DivModHints_mod_succ_2_1.v"><result status="valid" time="0.37"/></proof>
+ <proof prover="0" edited="euler001_DivModHints_mod_succ_2_1.v"><result status="valid" time="0.37"/></proof>
  </goal>
  <goal name="div_succ_1" expl="">
  <proof prover="1"><result status="valid" time="0.04"/></proof>
@@ -61,7 +61,7 @@
 </theory>
 <theory name="TriangularNumbers" sum="5dd3402674ce736b7bf98870de3440c5">
  <goal name="tr_mod_2" expl="">
- <proof prover="4" memlimit="1000" edited="euler001_TriangularNumbers_tr_mod_2_1.v"><result status="valid" time="0.31"/></proof>
+ <proof prover="0" memlimit="1000" edited="euler001_TriangularNumbers_tr_mod_2_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
  <goal name="tr_repr" expl="">
  <proof prover="2" timelimit="5"><result status="valid" time="0.02"/></proof>
@@ -115,7 +115,7 @@
  <proof prover="3"><result status="valid" time="0.01" steps="7"/></proof>
  </goal>
  <goal name="Closed_Formula" expl="">
- <proof prover="4" timelimit="30" memlimit="1000" edited="euler001_SumMultiple_Closed_Formula_1.v"><result status="valid" time="0.36"/></proof>
+ <proof prover="0" timelimit="30" memlimit="1000" edited="euler001_SumMultiple_Closed_Formula_1.v"><result status="valid" time="0.36"/></proof>
  </goal>
 </theory>
 <theory name="Euler001" sum="ac5e739bc4723e5c8ba7bae0a1b7655c">
diff --git a/examples/fibonacci/why3session.xml b/examples/fibonacci/why3session.xml
index 28dc49c3087394e42c75c0ec8eb4054009e7fe55..3ec7e59b6461d7f9ef77cc6bb8d34fb5f2d98b6d 100644
--- a/examples/fibonacci/why3session.xml
+++ b/examples/fibonacci/why3session.xml
@@ -2,9 +2,9 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="1" name="Alt-Ergo" version="1.30" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="4000"/>
-<prover id="3" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="4" name="Spass" version="3.7" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="7" name="Vampire" version="0.6" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="8" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -455,12 +455,12 @@
   <proof prover="1"><result status="valid" time="0.00" steps="5"/></proof>
   </goal>
   <goal name="WP_parameter logfib.4" expl="postcondition">
-  <proof prover="3" edited="fibonacci_WP_FibonacciLogarithmic_WP_parameter_logfib_1.v"><result status="valid" time="0.47"/></proof>
+  <proof prover="0" edited="fibonacci_WP_FibonacciLogarithmic_WP_parameter_logfib_1.v"><result status="valid" time="0.47"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="fib_m" expl="">
- <proof prover="3" edited="fibonacci_WP_FibonacciLogarithmic_fib_m_1.v"><result status="valid" time="0.40"/></proof>
+ <proof prover="0" edited="fibonacci_WP_FibonacciLogarithmic_fib_m_1.v"><result status="valid" time="0.40"/></proof>
  </goal>
  <goal name="WP_parameter fibo" expl="VC for fibo">
  <proof prover="1"><result status="valid" time="0.00" steps="6"/></proof>
diff --git a/examples/find/why3session.xml b/examples/find/why3session.xml
index 3bd158c1482f1ff7b2a0f2313f2d3241e12c0a61..3483c271b9f6eafe33e86c3c2f6655072370a287 100644
--- a/examples/find/why3session.xml
+++ b/examples/find/why3session.xml
@@ -2,8 +2,8 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="10" steplimit="0" memlimit="0"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="1000"/>
 <prover id="4" name="Alt-Ergo" version="0.99.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="6" name="Z3" version="4.3.2" timelimit="10" steplimit="0" memlimit="0"/>
 <file name="../find.mlw" expanded="true">
@@ -111,7 +111,7 @@
   <proof prover="4"><result status="valid" time="0.02" steps="42"/></proof>
   </goal>
   <goal name="WP_parameter find.22" expl="loop invariant preservation" expanded="true">
-  <proof prover="2" edited="find_WP_FIND_WP_parameter_find_4.v"><result status="valid" time="3.39"/></proof>
+  <proof prover="0" edited="find_WP_FIND_WP_parameter_find_4.v"><result status="valid" time="3.39"/></proof>
   </goal>
   <goal name="WP_parameter find.23" expl="loop variant decrease">
   <proof prover="4"><result status="valid" time="0.03" steps="45"/></proof>
diff --git a/examples/flag2/why3session.xml b/examples/flag2/why3session.xml
index 17cc586ed3d03cdad96e461adf618a84713ca7b4..dba9b4a5e717508488b54d2912c438f47c586bdc 100644
--- a/examples/flag2/why3session.xml
+++ b/examples/flag2/why3session.xml
@@ -2,18 +2,18 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="0" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="3" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="7" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="8" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../flag2.mlw" expanded="true">
 <theory name="Flag" sum="c6c2d27200bbbebb61772d0010cf5945" expanded="true">
  <goal name="nb_occ_split" expl="">
- <proof prover="0" edited="flag2_WP_Flag_nb_occ_split_1.v"><result status="valid" time="0.50"/></proof>
+ <proof prover="3" edited="flag2_WP_Flag_nb_occ_split_1.v"><result status="valid" time="0.79"/></proof>
  </goal>
  <goal name="nb_occ_ext" expl="">
- <proof prover="0" edited="flag2_Flag_nb_occ_ext_1.v"><result status="valid" time="0.25"/></proof>
+ <proof prover="3" edited="flag2_Flag_nb_occ_ext_1.v"><result status="valid" time="0.41"/></proof>
  </goal>
  <goal name="nb_occ_store_outside_up" expl="">
  <proof prover="1"><result status="valid" time="0.01"/></proof>
@@ -30,7 +30,7 @@
  <proof prover="8"><result status="valid" time="0.00" steps="5"/></proof>
  </goal>
  <goal name="nb_occ_store_eq_neq" expl="">
- <proof prover="0" timelimit="10" edited="flag2_WP_Flag_nb_occ_store_eq_neq_1.v"><result status="valid" time="1.40"/></proof>
+ <proof prover="3" timelimit="10" edited="flag2_WP_Flag_nb_occ_store_eq_neq_1.v"><result status="valid" time="1.40"/></proof>
  </goal>
  <goal name="nb_occ_store_neq_eq" expl="">
  <proof prover="7"><result status="valid" time="0.14"/></proof>
diff --git a/examples/foveoos11-cm/tree_max/why3session.xml b/examples/foveoos11-cm/tree_max/why3session.xml
index 7e09f6cb8f14b4d3dfe4d6f91ac5b56fa545be56..d69a37c0dbac1d283da5ef11f740b790413ecb61 100644
--- a/examples/foveoos11-cm/tree_max/why3session.xml
+++ b/examples/foveoos11-cm/tree_max/why3session.xml
@@ -2,12 +2,12 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="2" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="0"/>
 <file name="../tree_max.mlw" expanded="true">
 <theory name="BinTree" sum="3c0f973f96955032b99ccca24e3d7bec" expanded="true">
  <goal name="ge_trans" expl="" expanded="true">
- <proof prover="1" edited="tree_max_BinTree_ge_trans_1.v"><result status="valid" time="0.32"/></proof>
+ <proof prover="0" edited="tree_max_BinTree_ge_trans_1.v"><result status="valid" time="0.32"/></proof>
  </goal>
 </theory>
 <theory name="TreeMax" sum="d62eee5e2db38e36ed33ab715c6bb7b4" expanded="true">
diff --git a/examples/foveoos11_challenge2/why3session.xml b/examples/foveoos11_challenge2/why3session.xml
index fb2a06167bc44a17a1258cf251df9b12833f48f6..f065220611511d3d19b5a320019248a64ffad119 100644
--- a/examples/foveoos11_challenge2/why3session.xml
+++ b/examples/foveoos11_challenge2/why3session.xml
@@ -2,12 +2,12 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="2" name="Alt-Ergo" version="0.99.1" timelimit="10" steplimit="0" memlimit="0"/>
 <file name="../foveoos11_challenge2.mlw" expanded="true">
 <theory name="MaximumTree" sum="b84d6018d5f0503e635dc5c6b11bd979" expanded="true">
  <goal name="size_nonneg" expl="" expanded="true">
- <proof prover="1" edited="foveoos11_challenge2_WP_MaximumTree_size_nonneg_1.v"><result status="valid" time="0.30"/></proof>
+ <proof prover="0" edited="foveoos11_challenge2_WP_MaximumTree_size_nonneg_1.v"><result status="valid" time="0.30"/></proof>
  </goal>
  <goal name="WP_parameter maximum" expl="VC for maximum" expanded="true">
  <proof prover="2"><result status="valid" time="0.56" steps="812"/></proof>
diff --git a/examples/foveoos11_challenge3/why3session.xml b/examples/foveoos11_challenge3/why3session.xml
index 9962625c4283fc7e37cd8943fde8d6e7e30bdcdd..06320b8932dfb488ab42ff43688f75b913b2eb07 100644
--- a/examples/foveoos11_challenge3/why3session.xml
+++ b/examples/foveoos11_challenge3/why3session.xml
@@ -2,8 +2,8 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="15" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="15" steplimit="0" memlimit="1000"/>
 <prover id="4" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../foveoos11_challenge3.mlw" expanded="true">
 <theory name="TwoEqualElements" sum="424177d437408534f82651a9345d18ad" expanded="true">
@@ -49,7 +49,7 @@
   <proof prover="4"><result status="valid" time="0.01" steps="21"/></proof>
   </goal>
   <goal name="WP_parameter two_equal_elements.14" expl="loop invariant preservation">
-  <proof prover="2" edited="foveoos11_challenge3_WP_TwoEqualElements_WP_parameter_two_equal_elements_1.v"><result status="valid" time="12.18"/></proof>
+  <proof prover="0" edited="foveoos11_challenge3_WP_TwoEqualElements_WP_parameter_two_equal_elements_1.v"><result status="valid" time="7.06"/></proof>
   </goal>
   <goal name="WP_parameter two_equal_elements.15" expl="loop invariant preservation">
   <proof prover="4"><result status="valid" time="0.03" steps="21"/></proof>
@@ -85,7 +85,7 @@
   <proof prover="4"><result status="valid" time="0.01" steps="22"/></proof>
   </goal>
   <goal name="WP_parameter two_equal_elements.26" expl="loop invariant preservation">
-  <proof prover="2" edited="foveoos11_challenge3_WP_TwoEqualElements_WP_parameter_two_equal_elements_2.v"><result status="valid" time="2.22"/></proof>
+  <proof prover="0" edited="foveoos11_challenge3_WP_TwoEqualElements_WP_parameter_two_equal_elements_2.v"><result status="valid" time="1.43"/></proof>
   </goal>
   <goal name="WP_parameter two_equal_elements.27" expl="loop invariant preservation">
   <proof prover="4"><result status="valid" time="0.04" steps="21"/></proof>
@@ -121,10 +121,10 @@
   <proof prover="4"><result status="valid" time="0.14" steps="120"/></proof>
   </goal>
   <goal name="WP_parameter two_equal_elements.38" expl="loop invariant preservation">
-  <proof prover="2" edited="foveoos11_challenge3_WP_TwoEqualElements_WP_parameter_two_equal_elements_3.v"><result status="valid" time="2.51"/></proof>
+  <proof prover="0" edited="foveoos11_challenge3_WP_TwoEqualElements_WP_parameter_two_equal_elements_3.v"><result status="valid" time="2.15"/></proof>
   </goal>
   <goal name="WP_parameter two_equal_elements.39" expl="loop invariant preservation">
-  <proof prover="2" edited="foveoos11_challenge3_WP_TwoEqualElements_WP_parameter_two_equal_elements_4.v"><result status="valid" time="10.59"/></proof>
+  <proof prover="0" edited="foveoos11_challenge3_WP_TwoEqualElements_WP_parameter_two_equal_elements_4.v"><result status="valid" time="7.12"/></proof>
   </goal>
   <goal name="WP_parameter two_equal_elements.40" expl="postcondition">
   <transf name="split_goal_wp">
diff --git a/examples/gcd/why3session.xml b/examples/gcd/why3session.xml
index 4b1dcaf7762c4c3c82a121271f19e62a3bf06658..ca58e70df80c767ef6b5b7e9280decdb542ae178 100644
--- a/examples/gcd/why3session.xml
+++ b/examples/gcd/why3session.xml
@@ -2,6 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="10" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC4" version="1.4" timelimit="10" steplimit="0" memlimit="1000"/>
 <prover id="3" name="Z3" version="4.3.1" timelimit="6" steplimit="0" memlimit="1000"/>
@@ -9,7 +10,6 @@
 <prover id="5" name="Alt-Ergo" version="0.95.2" timelimit="6" steplimit="0" memlimit="1000"/>
 <prover id="6" name="CVC4" version="1.3" timelimit="6" steplimit="0" memlimit="1000"/>
 <prover id="7" name="Alt-Ergo" version="0.99.1" timelimit="6" steplimit="0" memlimit="1000"/>
-<prover id="8" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../gcd.mlw" expanded="true">
 <theory name="EuclideanAlgorithm" sum="be2015934b1733ec15064dd0125ec72f">
  <goal name="WP_parameter euclid" expl="VC for euclid">
@@ -30,9 +30,9 @@
   <proof prover="5" timelimit="10" memlimit="0"><result status="valid" time="0.02" steps="7"/></proof>
   </goal>
   <goal name="WP_parameter euclid.5" expl="postcondition">
+  <proof prover="0" timelimit="10" edited="gcd_WP_EuclideanAlgorithm_WP_parameter_gcd_1.v"><result status="valid" time="0.28"/></proof>
   <proof prover="2"><result status="valid" time="0.03"/></proof>
   <proof prover="5" timelimit="10"><result status="valid" time="0.04" steps="13"/></proof>
-  <proof prover="8" timelimit="10" edited="gcd_WP_EuclideanAlgorithm_WP_parameter_gcd_1.v"><result status="valid" time="0.28"/></proof>
   </goal>
  </transf>
  </goal>
@@ -76,7 +76,7 @@
  <proof prover="5"><result status="valid" time="0.03" steps="28"/></proof>
  </goal>
  <goal name="gcd_even_odd" expl="">
- <proof prover="8" edited="gcd_BinaryGcd_gcd_even_odd_2.v"><result status="valid" time="0.28"/></proof>
+ <proof prover="0" edited="gcd_BinaryGcd_gcd_even_odd_2.v"><result status="valid" time="0.28"/></proof>
  </goal>
  <goal name="gcd_even_odd2" expl="">
  <proof prover="5"><result status="valid" time="0.17" steps="28"/></proof>
diff --git a/examples/generate_all_trees/why3session.xml b/examples/generate_all_trees/why3session.xml
index ab4096f3adad8c8cc69265e0302037f822053ac7..83e4e282d5a3059dde3d73fe7c6e05b8c84b6643 100644
--- a/examples/generate_all_trees/why3session.xml
+++ b/examples/generate_all_trees/why3session.xml
@@ -2,6 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="1" name="Eprover" version="1.6" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -10,17 +11,16 @@
 <prover id="6" name="CVC3" version="2.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="7" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="8" name="Alt-Ergo" version="0.95.2" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="9" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
 <file name="../generate_all_trees.mlw" expanded="true">
 <theory name="GenerateAllTrees" sum="74df2f00d9dca900f8ace0afd56f044e" expanded="true">
  <goal name="size_nonneg" expl="" expanded="true">
- <proof prover="9" edited="generate_all_trees_WP_GenerateAllTrees_size_nonneg_1.v"><result status="valid" time="0.29"/></proof>
+ <proof prover="0" edited="generate_all_trees_WP_GenerateAllTrees_size_nonneg_1.v"><result status="valid" time="0.29"/></proof>
  </goal>
  <goal name="size_left" expl="" expanded="true">
  <proof prover="7"><result status="valid" time="0.14"/></proof>
  </goal>
  <goal name="all_trees_0" expl="" expanded="true">
- <proof prover="9" edited="generate_all_trees_WP_GenerateAllTrees_all_trees_0_1.v"><result status="valid" time="0.31"/></proof>
+ <proof prover="0" edited="generate_all_trees_WP_GenerateAllTrees_all_trees_0_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
  <goal name="tree_diff" expl="" expanded="true">
  <proof prover="8" timelimit="10" memlimit="0"><result status="valid" time="0.02" steps="9"/></proof>
@@ -52,9 +52,9 @@
   <goal name="WP_parameter combine.8" expl="postcondition" expanded="true">
   <transf name="split_goal_wp" expanded="true">
    <goal name="WP_parameter combine.8.1" expl="postcondition" expanded="true">
+   <proof prover="0" edited="generate_all_trees_WP_GenerateAllTrees_WP_parameter_combine_2.v"><result status="valid" time="0.33"/></proof>
    <proof prover="1"><result status="valid" time="0.01"/></proof>
    <proof prover="5"><result status="valid" time="0.09"/></proof>
-   <proof prover="9" edited="generate_all_trees_WP_GenerateAllTrees_WP_parameter_combine_2.v"><result status="valid" time="0.33"/></proof>
    </goal>
    <goal name="WP_parameter combine.8.2" expl="postcondition" expanded="true">
    <proof prover="8" timelimit="10" memlimit="0"><result status="valid" time="0.84" steps="1582"/></proof>
diff --git a/examples/hashtbl_impl/why3session.xml b/examples/hashtbl_impl/why3session.xml
index 0cdc5950f9dc7e7e00b518b09a61c2fb9c914043..3ad97fe6464a3ef0d4ef3237c0664dbd93a57fbf 100644
--- a/examples/hashtbl_impl/why3session.xml
+++ b/examples/hashtbl_impl/why3session.xml
@@ -5,7 +5,7 @@
 <prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="3" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="7" name="Z3" version="4.3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../hashtbl_impl.mlw" expanded="true">
 <theory name="HashtblImpl" sum="b788abe182377734cabd9f4f015151af" expanded="true">
@@ -149,7 +149,7 @@
   <proof prover="0"><result status="valid" time="0.02" steps="17"/></proof>
   </goal>
   <goal name="WP_parameter find.2" expl="postcondition">
-  <proof prover="3" edited="hashtbl_impl_HashtblImpl_WP_parameter_find_1.v"><result status="valid" time="0.34"/></proof>
+  <proof prover="4" edited="hashtbl_impl_HashtblImpl_WP_parameter_find_1.v"><result status="valid" time="0.34"/></proof>
   </goal>
  </transf>
  </goal>
@@ -180,7 +180,7 @@
   <proof prover="7"><result status="valid" time="0.08"/></proof>
   </goal>
   <goal name="WP_parameter remove.2" expl="postcondition">
-  <proof prover="3" edited="hashtbl_impl_HashtblImpl_WP_parameter_remove_2.v"><result status="valid" time="0.35"/></proof>
+  <proof prover="4" edited="hashtbl_impl_HashtblImpl_WP_parameter_remove_2.v"><result status="valid" time="0.35"/></proof>
   </goal>
   <goal name="WP_parameter remove.3" expl="index in array bounds">
   <proof prover="0"><result status="valid" time="0.06" steps="5"/></proof>
@@ -236,7 +236,7 @@
   <proof prover="1"><result status="valid" time="0.08"/></proof>
   </goal>
   <goal name="WP_parameter add.4" expl="type invariant">
-  <proof prover="3" edited="hashtbl_impl_HashtblImpl_WP_parameter_add_1.v"><result status="valid" time="2.74"/></proof>
+  <proof prover="4" edited="hashtbl_impl_HashtblImpl_WP_parameter_add_1.v"><result status="valid" time="2.74"/></proof>
   </goal>
   <goal name="WP_parameter add.5" expl="type invariant">
   <transf name="inline_all">
diff --git a/examples/insertion_sort/why3session.xml b/examples/insertion_sort/why3session.xml
index f09bae3ac7c9b360a3e7de9f34d8e7bded74291c..b1f983246b1fb25f62f50d469993659ea2b8f0d3 100644
--- a/examples/insertion_sort/why3session.xml
+++ b/examples/insertion_sort/why3session.xml
@@ -2,8 +2,8 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="1000"/>
 <prover id="6" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="7" name="Z3" version="3.2" timelimit="10" steplimit="0" memlimit="0"/>
 <file name="../insertion_sort.mlw" expanded="true">
@@ -55,7 +55,7 @@
   <proof prover="6"><result status="valid" time="0.00" steps="17"/></proof>
   </goal>
   <goal name="WP_parameter insertion_sort.15" expl="loop invariant preservation">
-  <proof prover="2" edited="insertion_sort_WP_InsertionSort_WP_parameter_insertion_sort_1.v"><result status="valid" time="0.30"/></proof>
+  <proof prover="0" edited="insertion_sort_WP_InsertionSort_WP_parameter_insertion_sort_1.v"><result status="valid" time="0.30"/></proof>
   </goal>
   <goal name="WP_parameter insertion_sort.16" expl="loop invariant preservation">
   <proof prover="6"><result status="valid" time="0.07" steps="52"/></proof>
@@ -152,7 +152,7 @@
   <proof prover="6"><result status="valid" time="0.01" steps="17"/></proof>
   </goal>
   <goal name="WP_parameter insertion_sort.15" expl="loop invariant preservation">
-  <proof prover="2" edited="insertion_sort_InsertionSortGen_WP_parameter_insertion_sort_1.v"><result status="valid" time="1.12"/></proof>
+  <proof prover="0" edited="insertion_sort_InsertionSortGen_WP_parameter_insertion_sort_1.v"><result status="valid" time="1.35"/></proof>
   </goal>
   <goal name="WP_parameter insertion_sort.16" expl="loop invariant preservation">
   <proof prover="1"><result status="valid" time="0.03"/></proof>
diff --git a/examples/kmp/why3session.xml b/examples/kmp/why3session.xml
index f92f51bf95d59572b9bc1bafc937185e61c743a4..bde1be735578e367f2f45e6510b2be98e623a0a9 100644
--- a/examples/kmp/why3session.xml
+++ b/examples/kmp/why3session.xml
@@ -2,8 +2,8 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="3" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Alt-Ergo" version="0.95.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../kmp.mlw" expanded="true">
@@ -15,7 +15,7 @@
  <proof prover="3" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="matches_contradiction_at_first" expl="">
- <proof prover="2" edited="kmp_WP_KnuthMorrisPratt_matches_contradiction_at_first_1.v"><result status="valid" time="0.31"/></proof>
+ <proof prover="0" edited="kmp_WP_KnuthMorrisPratt_matches_contradiction_at_first_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
  <goal name="matches_contradiction_at_i" expl="">
  <proof prover="3" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="15"/></proof>
@@ -24,7 +24,7 @@
  <proof prover="3" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="19"/></proof>
  </goal>
  <goal name="matches_left_weakening" expl="">
- <proof prover="2" edited="kmp_WP_KnuthMorrisPratt_matches_left_weakening_1.v"><result status="valid" time="0.34"/></proof>
+ <proof prover="0" edited="kmp_WP_KnuthMorrisPratt_matches_left_weakening_1.v"><result status="valid" time="0.34"/></proof>
  </goal>
  <goal name="matches_sym" expl="">
  <proof prover="3" timelimit="10" memlimit="0"><result status="valid" time="0.00" steps="11"/></proof>
@@ -33,10 +33,10 @@
  <proof prover="3" timelimit="10" memlimit="0"><result status="valid" time="0.01" steps="16"/></proof>
  </goal>
  <goal name="next_iteration" expl="">
- <proof prover="2" edited="kmp_WP_KnuthMorrisPratt_next_iteration_1.v"><result status="valid" time="0.38"/></proof>
+ <proof prover="0" edited="kmp_WP_KnuthMorrisPratt_next_iteration_1.v"><result status="valid" time="0.38"/></proof>
  </goal>
  <goal name="next_is_maximal" expl="">
- <proof prover="2" edited="kmp_WP_KnuthMorrisPratt_next_is_maximal_1.v"><result status="valid" time="0.36"/></proof>
+ <proof prover="0" edited="kmp_WP_KnuthMorrisPratt_next_is_maximal_1.v"><result status="valid" time="0.36"/></proof>
  </goal>
  <goal name="next_1_0" expl="">
  <proof prover="3" timelimit="10" memlimit="0"><result status="valid" time="0.00" steps="13"/></proof>
@@ -80,7 +80,7 @@
   <proof prover="3" timelimit="7"><result status="valid" time="0.02" steps="44"/></proof>
   </goal>
   <goal name="WP_parameter initnext.13" expl="loop invariant preservation">
-  <proof prover="2" timelimit="7" memlimit="1000" edited="kmp_WP_KnuthMorrisPratt_WP_parameter_initnext_2.v"><result status="valid" time="0.35"/></proof>
+  <proof prover="0" timelimit="7" memlimit="1000" edited="kmp_WP_KnuthMorrisPratt_WP_parameter_initnext_2.v"><result status="valid" time="0.35"/></proof>
   </goal>
   <goal name="WP_parameter initnext.14" expl="loop invariant preservation">
   <transf name="inline_goal">
@@ -118,7 +118,7 @@
   <proof prover="3"><result status="valid" time="0.02" steps="31"/></proof>
   </goal>
   <goal name="WP_parameter initnext.20" expl="loop invariant preservation">
-  <proof prover="2" timelimit="7" memlimit="1000" edited="kmp_WP_KnuthMorrisPratt_WP_parameter_initnext_3.v"><result status="valid" time="0.30"/></proof>
+  <proof prover="0" timelimit="7" memlimit="1000" edited="kmp_WP_KnuthMorrisPratt_WP_parameter_initnext_3.v"><result status="valid" time="0.46"/></proof>
   </goal>
   <goal name="WP_parameter initnext.21" expl="loop invariant preservation">
   <transf name="inline_goal">
@@ -156,7 +156,7 @@
   <proof prover="3"><result status="valid" time="0.04" steps="89"/></proof>
   </goal>
   <goal name="WP_parameter initnext.27" expl="loop invariant preservation">
-  <proof prover="2" timelimit="7" memlimit="1000" edited="kmp_WP_KnuthMorrisPratt_WP_parameter_initnext_4.v"><result status="valid" time="0.42"/></proof>
+  <proof prover="0" timelimit="7" memlimit="1000" edited="kmp_WP_KnuthMorrisPratt_WP_parameter_initnext_4.v"><result status="valid" time="0.42"/></proof>
   </goal>
   <goal name="WP_parameter initnext.28" expl="loop invariant preservation">
   <proof prover="1"><result status="valid" time="0.03"/></proof>
diff --git a/examples/knuth_prime_numbers/why3session.xml b/examples/knuth_prime_numbers/why3session.xml
index 42492904a2ad0a11e274032947bd8a0911f260ee..f3d5fdd8dfed48facb749d1c39fc198edc404200 100644
--- a/examples/knuth_prime_numbers/why3session.xml
+++ b/examples/knuth_prime_numbers/why3session.xml
@@ -5,8 +5,8 @@
 <prover id="0" name="CVC4" version="1.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="Alt-Ergo" version="1.01" timelimit="1" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="10" steplimit="0" memlimit="0"/>
-<prover id="3" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="4" name="Z3" version="2.19" timelimit="10" steplimit="0" memlimit="0"/>
+<prover id="5" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="6" name="Z3" version="4.3.1" timelimit="120" steplimit="0" memlimit="1000"/>
 <prover id="7" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="8" name="Alt-Ergo" version="0.95.2" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -17,7 +17,7 @@
 <file name="../knuth_prime_numbers.mlw" expanded="true">
 <theory name="PrimeNumbers" sum="a3a1b249c49aeffba734fd33dc03a147" expanded="true">
  <goal name="exists_prime" expl="">
- <proof prover="3" timelimit="10" memlimit="0" edited="knuth_prime_numbers_WP_PrimeNumbers_exists_prime_1.v"><result status="valid" time="0.40"/></proof>
+ <proof prover="5" timelimit="10" memlimit="0" edited="knuth_prime_numbers_WP_PrimeNumbers_exists_prime_1.v"><result status="valid" time="0.40"/></proof>
  </goal>
  <goal name="WP_parameter prime_numbers" expl="VC for prime_numbers">
  <transf name="split_goal_wp">
@@ -58,7 +58,7 @@
   <proof prover="9" memlimit="1000"><result status="valid" time="0.02" steps="28"/></proof>
   </goal>
   <goal name="WP_parameter prime_numbers.11" expl="assertion">
-  <proof prover="3" edited="knuth_prime_numbers_PrimeNumbers_WP_parameter_prime_numbers_2.v"><result status="valid" time="0.65"/></proof>
+  <proof prover="5" edited="knuth_prime_numbers_PrimeNumbers_WP_parameter_prime_numbers_2.v"><result status="valid" time="0.65"/></proof>
   </goal>
   <goal name="WP_parameter prime_numbers.12" expl="variant decrease">
   <proof prover="9"><result status="valid" time="0.02" steps="33"/></proof>
@@ -79,7 +79,7 @@
    <proof prover="9" memlimit="1000"><result status="valid" time="0.02" steps="33"/></proof>
    </goal>
    <goal name="WP_parameter prime_numbers.15.2" expl="VC for prime_numbers">
-   <proof prover="3" edited="knuth_prime_numbers_PrimeNumbers_WP_parameter_prime_numbers_3.v"><result status="valid" time="0.42"/></proof>
+   <proof prover="5" edited="knuth_prime_numbers_PrimeNumbers_WP_parameter_prime_numbers_3.v"><result status="valid" time="0.42"/></proof>
    </goal>
   </transf>
   </goal>
@@ -115,7 +115,7 @@
    <proof prover="9" memlimit="1000"><result status="valid" time="0.02" steps="32"/></proof>
    </goal>
    <goal name="WP_parameter prime_numbers.23.2" expl="VC for prime_numbers">
-   <proof prover="3" edited="knuth_prime_numbers_PrimeNumbers_WP_parameter_prime_numbers_5.v"><result status="valid" time="0.48"/></proof>
+   <proof prover="5" edited="knuth_prime_numbers_PrimeNumbers_WP_parameter_prime_numbers_5.v"><result status="valid" time="0.48"/></proof>
    </goal>
   </transf>
   </goal>
@@ -138,7 +138,7 @@
   <proof prover="10"><result status="valid" time="0.03"/></proof>
   </goal>
   <goal name="WP_parameter prime_numbers.30" expl="assertion">
-  <proof prover="3" edited="knuth_prime_numbers_PrimeNumbers_WP_parameter_prime_numbers_4.v"><result status="valid" time="1.12"/></proof>
+  <proof prover="5" edited="knuth_prime_numbers_PrimeNumbers_WP_parameter_prime_numbers_4.v"><result status="valid" time="1.12"/></proof>
   </goal>
   <goal name="WP_parameter prime_numbers.31" expl="postcondition">
   <proof prover="9"><result status="valid" time="0.01" steps="33"/></proof>
@@ -219,11 +219,11 @@
       <ip_library name="Unit"/>
       <ip_qualid name="unit"/>
      </ts_pos>
-     <ts_pos name="&apos;mark" arity="0" id="68"
+     <ts_pos name="&#39;mark" arity="0" id="68"
       ip_theory="Mark">
       <ip_library name="why3"/>
       <ip_library name="Mark"/>
-      <ip_qualid name="&apos;mark"/>
+      <ip_qualid name="&#39;mark"/>
      </ts_pos>
      <ts_pos name="tuple2" arity="2" id="1286"
       ip_theory="Tuple2">
@@ -231,7 +231,7 @@
       <ip_library name="Tuple2"/>
       <ip_qualid name="tuple2"/>
      </ts_pos>
-     <ts_pos name="ref" arity="1" id="2926"
+     <ts_pos name="ref" arity="1" id="2939"
       ip_theory="Ref">
       <ip_library name="ref"/>
       <ip_qualid name="ref"/>
@@ -317,52 +317,52 @@
       <ip_library name="int"/>
       <ip_qualid name="mod"/>
      </ls_pos>
-     <ls_pos name="even" id="2595"
+     <ls_pos name="even" id="2608"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even"/>
      </ls_pos>
-     <ls_pos name="odd" id="2603"
+     <ls_pos name="odd" id="2616"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd"/>
      </ls_pos>
-     <ls_pos name="prefix !" id="2932"
+     <ls_pos name="prefix !" id="2945"
       ip_theory="Ref">
       <ip_library name="ref"/>
       <ip_qualid name="prefix !"/>
      </ls_pos>
-     <ls_pos name="get" id="3078"
+     <ls_pos name="get" id="3091"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="get"/>
      </ls_pos>
-     <ls_pos name="set" id="3081"
+     <ls_pos name="set" id="3094"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="set"/>
      </ls_pos>
-     <ls_pos name="mixfix []" id="3088"
+     <ls_pos name="mixfix []" id="3101"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="mixfix []"/>
      </ls_pos>
-     <ls_pos name="mixfix [&lt;-]" id="3101"
+     <ls_pos name="mixfix [&lt;-]" id="3114"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="mixfix [&lt;-]"/>
      </ls_pos>
-     <ls_pos name="set" id="3528"
+     <ls_pos name="set" id="3541"
       ip_theory="Array">
       <ip_library name="array"/>
       <ip_qualid name="set"/>
      </ls_pos>
-     <ls_pos name="mixfix [&lt;-]" id="3570"
+     <ls_pos name="mixfix [&lt;-]" id="3583"
       ip_theory="Array">
       <ip_library name="array"/>
       <ip_qualid name="mixfix [&lt;-]"/>
      </ls_pos>
-     <ls_pos name="first_primes" id="6730"
+     <ls_pos name="first_primes" id="6743"
       ip_theory="PrimeNumbers">
       <ip_qualid name="first_primes"/>
      </ls_pos>
@@ -625,226 +625,226 @@
       <ip_library name="int"/>
       <ip_qualid name="Mod_mult"/>
      </pr_pos>
-     <pr_pos name="even_or_odd" id="2611"
+     <pr_pos name="even_or_odd" id="2624"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_or_odd"/>
      </pr_pos>
-     <pr_pos name="even_not_odd" id="2614"
+     <pr_pos name="even_not_odd" id="2627"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_not_odd"/>
      </pr_pos>
-     <pr_pos name="odd_not_even" id="2617"
+     <pr_pos name="odd_not_even" id="2630"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_not_even"/>
      </pr_pos>
-     <pr_pos name="even_odd" id="2620"
+     <pr_pos name="even_odd" id="2633"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_odd"/>
      </pr_pos>
-     <pr_pos name="odd_even" id="2623"
+     <pr_pos name="odd_even" id="2636"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_even"/>
      </pr_pos>
-     <pr_pos name="even_even" id="2626"
+     <pr_pos name="even_even" id="2639"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_even"/>
      </pr_pos>
-     <pr_pos name="odd_odd" id="2629"
+     <pr_pos name="odd_odd" id="2642"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_odd"/>
      </pr_pos>
-     <pr_pos name="even_2k" id="2632"
+     <pr_pos name="even_2k" id="2645"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_2k"/>
      </pr_pos>
-     <pr_pos name="odd_2k1" id="2635"
+     <pr_pos name="odd_2k1" id="2648"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_2k1"/>
      </pr_pos>
-     <pr_pos name="divides_refl" id="2651"
+     <pr_pos name="divides_refl" id="2664"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_refl"/>
      </pr_pos>
-     <pr_pos name="divides_1_n" id="2654"
+     <pr_pos name="divides_1_n" id="2667"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_1_n"/>
      </pr_pos>
-     <pr_pos name="divides_0" id="2657"
+     <pr_pos name="divides_0" id="2670"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_0"/>
      </pr_pos>
-     <pr_pos name="divides_left" id="2660"
+     <pr_pos name="divides_left" id="2673"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_left"/>
      </pr_pos>
-     <pr_pos name="divides_right" id="2667"
+     <pr_pos name="divides_right" id="2680"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_right"/>
      </pr_pos>
-     <pr_pos name="divides_oppr" id="2674"
+     <pr_pos name="divides_oppr" id="2687"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppr"/>
      </pr_pos>
-     <pr_pos name="divides_oppl" id="2679"
+     <pr_pos name="divides_oppl" id="2692"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppl"/>
      </pr_pos>
-     <pr_pos name="divides_oppr_rev" id="2684"
+     <pr_pos name="divides_oppr_rev" id="2697"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppr_rev"/>
      </pr_pos>
-     <pr_pos name="divides_oppl_rev" id="2689"
+     <pr_pos name="divides_oppl_rev" id="2702"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppl_rev"/>
      </pr_pos>
-     <pr_pos name="divides_plusr" id="2694"
+     <pr_pos name="divides_plusr" id="2707"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_plusr"/>
      </pr_pos>
-     <pr_pos name="divides_minusr" id="2701"
+     <pr_pos name="divides_minusr" id="2714"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_minusr"/>
      </pr_pos>
-     <pr_pos name="divides_multl" id="2708"
+     <pr_pos name="divides_multl" id="2721"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_multl"/>
      </pr_pos>
-     <pr_pos name="divides_multr" id="2715"
+     <pr_pos name="divides_multr" id="2728"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_multr"/>
      </pr_pos>
-     <pr_pos name="divides_factorl" id="2722"
+     <pr_pos name="divides_factorl" id="2735"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_factorl"/>
      </pr_pos>
-     <pr_pos name="divides_factorr" id="2727"
+     <pr_pos name="divides_factorr" id="2740"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_factorr"/>
      </pr_pos>
-     <pr_pos name="divides_n_1" id="2732"
+     <pr_pos name="divides_n_1" id="2745"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_n_1"/>
      </pr_pos>
-     <pr_pos name="divides_antisym" id="2735"
+     <pr_pos name="divides_antisym" id="2748"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_antisym"/>
      </pr_pos>
-     <pr_pos name="divides_trans" id="2740"
+     <pr_pos name="divides_trans" id="2753"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_trans"/>
      </pr_pos>
-     <pr_pos name="divides_bounds" id="2747"
+     <pr_pos name="divides_bounds" id="2760"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_bounds"/>
      </pr_pos>
-     <pr_pos name="mod_divides_euclidean" id="2752"
+     <pr_pos name="mod_divides_euclidean" id="2765"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="mod_divides_euclidean"/>
      </pr_pos>
-     <pr_pos name="divides_mod_euclidean" id="2757"
+     <pr_pos name="divides_mod_euclidean" id="2770"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_mod_euclidean"/>
      </pr_pos>
-     <pr_pos name="mod_divides_computer" id="2762"
+     <pr_pos name="mod_divides_computer" id="2775"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="mod_divides_computer"/>
      </pr_pos>
-     <pr_pos name="divides_mod_computer" id="2767"
+     <pr_pos name="divides_mod_computer" id="2780"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_mod_computer"/>
      </pr_pos>
-     <pr_pos name="even_divides" id="2772"
+     <pr_pos name="even_divides" id="2785"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="even_divides"/>
      </pr_pos>
-     <pr_pos name="odd_divides" id="2775"
+     <pr_pos name="odd_divides" id="2788"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="odd_divides"/>
      </pr_pos>
-     <pr_pos name="not_prime_1" id="2869"
+     <pr_pos name="not_prime_1" id="2882"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="not_prime_1"/>
      </pr_pos>
-     <pr_pos name="prime_2" id="2870"
+     <pr_pos name="prime_2" id="2883"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="prime_2"/>
      </pr_pos>
-     <pr_pos name="prime_3" id="2871"
+     <pr_pos name="prime_3" id="2884"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="prime_3"/>
      </pr_pos>
-     <pr_pos name="prime_divisors" id="2872"
+     <pr_pos name="prime_divisors" id="2885"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="prime_divisors"/>
      </pr_pos>
-     <pr_pos name="small_divisors" id="2877"
+     <pr_pos name="small_divisors" id="2890"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="small_divisors"/>
      </pr_pos>
-     <pr_pos name="even_prime" id="2882"
+     <pr_pos name="even_prime" id="2895"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="even_prime"/>
      </pr_pos>
-     <pr_pos name="odd_prime" id="2885"
+     <pr_pos name="odd_prime" id="2898"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="odd_prime"/>
      </pr_pos>
-     <pr_pos name="Select_eq" id="3114"
+     <pr_pos name="Select_eq" id="3127"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="Select_eq"/>
      </pr_pos>
-     <pr_pos name="Select_neq" id="3123"
+     <pr_pos name="Select_neq" id="3136"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="Select_neq"/>
      </pr_pos>
-     <pr_pos name="exists_prime" id="6757"
+     <pr_pos name="exists_prime" id="6770"
       ip_theory="PrimeNumbers">
       <ip_qualid name="exists_prime"/>
      </pr_pos>
-     <pr_pos name="Bertrand_postulate" id="6770"
+     <pr_pos name="Bertrand_postulate" id="6783"
       ip_theory="PrimeNumbers">
       <ip_qualid name="Bertrand_postulate"/>
      </pr_pos>
@@ -897,34 +897,34 @@
       <meta_arg_ls id="2064"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="2595"/>
+      <meta_arg_ls id="2608"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="2603"/>
+      <meta_arg_ls id="2616"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="2932"/>
+      <meta_arg_ls id="2945"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3078"/>
+      <meta_arg_ls id="3091"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3081"/>
+      <meta_arg_ls id="3094"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3088"/>
+      <meta_arg_ls id="3101"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3101"/>
+      <meta_arg_ls id="3114"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3528"/>
+      <meta_arg_ls id="3541"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3570"/>
+      <meta_arg_ls id="3583"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="6730"/>
+      <meta_arg_ls id="6743"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="1744"/>
@@ -1077,79 +1077,70 @@
       <meta_arg_pr id="2130"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2611"/>
-     </meta>
-     <meta name="remove_prop">
-      <meta_arg_pr id="2614"/>
-     </meta>
-     <meta name="remove_prop">
-      <meta_arg_pr id="2617"/>
+      <meta_arg_pr id="2624"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2620"/>
+      <meta_arg_pr id="2627"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2623"/>
+      <meta_arg_pr id="2630"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2626"/>
+      <meta_arg_pr id="2633"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2629"/>
+      <meta_arg_pr id="2636"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2632"/>
+      <meta_arg_pr id="2639"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2635"/>
+      <meta_arg_pr id="2642"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2651"/>
+      <meta_arg_pr id="2645"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2654"/>
+      <meta_arg_pr id="2648"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2657"/>
-     </meta>
-     <meta name="remove_prop">
-      <meta_arg_pr id="2660"/>
+      <meta_arg_pr id="2664"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2667"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2674"/>
+      <meta_arg_pr id="2670"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2679"/>
+      <meta_arg_pr id="2673"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2684"/>
+      <meta_arg_pr id="2680"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2689"/>
+      <meta_arg_pr id="2687"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2694"/>
+      <meta_arg_pr id="2692"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2701"/>
+      <meta_arg_pr id="2697"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2708"/>
+      <meta_arg_pr id="2702"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2715"/>
+      <meta_arg_pr id="2707"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2722"/>
+      <meta_arg_pr id="2714"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2727"/>
+      <meta_arg_pr id="2721"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2732"/>
+      <meta_arg_pr id="2728"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2735"/>
@@ -1158,59 +1149,68 @@
       <meta_arg_pr id="2740"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2747"/>
+      <meta_arg_pr id="2745"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2752"/>
+      <meta_arg_pr id="2748"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2757"/>
+      <meta_arg_pr id="2753"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2762"/>
+      <meta_arg_pr id="2760"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2767"/>
+      <meta_arg_pr id="2765"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2772"/>
+      <meta_arg_pr id="2770"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2775"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2869"/>
+      <meta_arg_pr id="2780"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2870"/>
+      <meta_arg_pr id="2785"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2871"/>
+      <meta_arg_pr id="2788"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2872"/>
+      <meta_arg_pr id="2882"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2877"/>
+      <meta_arg_pr id="2883"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2882"/>
+      <meta_arg_pr id="2884"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2885"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="3114"/>
+      <meta_arg_pr id="2890"/>
+     </meta>
+     <meta name="remove_prop">
+      <meta_arg_pr id="2895"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="3123"/>
+      <meta_arg_pr id="2898"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="6757"/>
+      <meta_arg_pr id="3127"/>
+     </meta>
+     <meta name="remove_prop">
+      <meta_arg_pr id="3136"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="6770"/>
      </meta>
+     <meta name="remove_prop">
+      <meta_arg_pr id="6783"/>
+     </meta>
      <meta name="remove_type">
       <meta_arg_ts id="2"/>
      </meta>
@@ -1230,7 +1230,7 @@
       <meta_arg_ts id="1286"/>
      </meta>
      <meta name="remove_type">
-      <meta_arg_ts id="2926"/>
+      <meta_arg_ts id="2939"/>
      </meta>
      <goal name="WP_parameter prime_numbers.40.1.2" expl="VC for prime_numbers">
      <transf name="eliminate_builtin">
@@ -1270,11 +1270,11 @@
       <ip_library name="Unit"/>
       <ip_qualid name="unit"/>
      </ts_pos>
-     <ts_pos name="&apos;mark" arity="0" id="68"
+     <ts_pos name="&#39;mark" arity="0" id="68"
       ip_theory="Mark">
       <ip_library name="why3"/>
       <ip_library name="Mark"/>
-      <ip_qualid name="&apos;mark"/>
+      <ip_qualid name="&#39;mark"/>
      </ts_pos>
      <ts_pos name="tuple2" arity="2" id="1286"
       ip_theory="Tuple2">
@@ -1282,7 +1282,7 @@
       <ip_library name="Tuple2"/>
       <ip_qualid name="tuple2"/>
      </ts_pos>
-     <ts_pos name="ref" arity="1" id="2926"
+     <ts_pos name="ref" arity="1" id="2939"
       ip_theory="Ref">
       <ip_library name="ref"/>
       <ip_qualid name="ref"/>
@@ -1368,52 +1368,52 @@
       <ip_library name="int"/>
       <ip_qualid name="mod"/>
      </ls_pos>
-     <ls_pos name="even" id="2595"
+     <ls_pos name="even" id="2608"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even"/>
      </ls_pos>
-     <ls_pos name="odd" id="2603"
+     <ls_pos name="odd" id="2616"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd"/>
      </ls_pos>
-     <ls_pos name="prefix !" id="2932"
+     <ls_pos name="prefix !" id="2945"
       ip_theory="Ref">
       <ip_library name="ref"/>
       <ip_qualid name="prefix !"/>
      </ls_pos>
-     <ls_pos name="get" id="3078"
+     <ls_pos name="get" id="3091"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="get"/>
      </ls_pos>
-     <ls_pos name="set" id="3081"
+     <ls_pos name="set" id="3094"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="set"/>
      </ls_pos>
-     <ls_pos name="mixfix []" id="3088"
+     <ls_pos name="mixfix []" id="3101"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="mixfix []"/>
      </ls_pos>
-     <ls_pos name="mixfix [&lt;-]" id="3101"
+     <ls_pos name="mixfix [&lt;-]" id="3114"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="mixfix [&lt;-]"/>
      </ls_pos>
-     <ls_pos name="set" id="3528"
+     <ls_pos name="set" id="3541"
       ip_theory="Array">
       <ip_library name="array"/>
       <ip_qualid name="set"/>
      </ls_pos>
-     <ls_pos name="mixfix [&lt;-]" id="3570"
+     <ls_pos name="mixfix [&lt;-]" id="3583"
       ip_theory="Array">
       <ip_library name="array"/>
       <ip_qualid name="mixfix [&lt;-]"/>
      </ls_pos>
-     <ls_pos name="first_primes" id="6730"
+     <ls_pos name="first_primes" id="6743"
       ip_theory="PrimeNumbers">
       <ip_qualid name="first_primes"/>
      </ls_pos>
@@ -1676,226 +1676,226 @@
       <ip_library name="int"/>
       <ip_qualid name="Mod_mult"/>
      </pr_pos>
-     <pr_pos name="even_or_odd" id="2611"
+     <pr_pos name="even_or_odd" id="2624"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_or_odd"/>
      </pr_pos>
-     <pr_pos name="even_not_odd" id="2614"
+     <pr_pos name="even_not_odd" id="2627"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_not_odd"/>
      </pr_pos>
-     <pr_pos name="odd_not_even" id="2617"
+     <pr_pos name="odd_not_even" id="2630"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_not_even"/>
      </pr_pos>
-     <pr_pos name="even_odd" id="2620"
+     <pr_pos name="even_odd" id="2633"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_odd"/>
      </pr_pos>
-     <pr_pos name="odd_even" id="2623"
+     <pr_pos name="odd_even" id="2636"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_even"/>
      </pr_pos>
-     <pr_pos name="even_even" id="2626"
+     <pr_pos name="even_even" id="2639"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_even"/>
      </pr_pos>
-     <pr_pos name="odd_odd" id="2629"
+     <pr_pos name="odd_odd" id="2642"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_odd"/>
      </pr_pos>
-     <pr_pos name="even_2k" id="2632"
+     <pr_pos name="even_2k" id="2645"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_2k"/>
      </pr_pos>
-     <pr_pos name="odd_2k1" id="2635"
+     <pr_pos name="odd_2k1" id="2648"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_2k1"/>
      </pr_pos>
-     <pr_pos name="divides_refl" id="2651"
+     <pr_pos name="divides_refl" id="2664"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_refl"/>
      </pr_pos>
-     <pr_pos name="divides_1_n" id="2654"
+     <pr_pos name="divides_1_n" id="2667"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_1_n"/>
      </pr_pos>
-     <pr_pos name="divides_0" id="2657"
+     <pr_pos name="divides_0" id="2670"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_0"/>
      </pr_pos>
-     <pr_pos name="divides_left" id="2660"
+     <pr_pos name="divides_left" id="2673"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_left"/>
      </pr_pos>
-     <pr_pos name="divides_right" id="2667"
+     <pr_pos name="divides_right" id="2680"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_right"/>
      </pr_pos>
-     <pr_pos name="divides_oppr" id="2674"
+     <pr_pos name="divides_oppr" id="2687"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppr"/>
      </pr_pos>
-     <pr_pos name="divides_oppl" id="2679"
+     <pr_pos name="divides_oppl" id="2692"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppl"/>
      </pr_pos>
-     <pr_pos name="divides_oppr_rev" id="2684"
+     <pr_pos name="divides_oppr_rev" id="2697"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppr_rev"/>
      </pr_pos>
-     <pr_pos name="divides_oppl_rev" id="2689"
+     <pr_pos name="divides_oppl_rev" id="2702"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppl_rev"/>
      </pr_pos>
-     <pr_pos name="divides_plusr" id="2694"
+     <pr_pos name="divides_plusr" id="2707"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_plusr"/>
      </pr_pos>
-     <pr_pos name="divides_minusr" id="2701"
+     <pr_pos name="divides_minusr" id="2714"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_minusr"/>
      </pr_pos>
-     <pr_pos name="divides_multl" id="2708"
+     <pr_pos name="divides_multl" id="2721"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_multl"/>
      </pr_pos>
-     <pr_pos name="divides_multr" id="2715"
+     <pr_pos name="divides_multr" id="2728"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_multr"/>
      </pr_pos>
-     <pr_pos name="divides_factorl" id="2722"
+     <pr_pos name="divides_factorl" id="2735"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_factorl"/>
      </pr_pos>
-     <pr_pos name="divides_factorr" id="2727"
+     <pr_pos name="divides_factorr" id="2740"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_factorr"/>
      </pr_pos>
-     <pr_pos name="divides_n_1" id="2732"
+     <pr_pos name="divides_n_1" id="2745"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_n_1"/>
      </pr_pos>
-     <pr_pos name="divides_antisym" id="2735"
+     <pr_pos name="divides_antisym" id="2748"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_antisym"/>
      </pr_pos>
-     <pr_pos name="divides_trans" id="2740"
+     <pr_pos name="divides_trans" id="2753"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_trans"/>
      </pr_pos>
-     <pr_pos name="divides_bounds" id="2747"
+     <pr_pos name="divides_bounds" id="2760"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_bounds"/>
      </pr_pos>
-     <pr_pos name="mod_divides_euclidean" id="2752"
+     <pr_pos name="mod_divides_euclidean" id="2765"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="mod_divides_euclidean"/>
      </pr_pos>
-     <pr_pos name="divides_mod_euclidean" id="2757"
+     <pr_pos name="divides_mod_euclidean" id="2770"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_mod_euclidean"/>
      </pr_pos>
-     <pr_pos name="mod_divides_computer" id="2762"
+     <pr_pos name="mod_divides_computer" id="2775"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="mod_divides_computer"/>
      </pr_pos>
-     <pr_pos name="divides_mod_computer" id="2767"
+     <pr_pos name="divides_mod_computer" id="2780"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_mod_computer"/>
      </pr_pos>
-     <pr_pos name="even_divides" id="2772"
+     <pr_pos name="even_divides" id="2785"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="even_divides"/>
      </pr_pos>
-     <pr_pos name="odd_divides" id="2775"
+     <pr_pos name="odd_divides" id="2788"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="odd_divides"/>
      </pr_pos>
-     <pr_pos name="not_prime_1" id="2869"
+     <pr_pos name="not_prime_1" id="2882"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="not_prime_1"/>
      </pr_pos>
-     <pr_pos name="prime_2" id="2870"
+     <pr_pos name="prime_2" id="2883"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="prime_2"/>
      </pr_pos>
-     <pr_pos name="prime_3" id="2871"
+     <pr_pos name="prime_3" id="2884"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="prime_3"/>
      </pr_pos>
-     <pr_pos name="prime_divisors" id="2872"
+     <pr_pos name="prime_divisors" id="2885"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="prime_divisors"/>
      </pr_pos>
-     <pr_pos name="small_divisors" id="2877"
+     <pr_pos name="small_divisors" id="2890"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="small_divisors"/>
      </pr_pos>
-     <pr_pos name="even_prime" id="2882"
+     <pr_pos name="even_prime" id="2895"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="even_prime"/>
      </pr_pos>
-     <pr_pos name="odd_prime" id="2885"
+     <pr_pos name="odd_prime" id="2898"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="odd_prime"/>
      </pr_pos>
-     <pr_pos name="Select_eq" id="3114"
+     <pr_pos name="Select_eq" id="3127"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="Select_eq"/>
      </pr_pos>
-     <pr_pos name="Select_neq" id="3123"
+     <pr_pos name="Select_neq" id="3136"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="Select_neq"/>
      </pr_pos>
-     <pr_pos name="exists_prime" id="6757"
+     <pr_pos name="exists_prime" id="6770"
       ip_theory="PrimeNumbers">
       <ip_qualid name="exists_prime"/>
      </pr_pos>
-     <pr_pos name="Bertrand_postulate" id="6770"
+     <pr_pos name="Bertrand_postulate" id="6783"
       ip_theory="PrimeNumbers">
       <ip_qualid name="Bertrand_postulate"/>
      </pr_pos>
@@ -1948,34 +1948,34 @@
       <meta_arg_ls id="2064"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="2595"/>
+      <meta_arg_ls id="2608"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="2603"/>
+      <meta_arg_ls id="2616"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="2932"/>
+      <meta_arg_ls id="2945"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3078"/>
+      <meta_arg_ls id="3091"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3081"/>
+      <meta_arg_ls id="3094"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3088"/>
+      <meta_arg_ls id="3101"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3101"/>
+      <meta_arg_ls id="3114"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3528"/>
+      <meta_arg_ls id="3541"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3570"/>
+      <meta_arg_ls id="3583"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="6730"/>
+      <meta_arg_ls id="6743"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="1744"/>
@@ -2128,79 +2128,70 @@
       <meta_arg_pr id="2130"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2611"/>
-     </meta>
-     <meta name="remove_prop">
-      <meta_arg_pr id="2614"/>
-     </meta>
-     <meta name="remove_prop">
-      <meta_arg_pr id="2617"/>
-     </meta>
-     <meta name="remove_prop">
-      <meta_arg_pr id="2620"/>
+      <meta_arg_pr id="2624"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2623"/>
+      <meta_arg_pr id="2627"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2626"/>
+      <meta_arg_pr id="2630"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2629"/>
+      <meta_arg_pr id="2633"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2632"/>
+      <meta_arg_pr id="2636"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2635"/>
+      <meta_arg_pr id="2639"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2651"/>
+      <meta_arg_pr id="2642"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2654"/>
+      <meta_arg_pr id="2645"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2657"/>
+      <meta_arg_pr id="2648"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2660"/>
+      <meta_arg_pr id="2664"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2667"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2674"/>
+      <meta_arg_pr id="2670"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2679"/>
+      <meta_arg_pr id="2673"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2684"/>
+      <meta_arg_pr id="2680"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2689"/>
+      <meta_arg_pr id="2687"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2694"/>
+      <meta_arg_pr id="2692"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2701"/>
+      <meta_arg_pr id="2697"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2708"/>
+      <meta_arg_pr id="2702"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2715"/>
+      <meta_arg_pr id="2707"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2722"/>
+      <meta_arg_pr id="2714"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2727"/>
+      <meta_arg_pr id="2721"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2732"/>
+      <meta_arg_pr id="2728"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2735"/>
@@ -2209,59 +2200,68 @@
       <meta_arg_pr id="2740"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2747"/>
+      <meta_arg_pr id="2745"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2752"/>
+      <meta_arg_pr id="2748"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2757"/>
+      <meta_arg_pr id="2753"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2762"/>
+      <meta_arg_pr id="2760"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2767"/>
+      <meta_arg_pr id="2765"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2772"/>
+      <meta_arg_pr id="2770"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2775"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2869"/>
+      <meta_arg_pr id="2780"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2870"/>
+      <meta_arg_pr id="2785"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2871"/>
+      <meta_arg_pr id="2788"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2872"/>
+      <meta_arg_pr id="2882"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2877"/>
+      <meta_arg_pr id="2883"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2882"/>
+      <meta_arg_pr id="2884"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2885"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="3114"/>
+      <meta_arg_pr id="2890"/>
+     </meta>
+     <meta name="remove_prop">
+      <meta_arg_pr id="2895"/>
+     </meta>
+     <meta name="remove_prop">
+      <meta_arg_pr id="2898"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="3123"/>
+      <meta_arg_pr id="3127"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="6757"/>
+      <meta_arg_pr id="3136"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="6770"/>
      </meta>
+     <meta name="remove_prop">
+      <meta_arg_pr id="6783"/>
+     </meta>
      <meta name="remove_type">
       <meta_arg_ts id="2"/>
      </meta>
@@ -2281,7 +2281,7 @@
       <meta_arg_ts id="1286"/>
      </meta>
      <meta name="remove_type">
-      <meta_arg_ts id="2926"/>
+      <meta_arg_ts id="2939"/>
      </meta>
      <goal name="WP_parameter prime_numbers.40.1.3" expl="VC for prime_numbers">
      <transf name="eliminate_builtin">
@@ -2320,11 +2320,11 @@
       <ip_library name="Unit"/>
       <ip_qualid name="unit"/>
      </ts_pos>
-     <ts_pos name="&apos;mark" arity="0" id="68"
+     <ts_pos name="&#39;mark" arity="0" id="68"
       ip_theory="Mark">
       <ip_library name="why3"/>
       <ip_library name="Mark"/>
-      <ip_qualid name="&apos;mark"/>
+      <ip_qualid name="&#39;mark"/>
      </ts_pos>
      <ts_pos name="tuple2" arity="2" id="1286"
       ip_theory="Tuple2">
@@ -2332,7 +2332,7 @@
       <ip_library name="Tuple2"/>
       <ip_qualid name="tuple2"/>
      </ts_pos>
-     <ts_pos name="ref" arity="1" id="2926"
+     <ts_pos name="ref" arity="1" id="2939"
       ip_theory="Ref">
       <ip_library name="ref"/>
       <ip_qualid name="ref"/>
@@ -2418,52 +2418,52 @@
       <ip_library name="int"/>
       <ip_qualid name="mod"/>
      </ls_pos>
-     <ls_pos name="even" id="2595"
+     <ls_pos name="even" id="2608"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even"/>
      </ls_pos>
-     <ls_pos name="odd" id="2603"
+     <ls_pos name="odd" id="2616"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd"/>
      </ls_pos>
-     <ls_pos name="prefix !" id="2932"
+     <ls_pos name="prefix !" id="2945"
       ip_theory="Ref">
       <ip_library name="ref"/>
       <ip_qualid name="prefix !"/>
      </ls_pos>
-     <ls_pos name="get" id="3078"
+     <ls_pos name="get" id="3091"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="get"/>
      </ls_pos>
-     <ls_pos name="set" id="3081"
+     <ls_pos name="set" id="3094"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="set"/>
      </ls_pos>
-     <ls_pos name="mixfix []" id="3088"
+     <ls_pos name="mixfix []" id="3101"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="mixfix []"/>
      </ls_pos>
-     <ls_pos name="mixfix [&lt;-]" id="3101"
+     <ls_pos name="mixfix [&lt;-]" id="3114"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="mixfix [&lt;-]"/>
      </ls_pos>
-     <ls_pos name="set" id="3528"
+     <ls_pos name="set" id="3541"
       ip_theory="Array">
       <ip_library name="array"/>
       <ip_qualid name="set"/>
      </ls_pos>
-     <ls_pos name="mixfix [&lt;-]" id="3570"
+     <ls_pos name="mixfix [&lt;-]" id="3583"
       ip_theory="Array">
       <ip_library name="array"/>
       <ip_qualid name="mixfix [&lt;-]"/>
      </ls_pos>
-     <ls_pos name="first_primes" id="6730"
+     <ls_pos name="first_primes" id="6743"
       ip_theory="PrimeNumbers">
       <ip_qualid name="first_primes"/>
      </ls_pos>
@@ -2726,226 +2726,226 @@
       <ip_library name="int"/>
       <ip_qualid name="Mod_mult"/>
      </pr_pos>
-     <pr_pos name="even_or_odd" id="2611"
+     <pr_pos name="even_or_odd" id="2624"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_or_odd"/>
      </pr_pos>
-     <pr_pos name="even_not_odd" id="2614"
+     <pr_pos name="even_not_odd" id="2627"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_not_odd"/>
      </pr_pos>
-     <pr_pos name="odd_not_even" id="2617"
+     <pr_pos name="odd_not_even" id="2630"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_not_even"/>
      </pr_pos>
-     <pr_pos name="even_odd" id="2620"
+     <pr_pos name="even_odd" id="2633"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_odd"/>
      </pr_pos>
-     <pr_pos name="odd_even" id="2623"
+     <pr_pos name="odd_even" id="2636"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_even"/>
      </pr_pos>
-     <pr_pos name="even_even" id="2626"
+     <pr_pos name="even_even" id="2639"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_even"/>
      </pr_pos>
-     <pr_pos name="odd_odd" id="2629"
+     <pr_pos name="odd_odd" id="2642"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_odd"/>
      </pr_pos>
-     <pr_pos name="even_2k" id="2632"
+     <pr_pos name="even_2k" id="2645"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="even_2k"/>
      </pr_pos>
-     <pr_pos name="odd_2k1" id="2635"
+     <pr_pos name="odd_2k1" id="2648"
       ip_theory="Parity">
       <ip_library name="number"/>
       <ip_qualid name="odd_2k1"/>
      </pr_pos>
-     <pr_pos name="divides_refl" id="2651"
+     <pr_pos name="divides_refl" id="2664"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_refl"/>
      </pr_pos>
-     <pr_pos name="divides_1_n" id="2654"
+     <pr_pos name="divides_1_n" id="2667"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_1_n"/>
      </pr_pos>
-     <pr_pos name="divides_0" id="2657"
+     <pr_pos name="divides_0" id="2670"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_0"/>
      </pr_pos>
-     <pr_pos name="divides_left" id="2660"
+     <pr_pos name="divides_left" id="2673"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_left"/>
      </pr_pos>
-     <pr_pos name="divides_right" id="2667"
+     <pr_pos name="divides_right" id="2680"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_right"/>
      </pr_pos>
-     <pr_pos name="divides_oppr" id="2674"
+     <pr_pos name="divides_oppr" id="2687"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppr"/>
      </pr_pos>
-     <pr_pos name="divides_oppl" id="2679"
+     <pr_pos name="divides_oppl" id="2692"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppl"/>
      </pr_pos>
-     <pr_pos name="divides_oppr_rev" id="2684"
+     <pr_pos name="divides_oppr_rev" id="2697"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppr_rev"/>
      </pr_pos>
-     <pr_pos name="divides_oppl_rev" id="2689"
+     <pr_pos name="divides_oppl_rev" id="2702"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_oppl_rev"/>
      </pr_pos>
-     <pr_pos name="divides_plusr" id="2694"
+     <pr_pos name="divides_plusr" id="2707"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_plusr"/>
      </pr_pos>
-     <pr_pos name="divides_minusr" id="2701"
+     <pr_pos name="divides_minusr" id="2714"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_minusr"/>
      </pr_pos>
-     <pr_pos name="divides_multl" id="2708"
+     <pr_pos name="divides_multl" id="2721"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_multl"/>
      </pr_pos>
-     <pr_pos name="divides_multr" id="2715"
+     <pr_pos name="divides_multr" id="2728"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_multr"/>
      </pr_pos>
-     <pr_pos name="divides_factorl" id="2722"
+     <pr_pos name="divides_factorl" id="2735"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_factorl"/>
      </pr_pos>
-     <pr_pos name="divides_factorr" id="2727"
+     <pr_pos name="divides_factorr" id="2740"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_factorr"/>
      </pr_pos>
-     <pr_pos name="divides_n_1" id="2732"
+     <pr_pos name="divides_n_1" id="2745"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_n_1"/>
      </pr_pos>
-     <pr_pos name="divides_antisym" id="2735"
+     <pr_pos name="divides_antisym" id="2748"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_antisym"/>
      </pr_pos>
-     <pr_pos name="divides_trans" id="2740"
+     <pr_pos name="divides_trans" id="2753"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_trans"/>
      </pr_pos>
-     <pr_pos name="divides_bounds" id="2747"
+     <pr_pos name="divides_bounds" id="2760"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_bounds"/>
      </pr_pos>
-     <pr_pos name="mod_divides_euclidean" id="2752"
+     <pr_pos name="mod_divides_euclidean" id="2765"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="mod_divides_euclidean"/>
      </pr_pos>
-     <pr_pos name="divides_mod_euclidean" id="2757"
+     <pr_pos name="divides_mod_euclidean" id="2770"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_mod_euclidean"/>
      </pr_pos>
-     <pr_pos name="mod_divides_computer" id="2762"
+     <pr_pos name="mod_divides_computer" id="2775"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="mod_divides_computer"/>
      </pr_pos>
-     <pr_pos name="divides_mod_computer" id="2767"
+     <pr_pos name="divides_mod_computer" id="2780"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="divides_mod_computer"/>
      </pr_pos>
-     <pr_pos name="even_divides" id="2772"
+     <pr_pos name="even_divides" id="2785"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="even_divides"/>
      </pr_pos>
-     <pr_pos name="odd_divides" id="2775"
+     <pr_pos name="odd_divides" id="2788"
       ip_theory="Divisibility">
       <ip_library name="number"/>
       <ip_qualid name="odd_divides"/>
      </pr_pos>
-     <pr_pos name="not_prime_1" id="2869"
+     <pr_pos name="not_prime_1" id="2882"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="not_prime_1"/>
      </pr_pos>
-     <pr_pos name="prime_2" id="2870"
+     <pr_pos name="prime_2" id="2883"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="prime_2"/>
      </pr_pos>
-     <pr_pos name="prime_3" id="2871"
+     <pr_pos name="prime_3" id="2884"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="prime_3"/>
      </pr_pos>
-     <pr_pos name="prime_divisors" id="2872"
+     <pr_pos name="prime_divisors" id="2885"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="prime_divisors"/>
      </pr_pos>
-     <pr_pos name="small_divisors" id="2877"
+     <pr_pos name="small_divisors" id="2890"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="small_divisors"/>
      </pr_pos>
-     <pr_pos name="even_prime" id="2882"
+     <pr_pos name="even_prime" id="2895"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="even_prime"/>
      </pr_pos>
-     <pr_pos name="odd_prime" id="2885"
+     <pr_pos name="odd_prime" id="2898"
       ip_theory="Prime">
       <ip_library name="number"/>
       <ip_qualid name="odd_prime"/>
      </pr_pos>
-     <pr_pos name="Select_eq" id="3114"
+     <pr_pos name="Select_eq" id="3127"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="Select_eq"/>
      </pr_pos>
-     <pr_pos name="Select_neq" id="3123"
+     <pr_pos name="Select_neq" id="3136"
       ip_theory="Map">
       <ip_library name="map"/>
       <ip_qualid name="Select_neq"/>
      </pr_pos>
-     <pr_pos name="exists_prime" id="6757"
+     <pr_pos name="exists_prime" id="6770"
       ip_theory="PrimeNumbers">
       <ip_qualid name="exists_prime"/>
      </pr_pos>
-     <pr_pos name="Bertrand_postulate" id="6770"
+     <pr_pos name="Bertrand_postulate" id="6783"
       ip_theory="PrimeNumbers">
       <ip_qualid name="Bertrand_postulate"/>
      </pr_pos>
@@ -2998,34 +2998,34 @@
       <meta_arg_ls id="2064"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="2595"/>
+      <meta_arg_ls id="2608"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="2603"/>
+      <meta_arg_ls id="2616"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="2932"/>
+      <meta_arg_ls id="2945"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3078"/>
+      <meta_arg_ls id="3091"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3081"/>
+      <meta_arg_ls id="3094"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3088"/>
+      <meta_arg_ls id="3101"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3101"/>
+      <meta_arg_ls id="3114"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3528"/>
+      <meta_arg_ls id="3541"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="3570"/>
+      <meta_arg_ls id="3583"/>
      </meta>
      <meta name="remove_logic">
-      <meta_arg_ls id="6730"/>
+      <meta_arg_ls id="6743"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="1744"/>
@@ -3178,79 +3178,70 @@
       <meta_arg_pr id="2130"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2611"/>
-     </meta>
-     <meta name="remove_prop">
-      <meta_arg_pr id="2614"/>
+      <meta_arg_pr id="2624"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2617"/>
+      <meta_arg_pr id="2627"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2620"/>
+      <meta_arg_pr id="2630"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2623"/>
+      <meta_arg_pr id="2633"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2626"/>
+      <meta_arg_pr id="2636"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2629"/>
+      <meta_arg_pr id="2639"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2632"/>
+      <meta_arg_pr id="2642"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2635"/>
+      <meta_arg_pr id="2645"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2651"/>
+      <meta_arg_pr id="2648"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2654"/>
-     </meta>
-     <meta name="remove_prop">
-      <meta_arg_pr id="2657"/>
-     </meta>
-     <meta name="remove_prop">
-      <meta_arg_pr id="2660"/>
+      <meta_arg_pr id="2664"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2667"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2674"/>
+      <meta_arg_pr id="2670"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2679"/>
+      <meta_arg_pr id="2673"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2684"/>
+      <meta_arg_pr id="2680"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2689"/>
+      <meta_arg_pr id="2687"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2694"/>
+      <meta_arg_pr id="2692"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2701"/>
+      <meta_arg_pr id="2697"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2708"/>
+      <meta_arg_pr id="2702"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2715"/>
+      <meta_arg_pr id="2707"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2722"/>
+      <meta_arg_pr id="2714"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2727"/>
+      <meta_arg_pr id="2721"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2732"/>
+      <meta_arg_pr id="2728"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2735"/>
@@ -3259,59 +3250,68 @@
       <meta_arg_pr id="2740"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2747"/>
+      <meta_arg_pr id="2745"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2752"/>
+      <meta_arg_pr id="2748"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2757"/>
+      <meta_arg_pr id="2753"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2762"/>
+      <meta_arg_pr id="2760"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2767"/>
+      <meta_arg_pr id="2765"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2772"/>
+      <meta_arg_pr id="2770"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2775"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2869"/>
+      <meta_arg_pr id="2780"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2870"/>
+      <meta_arg_pr id="2785"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2871"/>
+      <meta_arg_pr id="2788"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2872"/>
+      <meta_arg_pr id="2882"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2877"/>
+      <meta_arg_pr id="2883"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="2882"/>
+      <meta_arg_pr id="2884"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="2885"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="3114"/>
+      <meta_arg_pr id="2890"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="3123"/>
+      <meta_arg_pr id="2895"/>
      </meta>
      <meta name="remove_prop">
-      <meta_arg_pr id="6757"/>
+      <meta_arg_pr id="2898"/>
+     </meta>
+     <meta name="remove_prop">
+      <meta_arg_pr id="3127"/>
+     </meta>
+     <meta name="remove_prop">
+      <meta_arg_pr id="3136"/>
      </meta>
      <meta name="remove_prop">
       <meta_arg_pr id="6770"/>
      </meta>
+     <meta name="remove_prop">
+      <meta_arg_pr id="6783"/>
+     </meta>
      <meta name="remove_type">
       <meta_arg_ts id="2"/>
      </meta>
@@ -3331,7 +3331,7 @@
       <meta_arg_ts id="1286"/>
      </meta>
      <meta name="remove_type">
-      <meta_arg_ts id="2926"/>
+      <meta_arg_ts id="2939"/>
      </meta>
      <goal name="WP_parameter prime_numbers.40.1.4" expl="VC for prime_numbers">
      <transf name="eliminate_builtin">
diff --git a/examples/koda_ruskey/why3session.xml b/examples/koda_ruskey/why3session.xml
index bfe9f9cddda350314d5568980f7b6371c2451c9c..fa1aa116b361b7a4eba07c1f18436d60e770f13c 100644
--- a/examples/koda_ruskey/why3session.xml
+++ b/examples/koda_ruskey/why3session.xml
@@ -6,7 +6,7 @@
 <prover id="1" name="Z3" version="4.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="36" steplimit="0" memlimit="1000"/>
 <prover id="3" name="Eprover" version="1.8-001" timelimit="36" steplimit="0" memlimit="1000"/>
-<prover id="5" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="6" name="Z3" version="4.4.1" alternative="noBV" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="7" name="Alt-Ergo" version="1.30" timelimit="6" steplimit="0" memlimit="1000"/>
 <file name="../koda_ruskey.mlw" expanded="true">
@@ -524,7 +524,7 @@
   <proof prover="7" timelimit="11"><result status="valid" time="0.01" steps="13"/></proof>
   </goal>
   <goal name="WP_parameter sub_valid_coloring_white.10" expl="postcondition">
-  <proof prover="5" edited="koda_ruskey_KodaRuskey_Spec_WP_parameter_sub_valid_coloring_white_1.v"><result status="valid" time="2.37"/></proof>
+  <proof prover="4" edited="koda_ruskey_KodaRuskey_Spec_WP_parameter_sub_valid_coloring_white_1.v"><result status="valid" time="2.37"/></proof>
   </goal>
  </transf>
  </goal>
diff --git a/examples/logic/genealogy/why3session.xml b/examples/logic/genealogy/why3session.xml
index 396948970df7bbfd22eb525a1dcc5b50078dc6df..a0757a9a9655c9a8280173a56824b8a6c9ea3cf9 100644
--- a/examples/logic/genealogy/why3session.xml
+++ b/examples/logic/genealogy/why3session.xml
@@ -34,8 +34,8 @@
 <prover id="29" name="Alt-Ergo" version="1.30" timelimit="1" steplimit="0" memlimit="1000"/>
 <prover id="30" name="Isabelle" version="2016-1" timelimit="100" steplimit="1" memlimit="1000"/>
 <prover id="31" name="CVC4" version="1.5" timelimit="1" steplimit="0" memlimit="1000"/>
-<prover id="32" name="Coq" version="8.6.1" timelimit="5" steplimit="1" memlimit="4000"/>
 <prover id="33" name="Z3" version="4.6.0" timelimit="1" steplimit="0" memlimit="1000"/>
+<prover id="34" name="Coq" version="8.7.1" timelimit="5" steplimit="1" memlimit="4000"/>
 <file name="../genealogy.why" expanded="true">
 <theory name="Genealogy" sum="35e1439432a79e05534b2c5cf39ad9dc" expanded="true">
  <goal name="Child_is_son_or_daughter" expl="" expanded="true">
@@ -67,8 +67,8 @@
  <proof prover="29"><result status="valid" time="0.00" steps="10"/></proof>
  <proof prover="30" edited="genealogy_Genealogy_Child_is_son_or_daughter_1.xml"><result status="valid" time="21.67"/></proof>
  <proof prover="31"><result status="valid" time="0.00"/></proof>
- <proof prover="32" edited="genealogy_Genealogy_Child_is_son_or_daughter_1.v"><result status="valid" time="0.51"/></proof>
  <proof prover="33"><result status="valid" time="0.02"/></proof>
+ <proof prover="34" edited="genealogy_Genealogy_Child_is_son_or_daughter_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
  <goal name="Sibling_sym" expl="" expanded="true">
  <proof prover="0"><result status="valid" time="0.00" steps="3"/></proof>
diff --git a/examples/logic/hello_proof/why3session.xml b/examples/logic/hello_proof/why3session.xml
index 7bac9c1b6a69850486da944b6545b8ac4aa15672..b6109f29125ce129ff69b9e46f5b5f4a076bebf1 100644
--- a/examples/logic/hello_proof/why3session.xml
+++ b/examples/logic/hello_proof/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="4" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="4" steplimit="0" memlimit="0"/>
 <prover id="2" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../hello_proof.why" expanded="true">
 <theory name="HelloProof" sum="31cb0fe92366ba83b130a9ff030b37b9" expanded="true">
@@ -13,7 +13,7 @@
  <proof prover="2" timelimit="4" memlimit="0"><result status="unknown" time="0.00"/></proof>
  <transf name="split_goal_wp" expanded="true">
   <goal name="G2.1" expl="" expanded="true">
-  <proof prover="1" edited="hello_proof_HelloProof_G2_1.v"><result status="unknown" time="0.29"/></proof>
+  <proof prover="0" edited="hello_proof_HelloProof_G2_1.v"><result status="unknown" time="0.29"/></proof>
   <proof prover="2"><result status="unknown" time="0.00"/></proof>
   </goal>
   <goal name="G2.2" expl="" expanded="true">
diff --git a/examples/logic/lagrange_inequality/why3session.xml b/examples/logic/lagrange_inequality/why3session.xml
index 73f90894b6a8719513f428f29d711038c8125849..9c88f6fc60518104bbaa6190eea1f1856e4c89fc 100644
--- a/examples/logic/lagrange_inequality/why3session.xml
+++ b/examples/logic/lagrange_inequality/why3session.xml
@@ -2,9 +2,9 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="4000"/>
 <prover id="1" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="3" steplimit="0" memlimit="1000"/>
-<prover id="3" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="4000"/>
 <prover id="5" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="6" name="MetiTarski" version="2.4" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="11" name="Z3" version="4.3.2" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -31,11 +31,11 @@
  <proof prover="11"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="sqr_le_sqrt" expl="">
- <proof prover="3" edited="lagrange_inequality_CauchySchwarzInequality_sqr_le_sqrt_1.v"><result status="valid" time="0.72"/></proof>
+ <proof prover="0" edited="lagrange_inequality_CauchySchwarzInequality_sqr_le_sqrt_1.v"><result status="valid" time="0.97"/></proof>
  <proof prover="6"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="CauchySchwarz" expl="">
- <proof prover="3" edited="lagrange_inequality_CauchySchwarzInequality_CauchySchwarz_1.v"><result status="valid" time="0.59"/></proof>
+ <proof prover="0" edited="lagrange_inequality_CauchySchwarzInequality_CauchySchwarz_1.v"><result status="valid" time="0.59"/></proof>
  </goal>
 </theory>
 <theory name="TriangleInequality" sum="51121fb1817b220eb49dfcf272eb4733" expanded="true">
@@ -48,7 +48,7 @@
  <proof prover="6"><result status="valid" time="0.06"/></proof>
  </goal>
  <goal name="triangle" expl="">
- <proof prover="3" memlimit="1000" edited="lagrange_inequality_TriangleInequality_triangle_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="0" memlimit="1000" edited="lagrange_inequality_TriangleInequality_triangle_1.v"><result status="valid" time="0.33"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/logic/my_cosine/why3session.xml b/examples/logic/my_cosine/why3session.xml
index 8a760fa079fc9a8bc950b93d07e2dfa1b56013af..29e4c5c0d767e5b8e5afe924c3d301644015c95f 100644
--- a/examples/logic/my_cosine/why3session.xml
+++ b/examples/logic/my_cosine/why3session.xml
@@ -3,13 +3,13 @@
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
 <prover id="0" name="Gappa" version="1.3.0" timelimit="2" steplimit="0" memlimit="0"/>
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="2" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="MetiTarski" version="2.4" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Alt-Ergo" version="0.99.1" timelimit="3" steplimit="0" memlimit="0"/>
 <file name="../my_cosine.why" expanded="true">
 <theory name="CosineSingle" sum="23a24172e393e41730c2d2c33ef08241" expanded="true">
  <goal name="MethodError" expl="" expanded="true">
- <proof prover="1" edited="my_cosine_CosineSingle_MethodError_1.v"><result status="valid" time="1.74"/></proof>
+ <proof prover="2" edited="my_cosine_CosineSingle_MethodError_1.v"><result status="valid" time="1.74"/></proof>
  <proof prover="3"><result status="valid" time="0.24"/></proof>
  </goal>
  <goal name="TotalErrorFullyExpanded" expl="" expanded="true">
diff --git a/examples/logic/real/why3session.xml b/examples/logic/real/why3session.xml
index 5d333024999e00ddf5bb7053d011c032f0bc09a2..760f72a70cecec3717fa1fbeb1837b26b3e30267 100644
--- a/examples/logic/real/why3session.xml
+++ b/examples/logic/real/why3session.xml
@@ -2,12 +2,12 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="MetiTarski" version="2.4" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../real.why" expanded="true">
 <theory name="CosineSingle" sum="14a5c4aa392160a9ad642eb8d04a7af1" expanded="true">
  <goal name="MethodError" expl="" expanded="true">
- <proof prover="1" edited="real_CosineSingle_MethodError_1.v"><result status="valid" time="1.82"/></proof>
+ <proof prover="0" edited="real_CosineSingle_MethodError_1.v"><result status="valid" time="1.82"/></proof>
  <proof prover="2"><result status="valid" time="0.11"/></proof>
  </goal>
 </theory>
diff --git a/examples/logic/sorted_list/why3session.xml b/examples/logic/sorted_list/why3session.xml
index c8fdabe870448d2c4a5471963c9173819758f56e..663c6239990720eaed934c59741600c83f844ccb 100644
--- a/examples/logic/sorted_list/why3session.xml
+++ b/examples/logic/sorted_list/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="2" name="Z3" version="4.3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="6" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -17,7 +17,7 @@
  <proof prover="2"><result status="valid" time="0.00"/></proof>
  </goal>
  <goal name="sorted_mem" expl="" expanded="true">
- <proof prover="1" edited="sorted_list_SortedList_sorted_mem_1.v"><result status="valid" time="0.31"/></proof>
+ <proof prover="0" edited="sorted_list_SortedList_sorted_mem_1.v"><result status="valid" time="0.31"/></proof>
  </goal>
 </theory>
 <theory name="SortedIntList" sum="a5e1f86435a4837ecf6b8569084ac1bc" expanded="true">
diff --git a/examples/logic/triangle_inequality/why3session.xml b/examples/logic/triangle_inequality/why3session.xml
index a445290306cbb00ebaaddf3d937b82d968454fa1..08d74a044ff6878b9bd5fc7165ea736456177869 100644
--- a/examples/logic/triangle_inequality/why3session.xml
+++ b/examples/logic/triangle_inequality/why3session.xml
@@ -2,8 +2,8 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="4" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Z3" version="4.4.0" timelimit="5" steplimit="0" memlimit="4000"/>
@@ -75,7 +75,7 @@
    <ip_library name="real"/>
    <ip_qualid name="infix &gt;="/>
   </ls_pos>
-  <ls_pos name="sqrt" id="2647"
+  <ls_pos name="sqrt" id="2660"
    ip_theory="Square">
    <ip_library name="real"/>
    <ip_qualid name="sqrt"/>
@@ -214,40 +214,40 @@
    <ip_library name="real"/>
    <ip_qualid name="CompatOrderMult"/>
   </pr_pos>
-  <pr_pos name="Sqrt_positive" id="2649"
+  <pr_pos name="Sqrt_positive" id="2662"
    ip_theory="Square">
    <ip_library name="real"/>
    <ip_qualid name="Sqrt_positive"/>
   </pr_pos>
-  <pr_pos name="Sqrt_square" id="2652"
+  <pr_pos name="Sqrt_square" id="2665"
    ip_theory="Square">
    <ip_library name="real"/>
    <ip_qualid name="Sqrt_square"/>
   </pr_pos>
-  <pr_pos name="Square_sqrt" id="2655"
+  <pr_pos name="Square_sqrt" id="2668"
    ip_theory="Square">
    <ip_library name="real"/>
    <ip_qualid name="Square_sqrt"/>
   </pr_pos>
-  <pr_pos name="Sqrt_mul" id="2658"
+  <pr_pos name="Sqrt_mul" id="2671"
    ip_theory="Square">
    <ip_library name="real"/>
    <ip_qualid name="Sqrt_mul"/>
   </pr_pos>
-  <pr_pos name="Sqrt_le" id="2663"
+  <pr_pos name="Sqrt_le" id="2676"
    ip_theory="Square">
    <ip_library name="real"/>
    <ip_qualid name="Sqrt_le"/>
   </pr_pos>
-  <pr_pos name="norm2_pos" id="2935"
+  <pr_pos name="norm2_pos" id="2954"
    ip_theory="CauchySchwarzInequality">
    <ip_qualid name="norm2_pos"/>
   </pr_pos>
-  <pr_pos name="p_expr" id="2961"
+  <pr_pos name="p_expr" id="2980"
    ip_theory="CauchySchwarzInequality">
    <ip_qualid name="p_expr"/>
   </pr_pos>
-  <pr_pos name="p_pos" id="2972"
+  <pr_pos name="p_pos" id="2991"
    ip_theory="CauchySchwarzInequality">
    <ip_qualid name="p_pos"/>
   </pr_pos>
@@ -276,7 +276,7 @@
    <meta_arg_ls id="1445"/>
   </meta>
   <meta name="remove_logic">
-   <meta_arg_ls id="2647"/>
+   <meta_arg_ls id="2660"/>
   </meta>
   <meta name="remove_prop">
    <meta_arg_pr id="1323"/>
@@ -354,28 +354,28 @@
    <meta_arg_pr id="1482"/>
   </meta>
   <meta name="remove_prop">
-   <meta_arg_pr id="2649"/>
+   <meta_arg_pr id="2662"/>
   </meta>
   <meta name="remove_prop">
-   <meta_arg_pr id="2652"/>
+   <meta_arg_pr id="2665"/>
   </meta>
   <meta name="remove_prop">
-   <meta_arg_pr id="2655"/>
+   <meta_arg_pr id="2668"/>
   </meta>
   <meta name="remove_prop">
-   <meta_arg_pr id="2658"/>
+   <meta_arg_pr id="2671"/>
   </meta>
   <meta name="remove_prop">
-   <meta_arg_pr id="2663"/>
+   <meta_arg_pr id="2676"/>
   </meta>
   <meta name="remove_prop">
-   <meta_arg_pr id="2935"/>
+   <meta_arg_pr id="2954"/>
   </meta>
   <meta name="remove_prop">
-   <meta_arg_pr id="2961"/>
+   <meta_arg_pr id="2980"/>
   </meta>
   <meta name="remove_prop">
-   <meta_arg_pr id="2972"/>
+   <meta_arg_pr id="2991"/>
   </meta>
   <goal name="p_val_part" expl="">
   <transf name="eliminate_builtin">
@@ -398,7 +398,7 @@
  <proof prover="11"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="CauchySchwarz_aux_non_null" expl="">
- <proof prover="2" edited="triangle_inequality_CauchySchwarzInequality_CauchySchwarz_aux_non_null_1.v"><result status="valid" time="0.42"/></proof>
+ <proof prover="0" edited="triangle_inequality_CauchySchwarzInequality_CauchySchwarz_aux_non_null_1.v"><result status="valid" time="0.42"/></proof>
  <proof prover="11"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="norm_null" expl="">
@@ -430,7 +430,7 @@
  <proof prover="11"><result status="valid" time="0.07"/></proof>
  </goal>
  <goal name="CauchySchwarz" expl="">
- <proof prover="2" edited="triangle_inequality_CauchySchwarzInequality_CauchySchwarz_1.v"><result status="valid" time="0.48"/></proof>
+ <proof prover="0" edited="triangle_inequality_CauchySchwarzInequality_CauchySchwarz_1.v"><result status="valid" time="0.48"/></proof>
  </goal>
 </theory>
 <theory name="TriangleInequality" sum="c81c1e0efd1ec340bc35ab1ce72e8bb8" expanded="true">
@@ -443,7 +443,7 @@
  <proof prover="11"><result status="valid" time="0.04"/></proof>
  </goal>
  <goal name="triangle" expl="">
- <proof prover="2" edited="triangle_inequality_TriangleInequality_triangle_1.v"><result status="valid" time="0.40"/></proof>
+ <proof prover="0" edited="triangle_inequality_TriangleInequality_triangle_1.v"><result status="valid" time="0.40"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/maximum_subarray/why3session.xml b/examples/maximum_subarray/why3session.xml
index 25320ad7be06e314de1a7ce7446deeb2158057cf..f33b565733c9d50ff2212c1750ec0c5808116431 100644
--- a/examples/maximum_subarray/why3session.xml
+++ b/examples/maximum_subarray/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="Z3" version="4.3.2" timelimit="10" steplimit="0" memlimit="1000"/>
 <prover id="3" name="Spass" version="3.7" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -476,7 +476,7 @@
   <proof prover="6"><result status="valid" time="0.01" steps="28"/></proof>
   </goal>
   <goal name="WP_parameter maximum_subarray_rec.77" expl="loop invariant preservation">
-  <proof prover="1" edited="maximum_subarray_Algo3_WP_parameter_maximum_subarray_rec_1.v"><result status="valid" time="0.34"/></proof>
+  <proof prover="0" edited="maximum_subarray_Algo3_WP_parameter_maximum_subarray_rec_1.v"><result status="valid" time="0.34"/></proof>
   </goal>
   <goal name="WP_parameter maximum_subarray_rec.78" expl="loop invariant preservation">
   <proof prover="6"><result status="valid" time="0.02" steps="28"/></proof>
@@ -485,7 +485,7 @@
   <proof prover="6"><result status="valid" time="0.02" steps="26"/></proof>
   </goal>
   <goal name="WP_parameter maximum_subarray_rec.80" expl="loop invariant preservation">
-  <proof prover="1" edited="maximum_subarray_Algo3_WP_parameter_maximum_subarray_rec_3.v"><result status="valid" time="0.46"/></proof>
+  <proof prover="0" edited="maximum_subarray_Algo3_WP_parameter_maximum_subarray_rec_3.v"><result status="valid" time="0.46"/></proof>
   </goal>
   <goal name="WP_parameter maximum_subarray_rec.81" expl="loop invariant preservation">
   <proof prover="6"><result status="valid" time="0.02" steps="26"/></proof>
diff --git a/examples/my_cosine/why3session.xml b/examples/my_cosine/why3session.xml
index 2a3c218533ab1e8554460dfa2f0ace5198a455c1..9617a6b8213127da37f71b6a2c1575e63de32a63 100644
--- a/examples/my_cosine/why3session.xml
+++ b/examples/my_cosine/why3session.xml
@@ -3,15 +3,15 @@
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
 <prover id="0" name="Gappa" version="1.3.0" timelimit="2" steplimit="0" memlimit="0"/>
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="MetiTarski" version="2.4" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="3" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../my_cosine.mlw" expanded="true">
 <theory name="M" sum="a5814999cc93d0777a1fc58af5e655fe" expanded="true">
  <goal name="WP_parameter my_cosine" expl="VC for my_cosine" expanded="true">
  <transf name="split_goal_wp" expanded="true">
   <goal name="WP_parameter my_cosine.1" expl="assertion" expanded="true">
-  <proof prover="1" edited="my_cosine_M_WP_parameter_my_cosine_1.v"><result status="valid" time="1.79"/></proof>
   <proof prover="2"><result status="valid" time="0.17"/></proof>
+  <proof prover="3" edited="my_cosine_M_WP_parameter_my_cosine_1.v"><result status="valid" time="1.79"/></proof>
   </goal>
   <goal name="WP_parameter my_cosine.2" expl="precondition" expanded="true">
   <proof prover="0"><result status="valid" time="0.00"/></proof>
diff --git a/examples/prover/Prover/why3session.xml b/examples/prover/Prover/why3session.xml
index acf3ec68dde46070990b53f1041d17ceea2d62ec..4f94088211b22098df44fdea9b1b652141e7593c 100644
--- a/examples/prover/Prover/why3session.xml
+++ b/examples/prover/Prover/why3session.xml
@@ -60,7 +60,7 @@
  </transf>
  </goal>
 </theory>
-<theory name="Impl" sum="38516dc4a1b9f946a6c52acef589e6a0">
+<theory name="Impl" sum="032f778d2a5af213f9117989d600f1bd">
  <goal name="WP_parameter merge" expl="VC for merge">
  <transf name="split_goal_wp">
   <goal name="WP_parameter merge.1" expl="precondition">
@@ -140,13 +140,13 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="26"/></proof>
   </goal>
   <goal name="WP_parameter contract_tableau.3" expl="assertion">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="27"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="27"/></proof>
   </goal>
   <goal name="WP_parameter contract_tableau.4" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.23" steps="18"/></proof>
   </goal>
   <goal name="WP_parameter contract_tableau.5" expl="assertion">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="30"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.12" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contract_tableau.6" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="34"/></proof>
@@ -261,106 +261,97 @@
   <goal name="WP_parameter branch_conflict_atom.11" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="26"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.12" expl="variant decrease">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.32" steps="110"/></proof>
+  <goal name="WP_parameter branch_conflict_atom.12" expl="precondition">
+  <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter branch_conflict_atom.13" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="30"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.20" steps="174"/></proof>
   </goal>
   <goal name="WP_parameter branch_conflict_atom.14" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.20" steps="174"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.40" steps="296"/></proof>
   </goal>
   <goal name="WP_parameter branch_conflict_atom.15" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.40" steps="296"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.21" steps="193"/></proof>
   </goal>
   <goal name="WP_parameter branch_conflict_atom.16" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.21" steps="193"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter branch_conflict_atom.17" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="30"/></proof>
-  </goal>
-  <goal name="WP_parameter branch_conflict_atom.18" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="173"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.19" expl="postcondition">
+  <goal name="WP_parameter branch_conflict_atom.18" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.19" steps="70"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.20" expl="postcondition">
+  <goal name="WP_parameter branch_conflict_atom.19" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="35"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.21" expl="exceptional postcondition">
+  <goal name="WP_parameter branch_conflict_atom.20" expl="exceptional postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="68"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.22" expl="exceptional postcondition">
+  <goal name="WP_parameter branch_conflict_atom.21" expl="exceptional postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="30"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.23" expl="variant decrease">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.29" steps="101"/></proof>
-  </goal>
-  <goal name="WP_parameter branch_conflict_atom.24" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.22" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.23" steps="26"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.25" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.23" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.19" steps="161"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.26" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.24" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="238"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.27" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.25" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.19" steps="179"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.28" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="26"/></proof>
+  <goal name="WP_parameter branch_conflict_atom.26" expl="precondition">
+  <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="26"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.29" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.27" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.19" steps="160"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.30" expl="postcondition">
+  <goal name="WP_parameter branch_conflict_atom.28" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.25" steps="31"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.31" expl="postcondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="31"/></proof>
-  </goal>
-  <goal name="WP_parameter branch_conflict_atom.32" expl="exceptional postcondition">
+  <goal name="WP_parameter branch_conflict_atom.29" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="31"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.33" expl="variant decrease">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="93"/></proof>
+  <goal name="WP_parameter branch_conflict_atom.30" expl="exceptional postcondition">
+  <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="31"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.34" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.31" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.25" steps="23"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.35" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.32" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.20" steps="199"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.36" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.33" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.37" steps="255"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.37" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.34" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.21" steps="220"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.38" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.35" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="23"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.39" expl="precondition">
+  <goal name="WP_parameter branch_conflict_atom.36" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.30" steps="198"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.40" expl="postcondition">
+  <goal name="WP_parameter branch_conflict_atom.37" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="28"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.41" expl="postcondition">
+  <goal name="WP_parameter branch_conflict_atom.38" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.25" steps="28"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.42" expl="exceptional postcondition">
+  <goal name="WP_parameter branch_conflict_atom.39" expl="exceptional postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="28"/></proof>
   </goal>
-  <goal name="WP_parameter branch_conflict_atom.43" expl="unreachable point">
+  <goal name="WP_parameter branch_conflict_atom.40" expl="unreachable point">
   <transf name="eliminate_recursion">
-   <goal name="WP_parameter branch_conflict_atom.43.1" expl="unreachable point">
+   <goal name="WP_parameter branch_conflict_atom.40.1" expl="unreachable point">
    <transf name="eliminate_algebraic">
-    <goal name="WP_parameter branch_conflict_atom.43.1.1" expl="unreachable point">
+    <goal name="WP_parameter branch_conflict_atom.40.1.1" expl="unreachable point">
     <transf name="split_goal_wp">
-     <goal name="WP_parameter branch_conflict_atom.43.1.1.1" expl="unreachable point">
+     <goal name="WP_parameter branch_conflict_atom.40.1.1.1" expl="unreachable point">
      <proof prover="5" timelimit="5"><result status="valid" time="1.93" steps="3962"/></proof>
      </goal>
     </transf>
@@ -571,123 +562,117 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.19" steps="161"/></proof>
   </goal>
   <goal name="WP_parameter clause_conflicts.15" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="27"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.12" steps="27"/></proof>
   </goal>
   <goal name="WP_parameter clause_conflicts.16" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="27"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.12" steps="27"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.17" expl="variant decrease">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.28" steps="81"/></proof>
+  <goal name="WP_parameter clause_conflicts.17" expl="precondition">
+  <proof prover="5" timelimit="5"><result status="valid" time="0.31" steps="192"/></proof>
   </goal>
   <goal name="WP_parameter clause_conflicts.18" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.31" steps="192"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.28" steps="174"/></proof>
   </goal>
   <goal name="WP_parameter clause_conflicts.19" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.28" steps="174"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.37" steps="315"/></proof>
   </goal>
   <goal name="WP_parameter clause_conflicts.20" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.37" steps="315"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.30" steps="175"/></proof>
   </goal>
   <goal name="WP_parameter clause_conflicts.21" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.30" steps="175"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="31"/></proof>
   </goal>
   <goal name="WP_parameter clause_conflicts.22" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="31"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="31"/></proof>
   </goal>
   <goal name="WP_parameter clause_conflicts.23" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="31"/></proof>
-  </goal>
-  <goal name="WP_parameter clause_conflicts.24" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="31"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.25" expl="postcondition">
+  <goal name="WP_parameter clause_conflicts.24" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.16" steps="75"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.26" expl="postcondition">
+  <goal name="WP_parameter clause_conflicts.25" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="36"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.27" expl="exceptional postcondition">
+  <goal name="WP_parameter clause_conflicts.26" expl="exceptional postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="73"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.28" expl="exceptional postcondition">
+  <goal name="WP_parameter clause_conflicts.27" expl="exceptional postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="31"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.29" expl="assertion">
+  <goal name="WP_parameter clause_conflicts.28" expl="assertion">
   <proof prover="5" timelimit="5"><result status="valid" time="0.36" steps="666"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.30" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.29" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.45" steps="617"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.31" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.30" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.51" steps="977"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.32" expl="assertion">
+  <goal name="WP_parameter clause_conflicts.31" expl="assertion">
   <proof prover="5" timelimit="5"><result status="valid" time="0.88" steps="1706"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.33" expl="assertion">
+  <goal name="WP_parameter clause_conflicts.32" expl="assertion">
   <proof prover="5" timelimit="5"><result status="valid" time="0.17" steps="68"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.34" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.33" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.46" steps="845"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.35" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.34" expl="precondition">
   <proof prover="1" timelimit="5"><result status="valid" time="0.36"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.36" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.35" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.25" steps="32"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.37" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.36" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.32" steps="455"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.38" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.37" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="32"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.39" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.38" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="32"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.40" expl="variant decrease">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.31" steps="102"/></proof>
-  </goal>
-  <goal name="WP_parameter clause_conflicts.41" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.39" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.34" steps="503"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.42" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.40" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.32" steps="474"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.43" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.41" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.40" steps="409"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.44" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.42" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.32" steps="475"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.45" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.43" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="36"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.46" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.44" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.25" steps="36"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.47" expl="precondition">
+  <goal name="WP_parameter clause_conflicts.45" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="36"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.48" expl="postcondition">
+  <goal name="WP_parameter clause_conflicts.46" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.16" steps="84"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.49" expl="postcondition">
+  <goal name="WP_parameter clause_conflicts.47" expl="postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="41"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.50" expl="exceptional postcondition">
+  <goal name="WP_parameter clause_conflicts.48" expl="exceptional postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.25" steps="82"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.51" expl="exceptional postcondition">
+  <goal name="WP_parameter clause_conflicts.49" expl="exceptional postcondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="36"/></proof>
   </goal>
-  <goal name="WP_parameter clause_conflicts.52" expl="unreachable point">
+  <goal name="WP_parameter clause_conflicts.50" expl="unreachable point">
   <transf name="eliminate_recursion">
-   <goal name="WP_parameter clause_conflicts.52.1" expl="unreachable point">
+   <goal name="WP_parameter clause_conflicts.50.1" expl="unreachable point">
    <transf name="eliminate_algebraic">
-    <goal name="WP_parameter clause_conflicts.52.1.1" expl="unreachable point">
+    <goal name="WP_parameter clause_conflicts.50.1.1" expl="unreachable point">
     <transf name="split_goal_wp">
-     <goal name="WP_parameter clause_conflicts.52.1.1.1" expl="unreachable point">
+     <goal name="WP_parameter clause_conflicts.50.1.1.1" expl="unreachable point">
      <proof prover="5" timelimit="5"><result status="valid" time="3.18" steps="9389"/></proof>
      </goal>
     </transf>
@@ -696,7 +681,7 @@
    </goal>
   </transf>
   </goal>
-  <goal name="WP_parameter clause_conflicts.53" expl="unreachable point">
+  <goal name="WP_parameter clause_conflicts.51" expl="unreachable point">
   <proof prover="5" timelimit="5"><result status="valid" time="1.37" steps="2571"/></proof>
   </goal>
  </transf>
@@ -713,7 +698,7 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.16" steps="66"/></proof>
   </goal>
   <goal name="WP_parameter decompose.4" expl="assertion">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.28" steps="65"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="65"/></proof>
   </goal>
   <goal name="WP_parameter decompose.5" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.54" steps="696"/></proof>
@@ -821,7 +806,7 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.23" steps="34"/></proof>
   </goal>
   <goal name="WP_parameter decompose.40" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="34"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="34"/></proof>
   </goal>
   <goal name="WP_parameter decompose.41" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.22" steps="194"/></proof>
@@ -833,7 +818,7 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.21" steps="194"/></proof>
   </goal>
   <goal name="WP_parameter decompose.44" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="34"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="34"/></proof>
   </goal>
   <goal name="WP_parameter decompose.45" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.53" steps="656"/></proof>
@@ -934,7 +919,7 @@
   </transf>
   </goal>
   <goal name="WP_parameter decompose.69" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="48"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="48"/></proof>
   </goal>
   <goal name="WP_parameter decompose.70" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.13" steps="48"/></proof>
@@ -1072,7 +1057,7 @@
    <proof prover="5" timelimit="5"><result status="valid" time="0.38" steps="418"/></proof>
    </goal>
    <goal name="WP_parameter decompose.107.6" expl="assertion">
-   <proof prover="6" timelimit="20"><result status="valid" time="8.10"/></proof>
+   <proof prover="6" timelimit="20"><result status="valid" time="9.04"/></proof>
    </goal>
   </transf>
   </goal>
@@ -1111,7 +1096,7 @@
   </transf>
   </goal>
   <goal name="WP_parameter decompose.109" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="45"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="45"/></proof>
   </goal>
   <goal name="WP_parameter decompose.110" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.24" steps="45"/></proof>
@@ -1382,7 +1367,7 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="37"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.8" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.14" steps="37"/></proof>
+  <proof prover="5"><result status="valid" time="0.26" steps="37"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.9" expl="precondition">
   <proof prover="5"><result status="valid" time="0.16" steps="131"/></proof>
@@ -1397,7 +1382,7 @@
   <proof prover="5"><result status="valid" time="0.14" steps="37"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.13" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.26" steps="37"/></proof>
+  <proof prover="5"><result status="valid" time="0.14" steps="37"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.14" expl="precondition">
   <proof prover="5"><result status="valid" time="0.16" steps="131"/></proof>
@@ -1406,22 +1391,22 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.54" steps="339"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.16" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="37"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="37"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.17" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="37"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="37"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.18" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.25" steps="37"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="37"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.19" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="37"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="37"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.20" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="37"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="37"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.21" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="37"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.25" steps="37"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.22" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.24" steps="165"/></proof>
@@ -1574,7 +1559,7 @@
   <proof prover="5"><result status="valid" time="0.15" steps="53"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.72" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.28" steps="53"/></proof>
+  <proof prover="5"><result status="valid" time="0.15" steps="53"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.73" expl="precondition">
   <proof prover="5"><result status="valid" time="0.16" steps="53"/></proof>
@@ -1613,7 +1598,7 @@
   <proof prover="5"><result status="valid" time="0.24" steps="53"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.85" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.28" steps="53"/></proof>
+  <proof prover="5"><result status="valid" time="0.15" steps="53"/></proof>
   </goal>
   <goal name="WP_parameter decompose_literal.86" expl="precondition">
   <proof prover="5"><result status="valid" time="0.14" steps="53"/></proof>
@@ -1833,7 +1818,7 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.32" steps="482"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.22" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.28" steps="46"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="46"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.23" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="52"/></proof>
@@ -1842,7 +1827,7 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.35" steps="489"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.25" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.52" steps="462"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.36" steps="462"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.26" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.37" steps="521"/></proof>
@@ -1863,7 +1848,7 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="56"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.32" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.52" steps="501"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.34" steps="501"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.33" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.17" steps="56"/></proof>
@@ -1872,7 +1857,7 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.21" steps="56"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.35" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.28" steps="56"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="56"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.36" expl="assertion">
   <proof prover="5" timelimit="5"><result status="valid" time="0.24" steps="126"/></proof>
@@ -1972,7 +1957,7 @@
   <proof prover="5"><result status="valid" time="0.28" steps="62"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.49" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.30" steps="62"/></proof>
+  <proof prover="5"><result status="valid" time="0.16" steps="62"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.50" expl="precondition">
   <proof prover="5"><result status="valid" time="0.46" steps="692"/></proof>
@@ -2349,7 +2334,7 @@
   </transf>
   </goal>
   <goal name="WP_parameter contradiction_atom.137" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.28" steps="57"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.15" steps="57"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_atom.138" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.17" steps="57"/></proof>
@@ -2675,7 +2660,7 @@
   <proof prover="5"><result status="valid" time="0.30" steps="372"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.23" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.40" steps="272"/></proof>
+  <proof prover="5"><result status="valid" time="0.25" steps="272"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.24" expl="precondition">
   <proof prover="5"><result status="valid" time="0.27" steps="47"/></proof>
@@ -2693,7 +2678,7 @@
   <proof prover="5"><result status="valid" time="0.15" steps="51"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.29" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.40" steps="262"/></proof>
+  <proof prover="5"><result status="valid" time="0.25" steps="262"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.30" expl="precondition">
   <proof prover="5"><result status="valid" time="0.15" steps="51"/></proof>
@@ -2728,7 +2713,7 @@
    <proof prover="5"><result status="valid" time="0.66" steps="848"/></proof>
    </goal>
    <goal name="WP_parameter contradiction_neg_atom.34.7" expl="assertion">
-   <proof prover="5"><result status="valid" time="0.43" steps="306"/></proof>
+   <proof prover="5"><result status="valid" time="0.28" steps="306"/></proof>
    <proof prover="6"><result status="valid" time="1.58"/></proof>
    </goal>
    <goal name="WP_parameter contradiction_neg_atom.34.8" expl="assertion">
@@ -2767,7 +2752,7 @@
   <proof prover="5"><result status="valid" time="0.39" steps="273"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.39" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.29" steps="55"/></proof>
+  <proof prover="5"><result status="valid" time="0.16" steps="55"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.40" expl="precondition">
   <proof prover="5"><result status="valid" time="0.16" steps="55"/></proof>
@@ -2817,7 +2802,7 @@
   <proof prover="5"><result status="valid" time="1.45" steps="1035"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.50" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.29" steps="57"/></proof>
+  <proof prover="5"><result status="valid" time="0.16" steps="57"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.51" expl="precondition">
   <proof prover="5"><result status="valid" time="0.33" steps="422"/></proof>
@@ -3006,7 +2991,7 @@
   <proof prover="5"><result status="valid" time="0.38" steps="307"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.104" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.28" steps="54"/></proof>
+  <proof prover="5"><result status="valid" time="0.15" steps="54"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.105" expl="assertion">
   <transf name="inline_goal">
@@ -3135,7 +3120,7 @@
     <proof prover="5"><result status="valid" time="0.23" steps="80"/></proof>
     </goal>
     <goal name="WP_parameter contradiction_neg_atom.133.1.5" expl="VC for contradiction_neg_atom">
-    <proof prover="1"><result status="valid" time="7.03"/></proof>
+    <proof prover="1"><result status="valid" time="5.94"/></proof>
     </goal>
     <goal name="WP_parameter contradiction_neg_atom.133.1.6" expl="VC for contradiction_neg_atom">
     <proof prover="5"><result status="valid" time="0.34" steps="82"/></proof>
@@ -3157,7 +3142,7 @@
   <proof prover="5"><result status="valid" time="0.28" steps="241"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.137" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.28" steps="52"/></proof>
+  <proof prover="5"><result status="valid" time="0.15" steps="52"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.138" expl="precondition">
   <proof prover="5"><result status="valid" time="0.28" steps="241"/></proof>
@@ -3184,7 +3169,7 @@
   <proof prover="5"><result status="valid" time="0.26" steps="241"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.146" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.28" steps="52"/></proof>
+  <proof prover="5"><result status="valid" time="0.15" steps="52"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.147" expl="precondition">
   <proof prover="5"><result status="valid" time="0.15" steps="52"/></proof>
@@ -3199,7 +3184,7 @@
   <proof prover="5"><result status="valid" time="0.16" steps="52"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.151" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.41" steps="240"/></proof>
+  <proof prover="5"><result status="valid" time="0.26" steps="240"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.152" expl="precondition">
   <proof prover="5"><result status="valid" time="0.26" steps="224"/></proof>
@@ -3247,7 +3232,7 @@
   <proof prover="5"><result status="valid" time="0.25" steps="40"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.167" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.37" steps="240"/></proof>
+  <proof prover="5"><result status="valid" time="0.22" steps="240"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.168" expl="precondition">
   <proof prover="5"><result status="valid" time="0.15" steps="40"/></proof>
@@ -3319,7 +3304,7 @@
   <proof prover="5"><result status="valid" time="0.26" steps="278"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.191" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.27" steps="36"/></proof>
+  <proof prover="5"><result status="valid" time="0.14" steps="36"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.192" expl="precondition">
   <proof prover="5"><result status="valid" time="0.25" steps="278"/></proof>
@@ -3349,13 +3334,13 @@
   <proof prover="5"><result status="valid" time="0.26" steps="36"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.201" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.37" steps="254"/></proof>
+  <proof prover="5"><result status="valid" time="0.23" steps="254"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.202" expl="precondition">
   <proof prover="5"><result status="valid" time="0.23" steps="235"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.203" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.30" steps="72"/></proof>
+  <proof prover="5"><result status="valid" time="0.16" steps="72"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_neg_atom.204" expl="precondition">
   <proof prover="5"><result status="valid" time="0.18" steps="72"/></proof>
@@ -3401,10 +3386,10 @@
   <proof prover="5"><result status="valid" time="0.25" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.4" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.26" steps="23"/></proof>
+  <proof prover="5"><result status="valid" time="0.14" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.5" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.16" steps="70"/></proof>
+  <proof prover="5"><result status="valid" time="0.15" steps="70"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.6" expl="precondition">
   <proof prover="5"><result status="valid" time="0.24" steps="23"/></proof>
@@ -3416,37 +3401,37 @@
   <proof prover="5"><result status="valid" time="0.14" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.9" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.27" steps="23"/></proof>
+  <proof prover="5"><result status="valid" time="0.26" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.10" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.15" steps="70"/></proof>
+  <proof prover="5"><result status="valid" time="0.16" steps="70"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.11" expl="precondition">
   <proof prover="5"><result status="valid" time="0.12" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.12" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.24" steps="23"/></proof>
+  <proof prover="5"><result status="valid" time="0.13" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.13" expl="precondition">
   <proof prover="5"><result status="valid" time="0.13" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.14" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.25" steps="23"/></proof>
+  <proof prover="5"><result status="valid" time="0.14" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.15" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.13" steps="23"/></proof>
+  <proof prover="5"><result status="valid" time="0.24" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.16" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.26" steps="23"/></proof>
+  <proof prover="5"><result status="valid" time="0.13" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.17" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.14" steps="23"/></proof>
+  <proof prover="5"><result status="valid" time="0.25" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.18" expl="precondition">
   <proof prover="5"><result status="valid" time="0.23" steps="40"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.19" expl="postcondition">
-  <proof prover="5"><result status="valid" time="0.28" steps="43"/></proof>
+  <proof prover="5"><result status="valid" time="0.15" steps="43"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.20" expl="postcondition">
   <proof prover="5"><result status="valid" time="0.15" steps="26"/></proof>
@@ -3510,13 +3495,13 @@
   <proof prover="5"><result status="valid" time="0.29" steps="280"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.39" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.22" steps="188"/></proof>
+  <proof prover="5"><result status="valid" time="0.21" steps="188"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.40" expl="precondition">
   <proof prover="5"><result status="valid" time="0.29" steps="280"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.41" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.21" steps="188"/></proof>
+  <proof prover="5"><result status="valid" time="0.22" steps="188"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.42" expl="precondition">
   <proof prover="5"><result status="valid" time="0.23" steps="30"/></proof>
@@ -3540,7 +3525,7 @@
   <proof prover="5"><result status="valid" time="0.20" steps="169"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.49" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.27" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.13" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.50" expl="precondition">
   <proof prover="5"><result status="valid" time="0.26" steps="30"/></proof>
@@ -3606,16 +3591,16 @@
   <proof prover="5"><result status="valid" time="0.29" steps="387"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.71" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.31" steps="421"/></proof>
+  <proof prover="5"><result status="valid" time="0.35" steps="421"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.72" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.30" steps="416"/></proof>
+  <proof prover="5"><result status="valid" time="0.42" steps="416"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.73" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.35" steps="421"/></proof>
+  <proof prover="5"><result status="valid" time="0.31" steps="421"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.74" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.42" steps="416"/></proof>
+  <proof prover="5"><result status="valid" time="0.30" steps="416"/></proof>
   </goal>
   <goal name="WP_parameter extend_branch.75" expl="precondition">
   <proof prover="5"><result status="valid" time="0.15" steps="35"/></proof>
@@ -3701,13 +3686,13 @@
   <proof prover="5"><result status="valid" time="0.15" steps="63"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.3" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.27" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.14" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.4" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.26" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.14" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.5" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.18" steps="109"/></proof>
+  <proof prover="5"><result status="valid" time="0.17" steps="109"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.6" expl="precondition">
   <proof prover="5"><result status="valid" time="0.26" steps="30"/></proof>
@@ -3719,28 +3704,28 @@
   <proof prover="5"><result status="valid" time="0.15" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.9" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.14" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.26" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.10" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.17" steps="109"/></proof>
+  <proof prover="5"><result status="valid" time="0.18" steps="109"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.11" expl="precondition">
   <proof prover="5"><result status="valid" time="0.14" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.12" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.26" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.14" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.13" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.15" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.13" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.14" expl="precondition">
   <proof prover="5"><result status="valid" time="0.14" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.15" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.27" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.26" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.16" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.13" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.15" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_atom.17" expl="precondition">
   <proof prover="5"><result status="valid" time="0.14" steps="30"/></proof>
@@ -3916,7 +3901,7 @@
    <proof prover="5" timelimit="5"><result status="valid" time="0.24" steps="106"/></proof>
    </goal>
    <goal name="WP_parameter contradiction_find_atom.69.6" expl="assertion">
-   <proof prover="5" timelimit="5"><result status="valid" time="0.34" steps="182"/></proof>
+   <proof prover="5" timelimit="5"><result status="valid" time="0.20" steps="182"/></proof>
    </goal>
    <goal name="WP_parameter contradiction_find_atom.69.7" expl="assertion">
    <proof prover="5" timelimit="5"><result status="valid" time="0.41" steps="594"/></proof>
@@ -4410,22 +4395,22 @@
   <proof prover="5"><result status="valid" time="0.25" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.12" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.12" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.26" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.13" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.27" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.25" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.14" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.24" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.14" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.15" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.26" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.12" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.16" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.25" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.27" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.17" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.14" steps="30"/></proof>
+  <proof prover="5"><result status="valid" time="0.24" steps="30"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.18" expl="precondition">
   <proof prover="5"><result status="valid" time="0.16" steps="63"/></proof>
@@ -4686,7 +4671,7 @@
   <proof prover="5"><result status="valid" time="0.29" steps="48"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.84" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.29" steps="48"/></proof>
+  <proof prover="5"><result status="valid" time="0.16" steps="48"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.85" expl="precondition">
   <proof prover="5"><result status="valid" time="0.29" steps="98"/></proof>
@@ -4818,7 +4803,7 @@
   <proof prover="5"><result status="valid" time="0.17" steps="65"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.128" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.34" steps="130"/></proof>
+  <proof prover="5"><result status="valid" time="0.18" steps="130"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.129" expl="precondition">
   <proof prover="5"><result status="valid" time="0.51" steps="630"/></proof>
@@ -4923,7 +4908,7 @@
   <proof prover="5"><result status="valid" time="0.27" steps="50"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.159" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.28" steps="50"/></proof>
+  <proof prover="5"><result status="valid" time="0.14" steps="50"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.160" expl="precondition">
   <proof prover="5"><result status="valid" time="0.26" steps="50"/></proof>
@@ -4980,7 +4965,7 @@
   <proof prover="5"><result status="valid" time="0.15" steps="38"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.178" expl="precondition">
-  <proof prover="5"><result status="valid" time="0.28" steps="38"/></proof>
+  <proof prover="5"><result status="valid" time="0.14" steps="38"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.179" expl="precondition">
   <proof prover="5"><result status="valid" time="0.25" steps="210"/></proof>
@@ -5028,7 +5013,7 @@
   <proof prover="5"><result status="valid" time="0.16" steps="43"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.194" expl="exceptional postcondition">
-  <proof prover="5"><result status="valid" time="0.29" steps="43"/></proof>
+  <proof prover="5"><result status="valid" time="0.16" steps="43"/></proof>
   </goal>
   <goal name="WP_parameter contradiction_find_neg_atom.195" expl="unreachable point">
   <proof prover="5"><result status="valid" time="1.75" steps="3339"/></proof>
@@ -5086,16 +5071,16 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.30" steps="132"/></proof>
   </goal>
   <goal name="WP_parameter select_lemma.17" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="32"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.23" steps="32"/></proof>
   </goal>
   <goal name="WP_parameter select_lemma.18" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.17" steps="88"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.18" steps="88"/></proof>
   </goal>
   <goal name="WP_parameter select_lemma.19" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.23" steps="32"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="32"/></proof>
   </goal>
   <goal name="WP_parameter select_lemma.20" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.18" steps="88"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.17" steps="88"/></proof>
   </goal>
   <goal name="WP_parameter select_lemma.21" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.23" steps="32"/></proof>
@@ -5104,7 +5089,7 @@
   <proof prover="5" timelimit="5"><result status="valid" time="0.26" steps="32"/></proof>
   </goal>
   <goal name="WP_parameter select_lemma.23" expl="precondition">
-  <proof prover="5" timelimit="5"><result status="valid" time="0.27" steps="32"/></proof>
+  <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="32"/></proof>
   </goal>
   <goal name="WP_parameter select_lemma.24" expl="precondition">
   <proof prover="5" timelimit="5"><result status="valid" time="0.14" steps="32"/></proof>
diff --git a/examples/prover/Prover/why3shapes.gz b/examples/prover/Prover/why3shapes.gz
index 6bcae139b57ee690c7c5f24c06a5a05da8b2ac0d..bba44cdffc9593626a1339aa57a043280c647d42 100644
Binary files a/examples/prover/Prover/why3shapes.gz and b/examples/prover/Prover/why3shapes.gz differ
diff --git a/examples/queens/why3session.xml b/examples/queens/why3session.xml
index 30f1afc207b2bad32b878305292b57a59d36175f..5ed05b2c442af25762a05c698a9cbeb39ca1861c 100644
--- a/examples/queens/why3session.xml
+++ b/examples/queens/why3session.xml
@@ -3,8 +3,8 @@
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
 <prover id="0" name="CVC4" version="1.4" timelimit="25" steplimit="0" memlimit="1000"/>
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="10" steplimit="0" memlimit="0"/>
+<prover id="3" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="8" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="9" name="Z3" version="4.3.2" timelimit="25" steplimit="0" memlimit="1000"/>
 <prover id="11" name="Alt-Ergo" version="0.99.1" timelimit="25" steplimit="0" memlimit="1000"/>
@@ -87,21 +87,21 @@
    <proof prover="11" timelimit="5"><result status="valid" time="0.27" steps="290"/></proof>
    </goal>
    <goal name="WP_parameter t3.3.7" expl="VC for t3">
-   <proof prover="1" memlimit="1000" edited="queens_WP_NQueensSets_WP_parameter_t3_1.v"><result status="valid" time="1.12"/></proof>
+   <proof prover="3" memlimit="1000" edited="queens_WP_NQueensSets_WP_parameter_t3_1.v"><result status="valid" time="0.85"/></proof>
    <proof prover="11"><result status="valid" time="0.29" steps="290"/></proof>
    </goal>
    <goal name="WP_parameter t3.3.8" expl="VC for t3">
    <proof prover="11"><result status="valid" time="0.47" steps="383"/></proof>
    </goal>
    <goal name="WP_parameter t3.3.9" expl="VC for t3">
-   <proof prover="1" memlimit="1000" edited="queens_WP_NQueensSets_WP_parameter_t3_3.v"><result status="valid" time="2.71"/></proof>
+   <proof prover="3" memlimit="1000" edited="queens_WP_NQueensSets_WP_parameter_t3_3.v"><result status="valid" time="1.38"/></proof>
    </goal>
    <goal name="WP_parameter t3.3.10" expl="VC for t3">
    <proof prover="0"><result status="valid" time="0.42"/></proof>
    <proof prover="11"><result status="valid" time="0.16" steps="172"/></proof>
    </goal>
    <goal name="WP_parameter t3.3.11" expl="VC for t3">
-   <proof prover="1" memlimit="1000" edited="queens_WP_NQueensSets_WP_parameter_t3_4.v"><result status="valid" time="2.46"/></proof>
+   <proof prover="3" memlimit="1000" edited="queens_WP_NQueensSets_WP_parameter_t3_4.v"><result status="valid" time="1.35"/></proof>
    </goal>
    <goal name="WP_parameter t3.3.12" expl="VC for t3">
    <transf name="inline_goal">
@@ -155,10 +155,10 @@
    <proof prover="2"><result status="valid" time="0.19"/></proof>
    </goal>
    <goal name="WP_parameter t3.4.6" expl="VC for t3">
-   <proof prover="1" timelimit="10" edited="queens_WP_NQueensSets_WP_parameter_t3_5.v"><result status="valid" time="1.24"/></proof>
+   <proof prover="3" timelimit="10" edited="queens_WP_NQueensSets_WP_parameter_t3_5.v"><result status="valid" time="1.24"/></proof>
    </goal>
    <goal name="WP_parameter t3.4.7" expl="VC for t3">
-   <proof prover="1" timelimit="10" edited="queens_WP_NQueensSets_WP_parameter_t3_6.v"><result status="valid" time="0.75"/></proof>
+   <proof prover="3" timelimit="10" edited="queens_WP_NQueensSets_WP_parameter_t3_6.v"><result status="valid" time="0.75"/></proof>
    </goal>
    <goal name="WP_parameter t3.4.8" expl="VC for t3">
    <proof prover="2" timelimit="55"><result status="valid" time="18.50"/></proof>
@@ -211,7 +211,7 @@
    <proof prover="11"><result status="valid" time="0.01" steps="15"/></proof>
    </goal>
    <goal name="WP_parameter t3.6.5" expl="VC for t3">
-   <proof prover="1" timelimit="10" edited="queens_WP_NQueensSets_WP_parameter_t3_2.v"><result status="valid" time="1.08"/></proof>
+   <proof prover="3" timelimit="10" edited="queens_WP_NQueensSets_WP_parameter_t3_2.v"><result status="valid" time="1.08"/></proof>
    </goal>
    <goal name="WP_parameter t3.6.6" expl="VC for t3">
    <proof prover="0"><result status="valid" time="0.02"/></proof>
diff --git a/examples/residual/why3session.xml b/examples/residual/why3session.xml
index 9b4e698020e438d10a2dfe37fe14af47b31504f3..0aec54c9cad5645458c4ca7f5bd65b9b966c0493 100644
--- a/examples/residual/why3session.xml
+++ b/examples/residual/why3session.xml
@@ -5,8 +5,8 @@
 <prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="1" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="1" memlimit="1000"/>
 <prover id="2" name="CVC4" version="1.4" timelimit="5" steplimit="1" memlimit="1000"/>
-<prover id="3" name="Coq" version="8.6.1" timelimit="5" steplimit="1" memlimit="1000"/>
 <prover id="4" name="Alt-Ergo" version="1.01" timelimit="5" steplimit="1" memlimit="1000"/>
+<prover id="5" name="Coq" version="8.7.1" timelimit="5" steplimit="1" memlimit="1000"/>
 <prover id="6" name="Eprover" version="1.8-001" timelimit="5" steplimit="1" memlimit="1000"/>
 <prover id="7" name="Z3" version="4.3.2" timelimit="5" steplimit="1" memlimit="1000"/>
 <file name="../residual.mlw" expanded="true">
@@ -60,7 +60,7 @@
  </transf>
  </goal>
  <goal name="inversion_mem_star_gen" expl="">
- <proof prover="3" edited="residual_Residuals_inversion_mem_star_gen_1.v"><result status="valid" time="0.28"/></proof>
+ <proof prover="5" edited="residual_Residuals_inversion_mem_star_gen_1.v"><result status="valid" time="0.28"/></proof>
  <transf name="induction_pr">
   <goal name="inversion_mem_star_gen.1" expl="">
   <proof prover="4"><result status="valid" time="0.01" steps="7"/></proof>
@@ -131,7 +131,7 @@
   <proof prover="7"><result status="valid" time="0.01"/></proof>
   </goal>
   <goal name="WP_parameter residual.9" expl="postcondition">
-  <proof prover="3" edited="residual_Residuals_WP_parameter_residual_1.v"><result status="valid" time="0.35"/></proof>
+  <proof prover="5" edited="residual_Residuals_WP_parameter_residual_1.v"><result status="valid" time="0.35"/></proof>
   </goal>
   <goal name="WP_parameter residual.10" expl="variant decrease">
   <proof prover="0"><result status="valid" time="0.01" steps="54"/></proof>
@@ -140,7 +140,7 @@
   <proof prover="7"><result status="valid" time="0.00"/></proof>
   </goal>
   <goal name="WP_parameter residual.11" expl="postcondition" expanded="true">
-  <proof prover="3" edited="residual_Residuals_WP_parameter_residual_3.v"><result status="valid" time="0.39"/></proof>
+  <proof prover="5" edited="residual_Residuals_WP_parameter_residual_3.v"><result status="valid" time="0.39"/></proof>
   </goal>
   <goal name="WP_parameter residual.12" expl="variant decrease">
   <proof prover="0"><result status="valid" time="0.01" steps="52"/></proof>
@@ -149,7 +149,7 @@
   <proof prover="7"><result status="valid" time="0.00"/></proof>
   </goal>
   <goal name="WP_parameter residual.13" expl="postcondition" expanded="true">
-  <proof prover="3" edited="residual_Residuals_WP_parameter_residual_2.v"><result status="valid" time="0.34"/></proof>
+  <proof prover="5" edited="residual_Residuals_WP_parameter_residual_2.v"><result status="valid" time="0.34"/></proof>
   </goal>
  </transf>
  </goal>
diff --git a/examples/stdlib/array/why3session.xml b/examples/stdlib/array/why3session.xml
index 336945ed2970ba0035431e8f9dd633476816efff..903f627c335a06f4ff05fda8edbc013415240d6f 100644
--- a/examples/stdlib/array/why3session.xml
+++ b/examples/stdlib/array/why3session.xml
@@ -7,7 +7,7 @@
 <prover id="2" name="Alt-Ergo" version="1.30" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="Z3" version="4.4.0" timelimit="6" steplimit="0" memlimit="1000"/>
 <prover id="4" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="6" name="Coq" version="8.6.1" timelimit="6" steplimit="0" memlimit="1000"/>
+<prover id="5" name="Coq" version="8.7.1" timelimit="6" steplimit="0" memlimit="1000"/>
 <file name="../../../modules/array.mlw" expanded="true">
 <theory name="Array" sum="a4386c74c7fc0ab46ab3dd9d9d5cae40">
  <goal name="WP_parameter defensive_get" expl="VC for defensive_get">
@@ -36,10 +36,10 @@
 </theory>
 <theory name="ArrayPermut" sum="4df642c6a5d352ea5ec0e76c805c8f49">
  <goal name="exchange_permut_sub" expl="">
- <proof prover="6" edited="array_ArrayPermut_exchange_permut_sub_1.v"><result status="valid" time="1.57"/></proof>
+ <proof prover="5" edited="array_ArrayPermut_exchange_permut_sub_1.v"><result status="valid" time="1.57"/></proof>
  </goal>
  <goal name="permut_sub_weakening" expl="">
- <proof prover="6" edited="array_ArrayPermut_permut_sub_weakening_2.v"><result status="valid" time="0.51"/></proof>
+ <proof prover="5" edited="array_ArrayPermut_permut_sub_weakening_2.v"><result status="valid" time="0.51"/></proof>
  </goal>
  <goal name="exchange_permut_all" expl="">
  <proof prover="4"><result status="valid" time="0.06"/></proof>
diff --git a/examples/stdlib/list/why3session.xml b/examples/stdlib/list/why3session.xml
index e5508d9bd60ce161bc115f5edd1b330d62f7e617..76aaf1b5c095713bf7d2062667f1424c13132d31 100644
--- a/examples/stdlib/list/why3session.xml
+++ b/examples/stdlib/list/why3session.xml
@@ -8,7 +8,7 @@
 <prover id="3" name="Spass" version="3.7" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="4" name="Eprover" version="1.8-001" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Alt-Ergo" version="1.01" timelimit="6" steplimit="0" memlimit="1000"/>
-<prover id="6" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="4000"/>
+<prover id="7" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="4000"/>
 <file name="../../../theories/list.why">
 <theory name="List" sum="d41d8cd98f00b204e9800998ecf8427e">
 </theory>
@@ -431,7 +431,7 @@
  <proof prover="0"><result status="valid" time="0.01" steps="10"/></proof>
  </goal>
  <goal name="Permut_length" expl="">
- <proof prover="6" edited="list_Permut_Permut_length_2.v"><result status="valid" time="1.57"/></proof>
+ <proof prover="7" edited="list_Permut_Permut_length_2.v"><result status="valid" time="1.57"/></proof>
  </goal>
 </theory>
 <theory name="Distinct" sum="ad94f6328865dad5f532a625bdf96b79">
diff --git a/examples/tests-provers/coq-interval/why3session.xml b/examples/tests-provers/coq-interval/why3session.xml
index d7f80bd53733bace33e0c2889dd6fa09c7623eb9..2cea9c327216674f5d6c29472a094da821eb96a1 100644
--- a/examples/tests-provers/coq-interval/why3session.xml
+++ b/examples/tests-provers/coq-interval/why3session.xml
@@ -2,11 +2,11 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../coq-interval.why" expanded="true">
 <theory name="P" sum="1e4fe85b7d4e5d74721c865ee586cec8" expanded="true">
  <goal name="pow_eps2_max_int" expl="" expanded="true">
- <proof prover="1" edited="coqmninterval_P_pow_eps2_max_int_1.v"><result status="valid" time="1.21"/></proof>
+ <proof prover="0" edited="coqmninterval_P_pow_eps2_max_int_1.v"><result status="valid" time="0.94"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/tests-provers/coq/why3session.xml b/examples/tests-provers/coq/why3session.xml
index dfbe9aeb834629ed5e2c1651390e69e0d61d05f7..39cf47ca61367e179661b43f5baede9f4d1bd99d 100644
--- a/examples/tests-provers/coq/why3session.xml
+++ b/examples/tests-provers/coq/why3session.xml
@@ -2,11 +2,11 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../coq.why" expanded="true">
 <theory name="NonEmptyTypes" sum="4d631bbd4e65e6a7c65f6d4bfc42dd7a" expanded="true">
  <goal name="g1" expl="" expanded="true">
- <proof prover="1" edited="coq_NonEmptyTypes_g1_1.v"><result status="valid" time="0.30"/></proof>
+ <proof prover="0" edited="coq_NonEmptyTypes_g1_1.v"><result status="valid" time="0.30"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/there_and_back_again/why3session.xml b/examples/there_and_back_again/why3session.xml
index 290ded51bbd41ca9bd6f1fd73e1a7560a3894754..b1b85c097c8b9b0bc72a8141e9f640421dbf09b7 100644
--- a/examples/there_and_back_again/why3session.xml
+++ b/examples/there_and_back_again/why3session.xml
@@ -5,7 +5,7 @@
 <prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="3" name="Coq" version="8.6.1" timelimit="20" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Coq" version="8.7.1" timelimit="20" steplimit="0" memlimit="1000"/>
 <file name="../there_and_back_again.mlw" expanded="true">
 <theory name="Convolution" sum="7b8e5bc0e40791e86a2505c86830564b" expanded="true">
  <goal name="WP_parameter convolution_rec" expl="VC for convolution_rec">
@@ -80,7 +80,7 @@
   <proof prover="0"><result status="valid" time="0.02" steps="23"/></proof>
   </goal>
   <goal name="WP_parameter palindrome_rec.13" expl="exceptional postcondition">
-  <proof prover="3" edited="there_and_back_again_Palindrome_WP_parameter_palindrome_rec_2.v"><result status="valid" time="0.51"/></proof>
+  <proof prover="4" edited="there_and_back_again_Palindrome_WP_parameter_palindrome_rec_2.v"><result status="valid" time="0.51"/></proof>
   </goal>
   <goal name="WP_parameter palindrome_rec.14" expl="unreachable point">
   <proof prover="0"><result status="valid" time="0.01" steps="18"/></proof>
diff --git a/examples/tortoise_and_hare/why3session.xml b/examples/tortoise_and_hare/why3session.xml
index ab051e06ad5d8d45017eadd6c295f8d5251533fb..a82e73617d8a6e9edc2cbcff8daed1f16971ee1f 100644
--- a/examples/tortoise_and_hare/why3session.xml
+++ b/examples/tortoise_and_hare/why3session.xml
@@ -2,12 +2,12 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="2" name="Alt-Ergo" version="0.99.1" timelimit="10" steplimit="0" memlimit="0"/>
 <file name="../tortoise_and_hare.mlw" expanded="true">
 <theory name="TortoiseAndHare" sum="ac8e65800dbd0713f17edcc46d454e5f" expanded="true">
  <goal name="cycle_induction" expl="" expanded="true">
- <proof prover="1" edited="tortoise_and_hare_WP_TortoiseAndHare_cycle_induction_1.v"><result status="valid" time="0.35"/></proof>
+ <proof prover="0" edited="tortoise_and_hare_WP_TortoiseAndHare_cycle_induction_1.v"><result status="valid" time="0.35"/></proof>
  </goal>
  <goal name="WP_parameter tortoise_hare" expl="VC for tortoise_hare" expanded="true">
  <transf name="split_goal_wp" expanded="true">
@@ -15,10 +15,10 @@
   <proof prover="2"><result status="valid" time="0.02" steps="24"/></proof>
   </goal>
   <goal name="WP_parameter tortoise_hare.2" expl="loop invariant preservation" expanded="true">
-  <proof prover="1" edited="tortoise_and_hare_WP_TortoiseAndHare_WP_parameter_tortoise_hare_2.v"><result status="valid" time="0.57"/></proof>
+  <proof prover="0" edited="tortoise_and_hare_WP_TortoiseAndHare_WP_parameter_tortoise_hare_2.v"><result status="valid" time="0.57"/></proof>
   </goal>
   <goal name="WP_parameter tortoise_hare.3" expl="loop variant decrease" expanded="true">
-  <proof prover="1" edited="tortoise_and_hare_WP_TortoiseAndHare_WP_parameter_tortoise_hare_1.v"><result status="valid" time="0.39"/></proof>
+  <proof prover="0" edited="tortoise_and_hare_WP_TortoiseAndHare_WP_parameter_tortoise_hare_1.v"><result status="valid" time="0.39"/></proof>
   </goal>
  </transf>
  </goal>
diff --git a/examples/vacid_0_binary_heaps/proofs/why3session.xml b/examples/vacid_0_binary_heaps/proofs/why3session.xml
index 6b5ab8463eea54a7c7acd6711bfa4295b6858d11..0a7b44384170a860c52dd7bf86a9a309457b8a61 100644
--- a/examples/vacid_0_binary_heaps/proofs/why3session.xml
+++ b/examples/vacid_0_binary_heaps/proofs/why3session.xml
@@ -2,13 +2,13 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="Alt-Ergo" version="1.01" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="5" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../heapsort.mlw">
 <theory name="HeapSort" sum="ae3a1756696edab5e79bfec9096552d9">
  <goal name="Min_of_sorted" expl="">
- <proof prover="1" edited="heapsort_WP_HeapSort_Min_of_sorted_1.v"><result status="valid" time="0.52"/></proof>
+ <proof prover="0" edited="heapsort_WP_HeapSort_Min_of_sorted_1.v"><result status="valid" time="0.52"/></proof>
  </goal>
  <goal name="WP_parameter heapSort" expl="VC for heapSort">
  <transf name="split_goal_wp">
@@ -184,7 +184,7 @@
  <proof prover="3"><result status="valid" time="0.00" steps="8"/></proof>
  </goal>
  <goal name="Is_heap_relation" expl="">
- <proof prover="1" edited="heap_Heap_Is_heap_relation_1.v"><result status="valid" time="0.32"/></proof>
+ <proof prover="0" edited="heap_Heap_Is_heap_relation_1.v"><result status="valid" time="0.32"/></proof>
  </goal>
 </theory>
 </file>
@@ -248,22 +248,22 @@
  <proof prover="5"><result status="valid" time="0.03"/></proof>
  </goal>
  <goal name="Elements_union" expl="">
- <proof prover="1" edited="elements_Elements_Elements_union_1.v"><result status="valid" time="0.40"/></proof>
+ <proof prover="0" edited="elements_Elements_Elements_union_1.v"><result status="valid" time="0.40"/></proof>
  </goal>
  <goal name="Elements_add1" expl="">
- <proof prover="1" edited="elements_Elements_Elements_add1_1.v"><result status="valid" time="0.37"/></proof>
+ <proof prover="0" edited="elements_Elements_Elements_add1_1.v"><result status="valid" time="0.37"/></proof>
  </goal>
  <goal name="Elements_remove_last" expl="">
  <proof prover="3"><result status="valid" time="0.01" steps="8"/></proof>
  </goal>
  <goal name="Occ_elements" expl="">
- <proof prover="1" edited="elements_Elements_Occ_elements_1.v"><result status="valid" time="0.41"/></proof>
+ <proof prover="0" edited="elements_Elements_Occ_elements_1.v"><result status="valid" time="0.41"/></proof>
  </goal>
  <goal name="Elements_set_outside" expl="">
- <proof prover="1" edited="elements_Elements_Elements_set_outside_1.v"><result status="valid" time="0.50"/></proof>
+ <proof prover="0" edited="elements_Elements_Elements_set_outside_1.v"><result status="valid" time="0.50"/></proof>
  </goal>
  <goal name="Elements_set_inside" expl="">
- <proof prover="1" edited="elements_Elements_Elements_set_inside_1.v"><result status="valid" time="0.38"/></proof>
+ <proof prover="0" edited="elements_Elements_Elements_set_inside_1.v"><result status="valid" time="0.38"/></proof>
  </goal>
  <goal name="Elements_set_inside2" expl="">
  <proof prover="3"><result status="valid" time="0.01" steps="33"/></proof>
@@ -273,7 +273,7 @@
 <file name="../heap_implem.mlw">
 <theory name="Implementation" sum="cc4f3d6641601c1e50a7ae22972d1b81">
  <goal name="Is_heap_min" expl="">
- <proof prover="1" edited="heap_implem_WP_Implementation_Is_heap_min_1.v"><result status="valid" time="0.41"/></proof>
+ <proof prover="0" edited="heap_implem_WP_Implementation_Is_heap_min_1.v"><result status="valid" time="0.41"/></proof>
  </goal>
  <goal name="WP_parameter create" expl="VC for create">
  <proof prover="3"><result status="valid" time="0.01" steps="7"/></proof>
diff --git a/examples/vacid_0_red_black_trees/why3session.xml b/examples/vacid_0_red_black_trees/why3session.xml
index f61d8b6e9075136c01387c4e3d4a6676efabdbac..c14d10ccd69735ae65c238f786f742bc4838965a 100644
--- a/examples/vacid_0_red_black_trees/why3session.xml
+++ b/examples/vacid_0_red_black_trees/why3session.xml
@@ -3,8 +3,8 @@
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
 <prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="0"/>
+<prover id="1" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="0"/>
-<prover id="3" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="4" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Spass" version="3.7" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="8" name="Vampire" version="0.6" timelimit="10" steplimit="0" memlimit="1000"/>
@@ -27,10 +27,10 @@
  <proof prover="0" timelimit="10"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="lt_node_lt" expl="">
- <proof prover="3" edited="vacid_0_red_black_trees_WP_RedBlackTree_lt_node_lt_1.v"><result status="valid" time="0.30"/></proof>
+ <proof prover="1" edited="vacid_0_red_black_trees_WP_RedBlackTree_lt_node_lt_1.v"><result status="valid" time="0.30"/></proof>
  </goal>
  <goal name="gt_node_gt" expl="">
- <proof prover="3" edited="vacid_0_red_black_trees_WP_RedBlackTree_gt_node_gt_1.v"><result status="valid" time="0.25"/></proof>
+ <proof prover="1" edited="vacid_0_red_black_trees_WP_RedBlackTree_gt_node_gt_1.v"><result status="valid" time="0.25"/></proof>
  </goal>
  <goal name="lt_left" expl="">
  <proof prover="2" timelimit="10"><result status="valid" time="0.06"/></proof>
@@ -310,111 +310,111 @@
      <ip_library name="int"/>
      <ip_qualid name="CompatOrderMult"/>
     </pr_pos>
-    <pr_pos name="lt_leaf" id="2529"
+    <pr_pos name="lt_leaf" id="2542"
      ip_theory="RedBlackTree">
      <ip_qualid name="lt_leaf"/>
     </pr_pos>
-    <pr_pos name="gt_leaf" id="2533"
+    <pr_pos name="gt_leaf" id="2546"
      ip_theory="RedBlackTree">
      <ip_qualid name="gt_leaf"/>
     </pr_pos>
-    <pr_pos name="lt_tree_node" id="2537"
+    <pr_pos name="lt_tree_node" id="2550"
      ip_theory="RedBlackTree">
      <ip_qualid name="lt_tree_node"/>
     </pr_pos>
-    <pr_pos name="gt_tree_node" id="2556"
+    <pr_pos name="gt_tree_node" id="2569"
      ip_theory="RedBlackTree">
      <ip_qualid name="gt_tree_node"/>
     </pr_pos>
-    <pr_pos name="lt_node_lt" id="2575"
+    <pr_pos name="lt_node_lt" id="2588"
      ip_theory="RedBlackTree">
      <ip_qualid name="lt_node_lt"/>
     </pr_pos>
-    <pr_pos name="gt_node_gt" id="2594"
+    <pr_pos name="gt_node_gt" id="2607"
      ip_theory="RedBlackTree">
      <ip_qualid name="gt_node_gt"/>
     </pr_pos>
-    <pr_pos name="lt_left" id="2613"
+    <pr_pos name="lt_left" id="2626"
      ip_theory="RedBlackTree">
      <ip_qualid name="lt_left"/>
     </pr_pos>
-    <pr_pos name="lt_right" id="2632"
+    <pr_pos name="lt_right" id="2645"
      ip_theory="RedBlackTree">
      <ip_qualid name="lt_right"/>
     </pr_pos>
-    <pr_pos name="gt_left" id="2651"
+    <pr_pos name="gt_left" id="2664"
      ip_theory="RedBlackTree">
      <ip_qualid name="gt_left"/>
     </pr_pos>
-    <pr_pos name="gt_right" id="2670"
+    <pr_pos name="gt_right" id="2683"
      ip_theory="RedBlackTree">
      <ip_qualid name="gt_right"/>
     </pr_pos>
-    <pr_pos name="lt_tree_not_in" id="2689"
+    <pr_pos name="lt_tree_not_in" id="2702"
      ip_theory="RedBlackTree">
      <ip_qualid name="lt_tree_not_in"/>
     </pr_pos>
-    <pr_pos name="lt_tree_trans" id="2699"
+    <pr_pos name="lt_tree_trans" id="2712"
      ip_theory="RedBlackTree">
      <ip_qualid name="lt_tree_trans"/>
     </pr_pos>
-    <pr_pos name="gt_tree_not_in" id="2709"
+    <pr_pos name="gt_tree_not_in" id="2722"
      ip_theory="RedBlackTree">
      <ip_qualid name="gt_tree_not_in"/>
     </pr_pos>
-    <pr_pos name="gt_tree_trans" id="2719"
+    <pr_pos name="gt_tree_trans" id="2732"
      ip_theory="RedBlackTree">
      <ip_qualid name="gt_tree_trans"/>
     </pr_pos>
-    <pr_pos name="bst_Leaf" id="2763"
+    <pr_pos name="bst_Leaf" id="2776"
      ip_theory="RedBlackTree">
      <ip_qualid name="bst_Leaf"/>
     </pr_pos>
-    <pr_pos name="bst_left" id="2764"
+    <pr_pos name="bst_left" id="2777"
      ip_theory="RedBlackTree">
      <ip_qualid name="bst_left"/>
     </pr_pos>
-    <pr_pos name="bst_right" id="2780"
+    <pr_pos name="bst_right" id="2793"
      ip_theory="RedBlackTree">
      <ip_qualid name="bst_right"/>
     </pr_pos>
-    <pr_pos name="bst_color" id="2796"
+    <pr_pos name="bst_color" id="2809"
      ip_theory="RedBlackTree">
      <ip_qualid name="bst_color"/>
     </pr_pos>
-    <pr_pos name="rotate_left" id="2815"
+    <pr_pos name="rotate_left" id="2828"
      ip_theory="RedBlackTree">
      <ip_qualid name="rotate_left"/>
     </pr_pos>
-    <pr_pos name="rotate_right" id="2849"
+    <pr_pos name="rotate_right" id="2862"
      ip_theory="RedBlackTree">
      <ip_qualid name="rotate_right"/>
     </pr_pos>
-    <pr_pos name="rbtree_Leaf" id="2944"
+    <pr_pos name="rbtree_Leaf" id="2957"
      ip_theory="RedBlackTree">
      <ip_qualid name="rbtree_Leaf"/>
     </pr_pos>
-    <pr_pos name="rbtree_Node1" id="2945"
+    <pr_pos name="rbtree_Node1" id="2958"
      ip_theory="RedBlackTree">
      <ip_qualid name="rbtree_Node1"/>
     </pr_pos>
-    <pr_pos name="rbtree_left" id="2952"
+    <pr_pos name="rbtree_left" id="2965"
      ip_theory="RedBlackTree">
      <ip_qualid name="rbtree_left"/>
     </pr_pos>
-    <pr_pos name="rbtree_right" id="2974"
+    <pr_pos name="rbtree_right" id="2987"
      ip_theory="RedBlackTree">
      <ip_qualid name="rbtree_right"/>
     </pr_pos>
-    <pr_pos name="rbtree_almost_rbtree" id="3276"
+    <pr_pos name="rbtree_almost_rbtree" id="3289"
      ip_theory="RedBlackTree">
      <ip_qualid name="rbtree_almost_rbtree"/>
     </pr_pos>
-    <pr_pos name="rbtree_almost_rbtree_ex" id="3283"
+    <pr_pos name="rbtree_almost_rbtree_ex" id="3296"
      ip_theory="RedBlackTree">
      <ip_qualid name="rbtree_almost_rbtree_ex"/>
     </pr_pos>
-    <pr_pos name="almost_rbtree_rbtree_black" id="3293"
+    <pr_pos name="almost_rbtree_rbtree_black" id="3306"
      ip_theory="RedBlackTree">
      <ip_qualid name="almost_rbtree_rbtree_black"/>
     </pr_pos>
@@ -506,85 +506,85 @@
      <meta_arg_pr id="1745"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2529"/>
+     <meta_arg_pr id="2542"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2533"/>
+     <meta_arg_pr id="2546"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2537"/>
+     <meta_arg_pr id="2550"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2556"/>
+     <meta_arg_pr id="2569"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2575"/>
+     <meta_arg_pr id="2588"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2594"/>
+     <meta_arg_pr id="2607"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2613"/>
+     <meta_arg_pr id="2626"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2632"/>
+     <meta_arg_pr id="2645"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2651"/>
+     <meta_arg_pr id="2664"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2670"/>
+     <meta_arg_pr id="2683"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2689"/>
+     <meta_arg_pr id="2702"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2699"/>
+     <meta_arg_pr id="2712"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2709"/>
+     <meta_arg_pr id="2722"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2719"/>
+     <meta_arg_pr id="2732"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2763"/>
+     <meta_arg_pr id="2776"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2764"/>
+     <meta_arg_pr id="2777"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2780"/>
+     <meta_arg_pr id="2793"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2796"/>
+     <meta_arg_pr id="2809"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2815"/>
+     <meta_arg_pr id="2828"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2849"/>
+     <meta_arg_pr id="2862"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2944"/>
+     <meta_arg_pr id="2957"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2945"/>
+     <meta_arg_pr id="2958"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2952"/>
+     <meta_arg_pr id="2965"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2974"/>
+     <meta_arg_pr id="2987"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3276"/>
+     <meta_arg_pr id="3289"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3283"/>
+     <meta_arg_pr id="3296"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3293"/>
+     <meta_arg_pr id="3306"/>
     </meta>
     <meta name="remove_type">
      <meta_arg_ts id="383"/>
@@ -898,111 +898,111 @@
     <ip_library name="int"/>
     <ip_qualid name="CompatOrderMult"/>
    </pr_pos>
-   <pr_pos name="lt_leaf" id="2529"
+   <pr_pos name="lt_leaf" id="2542"
     ip_theory="RedBlackTree">
     <ip_qualid name="lt_leaf"/>
    </pr_pos>
-   <pr_pos name="gt_leaf" id="2533"
+   <pr_pos name="gt_leaf" id="2546"
     ip_theory="RedBlackTree">
     <ip_qualid name="gt_leaf"/>
    </pr_pos>
-   <pr_pos name="lt_tree_node" id="2537"
+   <pr_pos name="lt_tree_node" id="2550"
     ip_theory="RedBlackTree">
     <ip_qualid name="lt_tree_node"/>
    </pr_pos>
-   <pr_pos name="gt_tree_node" id="2556"
+   <pr_pos name="gt_tree_node" id="2569"
     ip_theory="RedBlackTree">
     <ip_qualid name="gt_tree_node"/>
    </pr_pos>
-   <pr_pos name="lt_node_lt" id="2575"
+   <pr_pos name="lt_node_lt" id="2588"
     ip_theory="RedBlackTree">
     <ip_qualid name="lt_node_lt"/>
    </pr_pos>
-   <pr_pos name="gt_node_gt" id="2594"
+   <pr_pos name="gt_node_gt" id="2607"
     ip_theory="RedBlackTree">
     <ip_qualid name="gt_node_gt"/>
    </pr_pos>
-   <pr_pos name="lt_left" id="2613"
+   <pr_pos name="lt_left" id="2626"
     ip_theory="RedBlackTree">
     <ip_qualid name="lt_left"/>
    </pr_pos>
-   <pr_pos name="lt_right" id="2632"
+   <pr_pos name="lt_right" id="2645"
     ip_theory="RedBlackTree">
     <ip_qualid name="lt_right"/>
    </pr_pos>
-   <pr_pos name="gt_left" id="2651"
+   <pr_pos name="gt_left" id="2664"
     ip_theory="RedBlackTree">
     <ip_qualid name="gt_left"/>
    </pr_pos>
-   <pr_pos name="gt_right" id="2670"
+   <pr_pos name="gt_right" id="2683"
     ip_theory="RedBlackTree">
     <ip_qualid name="gt_right"/>
    </pr_pos>
-   <pr_pos name="lt_tree_not_in" id="2689"
+   <pr_pos name="lt_tree_not_in" id="2702"
     ip_theory="RedBlackTree">
     <ip_qualid name="lt_tree_not_in"/>
    </pr_pos>
-   <pr_pos name="lt_tree_trans" id="2699"
+   <pr_pos name="lt_tree_trans" id="2712"
     ip_theory="RedBlackTree">
     <ip_qualid name="lt_tree_trans"/>
    </pr_pos>
-   <pr_pos name="gt_tree_not_in" id="2709"
+   <pr_pos name="gt_tree_not_in" id="2722"
     ip_theory="RedBlackTree">
     <ip_qualid name="gt_tree_not_in"/>
    </pr_pos>
-   <pr_pos name="gt_tree_trans" id="2719"
+   <pr_pos name="gt_tree_trans" id="2732"
     ip_theory="RedBlackTree">
     <ip_qualid name="gt_tree_trans"/>
    </pr_pos>
-   <pr_pos name="bst_Leaf" id="2763"
+   <pr_pos name="bst_Leaf" id="2776"
     ip_theory="RedBlackTree">
     <ip_qualid name="bst_Leaf"/>
    </pr_pos>
-   <pr_pos name="bst_left" id="2764"
+   <pr_pos name="bst_left" id="2777"
     ip_theory="RedBlackTree">
     <ip_qualid name="bst_left"/>
    </pr_pos>
-   <pr_pos name="bst_right" id="2780"
+   <pr_pos name="bst_right" id="2793"
     ip_theory="RedBlackTree">
     <ip_qualid name="bst_right"/>
    </pr_pos>
-   <pr_pos name="bst_color" id="2796"
+   <pr_pos name="bst_color" id="2809"
     ip_theory="RedBlackTree">
     <ip_qualid name="bst_color"/>
    </pr_pos>
-   <pr_pos name="rotate_left" id="2815"
+   <pr_pos name="rotate_left" id="2828"
     ip_theory="RedBlackTree">
     <ip_qualid name="rotate_left"/>
    </pr_pos>
-   <pr_pos name="rotate_right" id="2849"
+   <pr_pos name="rotate_right" id="2862"
     ip_theory="RedBlackTree">
     <ip_qualid name="rotate_right"/>
    </pr_pos>
-   <pr_pos name="rbtree_Leaf" id="2944"
+   <pr_pos name="rbtree_Leaf" id="2957"
     ip_theory="RedBlackTree">
     <ip_qualid name="rbtree_Leaf"/>
    </pr_pos>
-   <pr_pos name="rbtree_Node1" id="2945"
+   <pr_pos name="rbtree_Node1" id="2958"
     ip_theory="RedBlackTree">
     <ip_qualid name="rbtree_Node1"/>
    </pr_pos>
-   <pr_pos name="rbtree_left" id="2952"
+   <pr_pos name="rbtree_left" id="2965"
     ip_theory="RedBlackTree">
     <ip_qualid name="rbtree_left"/>
    </pr_pos>
-   <pr_pos name="rbtree_right" id="2974"
+   <pr_pos name="rbtree_right" id="2987"
     ip_theory="RedBlackTree">
     <ip_qualid name="rbtree_right"/>
    </pr_pos>
-   <pr_pos name="rbtree_almost_rbtree" id="3276"
+   <pr_pos name="rbtree_almost_rbtree" id="3289"
     ip_theory="RedBlackTree">
     <ip_qualid name="rbtree_almost_rbtree"/>
    </pr_pos>
-   <pr_pos name="rbtree_almost_rbtree_ex" id="3283"
+   <pr_pos name="rbtree_almost_rbtree_ex" id="3296"
     ip_theory="RedBlackTree">
     <ip_qualid name="rbtree_almost_rbtree_ex"/>
    </pr_pos>
-   <pr_pos name="almost_rbtree_rbtree_black" id="3293"
+   <pr_pos name="almost_rbtree_rbtree_black" id="3306"
     ip_theory="RedBlackTree">
     <ip_qualid name="almost_rbtree_rbtree_black"/>
    </pr_pos>
@@ -1094,85 +1094,85 @@
     <meta_arg_pr id="1745"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2529"/>
+    <meta_arg_pr id="2542"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2533"/>
+    <meta_arg_pr id="2546"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2537"/>
+    <meta_arg_pr id="2550"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2556"/>
+    <meta_arg_pr id="2569"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2575"/>
+    <meta_arg_pr id="2588"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2594"/>
+    <meta_arg_pr id="2607"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2613"/>
+    <meta_arg_pr id="2626"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2632"/>
+    <meta_arg_pr id="2645"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2651"/>
+    <meta_arg_pr id="2664"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2670"/>
+    <meta_arg_pr id="2683"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2689"/>
+    <meta_arg_pr id="2702"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2699"/>
+    <meta_arg_pr id="2712"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2709"/>
+    <meta_arg_pr id="2722"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2719"/>
+    <meta_arg_pr id="2732"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2763"/>
+    <meta_arg_pr id="2776"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2764"/>
+    <meta_arg_pr id="2777"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2780"/>
+    <meta_arg_pr id="2793"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2796"/>
+    <meta_arg_pr id="2809"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2815"/>
+    <meta_arg_pr id="2828"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2849"/>
+    <meta_arg_pr id="2862"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2944"/>
+    <meta_arg_pr id="2957"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2945"/>
+    <meta_arg_pr id="2958"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2952"/>
+    <meta_arg_pr id="2965"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="2974"/>
+    <meta_arg_pr id="2987"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="3276"/>
+    <meta_arg_pr id="3289"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="3283"/>
+    <meta_arg_pr id="3296"/>
    </meta>
    <meta name="remove_prop">
-    <meta_arg_pr id="3293"/>
+    <meta_arg_pr id="3306"/>
    </meta>
    <meta name="remove_type">
     <meta_arg_ts id="383"/>
@@ -1503,7 +1503,7 @@
    <goal name="WP_parameter add.2.2" expl="VC for add">
    <transf name="inline_goal">
     <goal name="WP_parameter add.2.2.1" expl="VC for add">
-    <proof prover="3" edited="vacid_0_red_black_trees_WP_RedBlackTree_WP_parameter_add_1.v"><result status="valid" time="0.32"/></proof>
+    <proof prover="1" edited="vacid_0_red_black_trees_WP_RedBlackTree_WP_parameter_add_1.v"><result status="valid" time="0.32"/></proof>
     </goal>
    </transf>
    </goal>
diff --git a/examples/vacid_0_sparse_array/why3session.xml b/examples/vacid_0_sparse_array/why3session.xml
index af5969d441d839b574ea130085ac554ed370e8f3..38f791ca6e18faa043df6bacfbdbc81b9bdb8ed3 100644
--- a/examples/vacid_0_sparse_array/why3session.xml
+++ b/examples/vacid_0_sparse_array/why3session.xml
@@ -2,8 +2,8 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="17" steplimit="0" memlimit="1000"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="Z3" version="3.2" timelimit="17" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../vacid_0_sparse_array.mlw" expanded="true">
@@ -18,7 +18,7 @@
  <proof prover="5"><result status="valid" time="0.07" steps="22"/></proof>
  </goal>
  <goal name="permutation" expl="">
- <proof prover="2" edited="vacid_0_sparse_array_2_SparseArray_permutation_1.v"><result status="valid" time="0.64"/></proof>
+ <proof prover="0" edited="vacid_0_sparse_array_2_SparseArray_permutation_1.v"><result status="valid" time="0.84"/></proof>
  </goal>
  <goal name="WP_parameter set" expl="VC for set">
  <transf name="split_goal_wp">
diff --git a/examples/verifythis_fm2012_LRS/why3session.xml b/examples/verifythis_fm2012_LRS/why3session.xml
index 2b87a6f0b5e7d79a2412a261536a2875717d2e2e..9f27fa81b75d2c34fad238d92d2133fd648f0cc2 100644
--- a/examples/verifythis_fm2012_LRS/why3session.xml
+++ b/examples/verifythis_fm2012_LRS/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC3" version="2.4.1" timelimit="10" steplimit="0" memlimit="1000"/>
 <prover id="11" name="Vampire" version="0.6" timelimit="5" steplimit="0" memlimit="4000"/>
 <prover id="12" name="Alt-Ergo" version="0.99.1" timelimit="10" steplimit="0" memlimit="1000"/>
@@ -532,7 +532,7 @@
  <proof prover="15"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="permut_permutation" expl="">
- <proof prover="1" timelimit="6" edited="verifythis_fm2012_lcp_SuffixArray_permut_permutation_1.v"><result status="valid" time="1.12"/></proof>
+ <proof prover="0" timelimit="6" edited="verifythis_fm2012_lcp_SuffixArray_permut_permutation_1.v"><result status="valid" time="1.12"/></proof>
  </goal>
  <goal name="WP_parameter create" expl="VC for create">
  <transf name="split_goal_wp">
@@ -830,7 +830,7 @@
   <proof prover="15"><result status="valid" time="1.10"/></proof>
   </goal>
   <goal name="WP_parameter lrs.23" expl="assertion">
-  <proof prover="1" edited="verifythis_fm2012_lcp_LRS_WP_parameter_lrs_10.v"><result status="valid" time="0.88"/></proof>
+  <proof prover="0" edited="verifythis_fm2012_lcp_LRS_WP_parameter_lrs_10.v"><result status="valid" time="0.88"/></proof>
   </goal>
   <goal name="WP_parameter lrs.24" expl="postcondition">
   <proof prover="3"><result status="valid" time="0.02"/></proof>
@@ -856,7 +856,7 @@
   <proof prover="15"><result status="valid" time="0.01"/></proof>
   </goal>
   <goal name="WP_parameter lrs.27" expl="postcondition">
-  <proof prover="1" memlimit="4000" edited="verifythis_fm2012_lcp_LRS_WP_parameter_lrs_12.v"><result status="valid" time="0.69"/></proof>
+  <proof prover="0" memlimit="4000" edited="verifythis_fm2012_lcp_LRS_WP_parameter_lrs_12.v"><result status="valid" time="0.69"/></proof>
   </goal>
  </transf>
  </goal>
diff --git a/examples/verifythis_fm2012_treedel/why3session.xml b/examples/verifythis_fm2012_treedel/why3session.xml
index ac2fc046146cabb3cbc02c06830ef83303ff5376..40889d67a544608d04ad73f79944542332d3bc68 100644
--- a/examples/verifythis_fm2012_treedel/why3session.xml
+++ b/examples/verifythis_fm2012_treedel/why3session.xml
@@ -3,9 +3,9 @@
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
 <prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="4000"/>
-<prover id="1" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="4000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="4000"/>
 <prover id="3" name="CVC4" version="1.4" timelimit="5" steplimit="0" memlimit="4000"/>
+<prover id="4" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="4000"/>
 <prover id="5" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="4000"/>
 <prover id="7" name="Vampire" version="0.6" timelimit="5" steplimit="0" memlimit="4000"/>
 <prover id="8" name="Eprover" version="1.8-001" timelimit="5" steplimit="0" memlimit="4000"/>
@@ -82,7 +82,7 @@
  <proof prover="10"><result status="valid" time="0.01"/></proof>
  </goal>
  <goal name="main_lemma" expl="">
- <proof prover="1" edited="verifythis_fm2012_treedel_Treedel_main_lemma_1.v"><result status="valid" time="8.32"/></proof>
+ <proof prover="4" edited="verifythis_fm2012_treedel_Treedel_main_lemma_1.v"><result status="valid" time="8.32"/></proof>
  </goal>
  <goal name="WP_parameter search_tree_delete_min" expl="VC for search_tree_delete_min">
  <transf name="split_goal_wp">
diff --git a/examples/vstte10_inverting/why3session.xml b/examples/vstte10_inverting/why3session.xml
index 93479f889617422d59f9e7cec97afc0edbcddeb2..7f8268f744943ee4dd3f3218db59431bdd9cd861 100644
--- a/examples/vstte10_inverting/why3session.xml
+++ b/examples/vstte10_inverting/why3session.xml
@@ -2,8 +2,8 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="30" steplimit="0" memlimit="4000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="20" steplimit="0" memlimit="1000"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="30" steplimit="0" memlimit="4000"/>
 <prover id="3" name="Alt-Ergo" version="0.99.1" timelimit="20" steplimit="0" memlimit="0"/>
 <prover id="4" name="CVC4" version="1.4" timelimit="30" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Z3" version="4.3.2" timelimit="30" steplimit="0" memlimit="1000"/>
@@ -33,7 +33,7 @@
   <proof prover="3" timelimit="5" memlimit="1000"><result status="valid" time="0.01" steps="7"/></proof>
   </goal>
   <goal name="WP_parameter inverting.8" expl="postcondition">
-  <proof prover="2" timelimit="5" edited="vstte10_inverting_WP_InvertingAnInjection_WP_parameter_inverting_1.v"><result status="valid" time="0.34"/></proof>
+  <proof prover="0" timelimit="5" edited="vstte10_inverting_WP_InvertingAnInjection_WP_parameter_inverting_1.v"><result status="valid" time="0.34"/></proof>
   </goal>
  </transf>
  </goal>
@@ -88,7 +88,7 @@
    <proof prover="3" timelimit="30" memlimit="1000"><result status="valid" time="0.00" steps="8"/></proof>
    </goal>
    <goal name="WP_parameter inverting2.9.2" expl="VC for inverting2">
-   <proof prover="2" memlimit="1000" edited="vstte10_inverting_InvertingAnInjection_WP_parameter_inverting2_1.v"><result status="valid" time="0.32"/></proof>
+   <proof prover="0" memlimit="1000" edited="vstte10_inverting_InvertingAnInjection_WP_parameter_inverting2_1.v"><result status="valid" time="0.32"/></proof>
    </goal>
    <goal name="WP_parameter inverting2.9.3" expl="VC for inverting2">
    <proof prover="3" timelimit="30" memlimit="1000"><result status="valid" time="0.01" steps="14"/></proof>
diff --git a/examples/vstte10_max_sum/why3session.xml b/examples/vstte10_max_sum/why3session.xml
index 6d86e99750d95c5683eef420e3f467c1df3400f8..f0350c06d0acbe7d78b58a00933fde7e0b7d2e6d 100644
--- a/examples/vstte10_max_sum/why3session.xml
+++ b/examples/vstte10_max_sum/why3session.xml
@@ -3,9 +3,9 @@
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
 <prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="1" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="CVC3" version="2.4.1" timelimit="10" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC4" version="1.4" timelimit="10" steplimit="0" memlimit="1000"/>
-<prover id="4" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="6" name="Z3" version="4.3.2" timelimit="10" steplimit="0" memlimit="1000"/>
 <file name="../vstte10_max_sum.mlw" expanded="true">
@@ -30,7 +30,7 @@
   <proof prover="0"><result status="valid" time="0.00" steps="9"/></proof>
   </goal>
   <goal name="WP_parameter max_sum.6" expl="loop invariant preservation">
-  <proof prover="4" edited="vstte10_max_sum_MaxAndSum_WP_parameter_max_sum_1.v"><result status="valid" time="0.29"/></proof>
+  <proof prover="1" edited="vstte10_max_sum_MaxAndSum_WP_parameter_max_sum_1.v"><result status="valid" time="0.29"/></proof>
   </goal>
   <goal name="WP_parameter max_sum.7" expl="index in array bounds">
   <proof prover="0"><result status="valid" time="0.01" steps="8"/></proof>
@@ -74,7 +74,7 @@
    <proof prover="5"><result status="valid" time="0.02"/></proof>
    </goal>
    <goal name="WP_parameter max_sum.6.3" expl="VC for max_sum">
-   <proof prover="4" edited="vstte10_max_sum_WP_MaxAndSum2_WP_parameter_max_sum_1.v"><result status="valid" time="0.30"/></proof>
+   <proof prover="1" edited="vstte10_max_sum_WP_MaxAndSum2_WP_parameter_max_sum_1.v"><result status="valid" time="0.30"/></proof>
    </goal>
   </transf>
   </goal>
diff --git a/examples/vstte10_search_list/why3session.xml b/examples/vstte10_search_list/why3session.xml
index 8cafed97a9220332fe38892c0662b1b6ebb5a800..fbc058e923ce0cfa69737fe3b6bdb8b92f97e465 100644
--- a/examples/vstte10_search_list/why3session.xml
+++ b/examples/vstte10_search_list/why3session.xml
@@ -2,8 +2,8 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
+<prover id="0" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="0"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="5" name="Alt-Ergo" version="0.99.1" timelimit="20" steplimit="0" memlimit="0"/>
 <prover id="6" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="0"/>
 <file name="../vstte10_search_list.mlw" expanded="true">
@@ -56,10 +56,10 @@
    <proof prover="6"><result status="valid" time="0.02"/></proof>
    </goal>
    <goal name="WP_parameter search_loop.4.3" expl="VC for search_loop">
-   <proof prover="2" edited="vstte10_search_list_WP_SearchingALinkedList_WP_parameter_search_loop_3.v"><result status="valid" time="0.36"/></proof>
+   <proof prover="0" edited="vstte10_search_list_WP_SearchingALinkedList_WP_parameter_search_loop_3.v"><result status="valid" time="0.36"/></proof>
    </goal>
    <goal name="WP_parameter search_loop.4.4" expl="VC for search_loop">
-   <proof prover="2" edited="vstte10_search_list_WP_SearchingALinkedList_WP_parameter_search_loop_4.v"><result status="valid" time="0.55"/></proof>
+   <proof prover="0" edited="vstte10_search_list_WP_SearchingALinkedList_WP_parameter_search_loop_4.v"><result status="valid" time="0.55"/></proof>
    </goal>
   </transf>
   </goal>
@@ -68,7 +68,7 @@
   <proof prover="5"><result status="valid" time="0.01" steps="20"/></proof>
   </goal>
   <goal name="WP_parameter search_loop.6" expl="postcondition">
-  <proof prover="2" edited="vstte10_search_list_WP_SearchingALinkedList_WP_parameter_search_loop_1.v"><result status="valid" time="0.44"/></proof>
+  <proof prover="0" edited="vstte10_search_list_WP_SearchingALinkedList_WP_parameter_search_loop_1.v"><result status="valid" time="0.44"/></proof>
   </goal>
   <goal name="WP_parameter search_loop.7" expl="postcondition">
   <proof prover="1"><result status="valid" time="0.02"/></proof>
diff --git a/examples/vstte12_bfs/why3session.xml b/examples/vstte12_bfs/why3session.xml
index 34340e8e51fa098f260e27c9ef7200109bfcf3bf..4d3425dbb0b63d02797ecc5495b900a3bef18dcc 100644
--- a/examples/vstte12_bfs/why3session.xml
+++ b/examples/vstte12_bfs/why3session.xml
@@ -2,7 +2,7 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="1" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
+<prover id="0" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="3" name="CVC3" version="2.4.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="4" name="CVC4" version="1.4" timelimit="6" steplimit="0" memlimit="1000"/>
 <prover id="5" name="Spass" version="3.7" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -223,7 +223,7 @@
   <proof prover="9" timelimit="5" memlimit="1000"><result status="valid" time="0.02" steps="14"/></proof>
   </goal>
   <goal name="WP_parameter bfs.8" expl="postcondition">
-  <proof prover="1" edited="vstte12_bfs_WP_BFS_WP_parameter_bfs_1.v"><result status="valid" time="0.47"/></proof>
+  <proof prover="0" edited="vstte12_bfs_WP_BFS_WP_parameter_bfs_1.v"><result status="valid" time="0.47"/></proof>
   </goal>
  </transf>
  </goal>
diff --git a/examples/vstte12_combinators/why3session.xml b/examples/vstte12_combinators/why3session.xml
index bbb5d99e3a8930c95ed9829dfd101749d2a5d999..1d288c3de5583f5d41fa6107ab609ce96f6e8663 100644
--- a/examples/vstte12_combinators/why3session.xml
+++ b/examples/vstte12_combinators/why3session.xml
@@ -4,9 +4,9 @@
 <why3session shape_version="4">
 <prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="0"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="10" steplimit="0" memlimit="0"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="3" name="Spass" version="3.7" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="4" name="Z3" version="3.2" timelimit="10" steplimit="0" memlimit="0"/>
+<prover id="5" name="Coq" version="8.7.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="6" name="Vampire" version="0.6" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="7" name="Eprover" version="1.8-001" timelimit="5" steplimit="0" memlimit="1000"/>
 <file name="../vstte12_combinators.mlw" expanded="true">
@@ -18,10 +18,10 @@
  <proof prover="4"><result status="valid" time="3.82"/></proof>
  </goal>
  <goal name="red_star_left" expl="">
- <proof prover="2" timelimit="10" memlimit="0" edited="vstte12_combinators_WP_Combinators_red_star_left_1.v"><result status="valid" time="0.27"/></proof>
+ <proof prover="5" timelimit="10" memlimit="0" edited="vstte12_combinators_WP_Combinators_red_star_left_1.v"><result status="valid" time="0.27"/></proof>
  </goal>
  <goal name="red_star_right" expl="">
- <proof prover="2" timelimit="10" memlimit="0" edited="vstte12_combinators_WP_Combinators_red_star_right_1.v"><result status="valid" time="0.28"/></proof>
+ <proof prover="5" timelimit="10" memlimit="0" edited="vstte12_combinators_WP_Combinators_red_star_right_1.v"><result status="valid" time="0.28"/></proof>
  </goal>
  <goal name="WP_parameter reduction" expl="VC for reduction">
  <transf name="split_goal_wp">
@@ -34,8 +34,8 @@
   <goal name="WP_parameter reduction.3" expl="postcondition">
   <transf name="split_goal_wp">
    <goal name="WP_parameter reduction.3.1" expl="VC for reduction">
-   <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction_1.v"><result status="unknown" time="0.27"/></proof>
    <proof prover="3"><result status="valid" time="0.03"/></proof>
+   <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction_1.v"><result status="unknown" time="0.27"/></proof>
    <proof prover="6"><result status="valid" time="0.04"/></proof>
    </goal>
    <goal name="WP_parameter reduction.3.2" expl="VC for reduction">
@@ -46,8 +46,8 @@
   <goal name="WP_parameter reduction.4" expl="postcondition">
   <transf name="split_goal_wp">
    <goal name="WP_parameter reduction.4.1" expl="VC for reduction">
-   <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction_2.v"><result status="unknown" time="0.26"/></proof>
    <proof prover="3"><result status="valid" time="0.03"/></proof>
+   <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction_2.v"><result status="unknown" time="0.26"/></proof>
    <proof prover="6"><result status="valid" time="0.06"/></proof>
    </goal>
    <goal name="WP_parameter reduction.4.2" expl="VC for reduction">
@@ -58,8 +58,8 @@
   <goal name="WP_parameter reduction.5" expl="postcondition">
   <transf name="split_goal_wp">
    <goal name="WP_parameter reduction.5.1" expl="VC for reduction">
-   <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction_3.v"><result status="unknown" time="0.22"/></proof>
    <proof prover="3"><result status="valid" time="0.07"/></proof>
+   <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction_3.v"><result status="unknown" time="0.22"/></proof>
    <proof prover="6"><result status="valid" time="0.03"/></proof>
    </goal>
    <goal name="WP_parameter reduction.5.2" expl="VC for reduction">
@@ -70,8 +70,8 @@
   <goal name="WP_parameter reduction.6" expl="postcondition">
   <transf name="split_goal_wp">
    <goal name="WP_parameter reduction.6.1" expl="VC for reduction">
-   <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction_4.v"><result status="unknown" time="0.20"/></proof>
    <proof prover="3"><result status="valid" time="0.04"/></proof>
+   <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction_4.v"><result status="unknown" time="0.20"/></proof>
    <proof prover="6"><result status="valid" time="0.08"/></proof>
    <proof prover="7"><result status="valid" time="0.04"/></proof>
    </goal>
@@ -83,7 +83,7 @@
   <goal name="WP_parameter reduction.7" expl="postcondition">
   <transf name="split_goal_wp">
    <goal name="WP_parameter reduction.7.1" expl="VC for reduction">
-   <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction_5.v"><result status="unknown" time="0.26"/></proof>
+   <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction_5.v"><result status="unknown" time="0.26"/></proof>
    <proof prover="6"><result status="valid" time="0.32"/></proof>
    </goal>
    <goal name="WP_parameter reduction.7.2" expl="VC for reduction">
@@ -100,16 +100,16 @@
  <proof prover="0" memlimit="1000"><result status="valid" time="0.01" steps="6"/></proof>
  </goal>
  <goal name="reducible_or_value" expl="">
- <proof prover="2" edited="vstte12_combinators_WP_Combinators_reducible_or_value_1.v"><result status="valid" time="0.69"/></proof>
+ <proof prover="5" edited="vstte12_combinators_WP_Combinators_reducible_or_value_1.v"><result status="valid" time="0.69"/></proof>
  </goal>
  <goal name="irreducible_is_value" expl="">
- <proof prover="2" edited="vstte12_combinators_WP_Combinators_irreducible_is_value_1.v"><result status="valid" time="1.76"/></proof>
+ <proof prover="5" edited="vstte12_combinators_WP_Combinators_irreducible_is_value_1.v"><result status="valid" time="2.06"/></proof>
  </goal>
  <goal name="only_K_reduces" expl="">
- <proof prover="2" edited="vstte12_combinators_WP_Combinators_only_K_reduces_1.v"><result status="valid" time="0.69"/></proof>
+ <proof prover="5" edited="vstte12_combinators_WP_Combinators_only_K_reduces_1.v"><result status="valid" time="0.88"/></proof>
  </goal>
  <goal name="size_nonneg" expl="">
- <proof prover="2" edited="vstte12_combinators_WP_Combinators_size_nonneg_1.v"><result status="valid" time="0.36"/></proof>
+ <proof prover="5" edited="vstte12_combinators_WP_Combinators_size_nonneg_1.v"><result status="valid" time="0.36"/></proof>
  </goal>
  <goal name="WP_parameter reduction2" expl="VC for reduction2">
  <transf name="split_goal_wp">
@@ -187,7 +187,7 @@
   <transf name="split_goal_wp">
    <goal name="WP_parameter reduction2.20.1" expl="precondition">
    <proof prover="1" timelimit="5" memlimit="1000"><result status="valid" time="0.07"/></proof>
-   <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction2_2.v"><result status="unknown" time="0.29"/></proof>
+   <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction2_2.v"><result status="unknown" time="0.29"/></proof>
    <proof prover="7"><result status="valid" time="0.61"/></proof>
    </goal>
   </transf>
@@ -204,13 +204,13 @@
  <proof prover="0"><result status="valid" time="0.01" steps="15"/></proof>
  </goal>
  <goal name="only_K_ks" expl="">
- <proof prover="2" edited="vstte12_combinators_WP_Combinators_only_K_ks_1.v"><result status="valid" time="0.30"/></proof>
+ <proof prover="5" edited="vstte12_combinators_WP_Combinators_only_K_ks_1.v"><result status="valid" time="0.30"/></proof>
  </goal>
  <goal name="ks_inversion" expl="">
  <proof prover="0"><result status="valid" time="0.01" steps="18"/></proof>
  </goal>
  <goal name="ks_injective" expl="">
- <proof prover="2" edited="vstte12_combinators_WP_Combinators_ks_injective_1.v"><result status="valid" time="0.71"/></proof>
+ <proof prover="5" edited="vstte12_combinators_WP_Combinators_ks_injective_1.v"><result status="valid" time="0.71"/></proof>
  </goal>
  <goal name="WP_parameter reduction3" expl="VC for reduction3">
  <transf name="split_goal_wp">
@@ -241,10 +241,10 @@
    <proof prover="0"><result status="valid" time="0.01" steps="26"/></proof>
    </goal>
    <goal name="WP_parameter reduction3.5.2" expl="VC for reduction3">
-   <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_3.v"><result status="valid" time="1.50"/></proof>
+   <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_3.v"><result status="valid" time="1.50"/></proof>
    </goal>
    <goal name="WP_parameter reduction3.5.3" expl="VC for reduction3">
-   <proof prover="2" memlimit="4000" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_4.v"><result status="valid" time="0.78"/></proof>
+   <proof prover="5" memlimit="4000" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_4.v"><result status="valid" time="0.78"/></proof>
    </goal>
   </transf>
   </goal>
@@ -252,7 +252,7 @@
   <proof prover="1"><result status="valid" time="0.05"/></proof>
   </goal>
   <goal name="WP_parameter reduction3.7" expl="postcondition">
-  <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_6.v"><result status="valid" time="1.07"/></proof>
+  <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_6.v"><result status="valid" time="1.07"/></proof>
   </goal>
   <goal name="WP_parameter reduction3.8" expl="precondition">
   <proof prover="1"><result status="valid" time="0.09"/></proof>
@@ -265,7 +265,7 @@
    <proof prover="4"><result status="valid" time="0.13"/></proof>
    </goal>
    <goal name="WP_parameter reduction3.9.2" expl="VC for reduction3">
-   <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_5.v"><result status="valid" time="0.68"/></proof>
+   <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_5.v"><result status="valid" time="0.85"/></proof>
    </goal>
    <goal name="WP_parameter reduction3.9.3" expl="VC for reduction3">
    <proof prover="0"><result status="valid" time="0.10" steps="142"/></proof>
@@ -276,16 +276,16 @@
   <proof prover="1"><result status="valid" time="0.07"/></proof>
   </goal>
   <goal name="WP_parameter reduction3.11" expl="postcondition">
-  <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_9.v"><result status="valid" time="1.86"/></proof>
+  <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_9.v"><result status="valid" time="1.57"/></proof>
   </goal>
   <goal name="WP_parameter reduction3.12" expl="precondition">
   <proof prover="1"><result status="valid" time="0.08"/></proof>
   </goal>
   <goal name="WP_parameter reduction3.13" expl="precondition">
-  <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_7.v"><result status="valid" time="0.68"/></proof>
+  <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_7.v"><result status="valid" time="0.94"/></proof>
   </goal>
   <goal name="WP_parameter reduction3.14" expl="postcondition">
-  <proof prover="2" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_8.v"><result status="valid" time="0.88"/></proof>
+  <proof prover="5" edited="vstte12_combinators_WP_Combinators_WP_parameter_reduction3_8.v"><result status="valid" time="0.88"/></proof>
   </goal>
   <goal name="WP_parameter reduction3.15" expl="unreachable point">
   <proof prover="0"><result status="valid" time="0.08" steps="114"/></proof>
@@ -295,10 +295,10 @@
  </transf>
  </goal>
  <goal name="ks_value" expl="">
- <proof prover="2" edited="vstte12_combinators_WP_Combinators_ks_value_1.v"><result status="valid" time="0.34"/></proof>
+ <proof prover="5" edited="vstte12_combinators_WP_Combinators_ks_value_1.v"><result status="valid" time="0.34"/></proof>
  </goal>
  <goal name="ks_even_odd" expl="">
- <proof prover="2" edited="vstte12_combinators_WP_Combinators_ks_even_odd_1.v"><result status="valid" time="0.32"/></proof>
+ <proof prover="5" edited="vstte12_combinators_WP_Combinators_ks_even_odd_1.v"><result status="valid" time="0.32"/></proof>
  </goal>
 </theory>
 </file>
diff --git a/examples/vstte12_ring_buffer/why3session.xml b/examples/vstte12_ring_buffer/why3session.xml
index bf7223da7de8bf65fd37670bcb2084fea9b55256..f477129658033aee66f4014482592a1a8eeafdc9 100644
--- a/examples/vstte12_ring_buffer/why3session.xml
+++ b/examples/vstte12_ring_buffer/why3session.xml
@@ -2,8 +2,8 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="0" name="Coq" version="8.6.1" timelimit="20" steplimit="0" memlimit="4000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
+<prover id="2" name="Coq" version="8.7.1" timelimit="20" steplimit="0" memlimit="4000"/>
 <prover id="5" name="Alt-Ergo" version="0.99.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="7" name="Z3" version="3.2" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="8" name="Z3" version="4.3.2" timelimit="5" steplimit="0" memlimit="1000"/>
@@ -69,7 +69,7 @@
   <proof prover="5"><result status="valid" time="0.02" steps="7"/></proof>
   </goal>
   <goal name="WP_parameter head.2" expl="postcondition">
-  <proof prover="0" timelimit="5" memlimit="1000" edited="vstte12_ring_buffer_2_RingBuffer_WP_parameter_head_1.v"><result status="valid" time="0.62"/></proof>
+  <proof prover="2" timelimit="5" memlimit="1000" edited="vstte12_ring_buffer_2_RingBuffer_WP_parameter_head_1.v"><result status="valid" time="0.62"/></proof>
   </goal>
  </transf>
  </goal>
@@ -170,18 +170,18 @@
      <ip_library name="Unit"/>
      <ip_qualid name="unit"/>
     </ts_pos>
-    <ts_pos name="&apos;mark" arity="0" id="68"
+    <ts_pos name="&#39;mark" arity="0" id="68"
      ip_theory="Mark">
      <ip_library name="why3"/>
      <ip_library name="Mark"/>
-     <ip_qualid name="&apos;mark"/>
+     <ip_qualid name="&#39;mark"/>
     </ts_pos>
-    <ts_pos name="array" arity="1" id="4389"
+    <ts_pos name="array" arity="1" id="4402"
      ip_theory="Array">
      <ip_library name="array"/>
      <ip_qualid name="array"/>
     </ts_pos>
-    <ts_pos name="buffer" arity="1" id="5965"
+    <ts_pos name="buffer" arity="1" id="5978"
      ip_theory="RingBuffer">
      <ip_qualid name="buffer"/>
     </ts_pos>
@@ -221,61 +221,61 @@
      <ip_library name="int"/>
      <ip_qualid name="infix *"/>
     </ls_pos>
-    <ls_pos name="mem" id="2349"
+    <ls_pos name="mem" id="2362"
      ip_theory="Mem">
      <ip_library name="list"/>
      <ip_qualid name="mem"/>
     </ls_pos>
-    <ls_pos name="get" id="2999"
+    <ls_pos name="get" id="3012"
      ip_theory="Map">
      <ip_library name="map"/>
      <ip_qualid name="get"/>
     </ls_pos>
-    <ls_pos name="set" id="3002"
+    <ls_pos name="set" id="3015"
      ip_theory="Map">
      <ip_library name="map"/>
      <ip_qualid name="set"/>
     </ls_pos>
-    <ls_pos name="mixfix []" id="3009"
+    <ls_pos name="mixfix []" id="3022"
      ip_theory="Map">
      <ip_library name="map"/>
      <ip_qualid name="mixfix []"/>
     </ls_pos>
-    <ls_pos name="mixfix [&lt;-]" id="3022"
+    <ls_pos name="mixfix [&lt;-]" id="3035"
      ip_theory="Map">
      <ip_library name="map"/>
      <ip_qualid name="mixfix [&lt;-]"/>
     </ls_pos>
-    <ls_pos name="infix ++" id="3718"
+    <ls_pos name="infix ++" id="3731"
      ip_theory="Append">
      <ip_library name="list"/>
      <ip_qualid name="infix ++"/>
     </ls_pos>
-    <ls_pos name="get" id="4397"
+    <ls_pos name="get" id="4410"
      ip_theory="Array">
      <ip_library name="array"/>
      <ip_qualid name="get"/>
     </ls_pos>
-    <ls_pos name="set" id="4412"
+    <ls_pos name="set" id="4425"
      ip_theory="Array">
      <ip_library name="array"/>
      <ip_qualid name="set"/>
     </ls_pos>
-    <ls_pos name="mixfix []" id="4437"
+    <ls_pos name="mixfix []" id="4450"
      ip_theory="Array">
      <ip_library name="array"/>
      <ip_qualid name="mixfix []"/>
     </ls_pos>
-    <ls_pos name="mixfix [&lt;-]" id="4454"
+    <ls_pos name="mixfix [&lt;-]" id="4467"
      ip_theory="Array">
      <ip_library name="array"/>
      <ip_qualid name="mixfix [&lt;-]"/>
     </ls_pos>
-    <ls_pos name="size" id="5979"
+    <ls_pos name="size" id="5992"
      ip_theory="RingBuffer">
      <ip_qualid name="size"/>
     </ls_pos>
-    <ls_pos name="length" id="5988"
+    <ls_pos name="length" id="6001"
      ip_theory="RingBuffer">
      <ip_qualid name="length"/>
     </ls_pos>
@@ -383,67 +383,67 @@
      <ip_library name="int"/>
      <ip_qualid name="CompatOrderMult"/>
     </pr_pos>
-    <pr_pos name="Length_nonnegative" id="2342"
+    <pr_pos name="Length_nonnegative" id="2355"
      ip_theory="Length">
      <ip_library name="list"/>
      <ip_qualid name="Length_nonnegative"/>
     </pr_pos>
-    <pr_pos name="Length_nil" id="2345"
+    <pr_pos name="Length_nil" id="2358"
      ip_theory="Length">
      <ip_library name="list"/>
      <ip_qualid name="Length_nil"/>
     </pr_pos>
-    <pr_pos name="Select_eq" id="3035"
+    <pr_pos name="Select_eq" id="3048"
      ip_theory="Map">
      <ip_library name="map"/>
      <ip_qualid name="Select_eq"/>
     </pr_pos>
-    <pr_pos name="Select_neq" id="3044"
+    <pr_pos name="Select_neq" id="3057"
      ip_theory="Map">
      <ip_library name="map"/>
      <ip_qualid name="Select_neq"/>
     </pr_pos>
-    <pr_pos name="nth_none_1" id="3644"
+    <pr_pos name="nth_none_1" id="3657"
      ip_theory="NthLength">
      <ip_library name="list"/>
      <ip_qualid name="nth_none_1"/>
     </pr_pos>
-    <pr_pos name="nth_none_2" id="3649"
+    <pr_pos name="nth_none_2" id="3662"
      ip_theory="NthLength">
      <ip_library name="list"/>
      <ip_qualid name="nth_none_2"/>
     </pr_pos>
-    <pr_pos name="Append_assoc" id="3735"
+    <pr_pos name="Append_assoc" id="3748"
      ip_theory="Append">
      <ip_library name="list"/>
      <ip_qualid name="Append_assoc"/>
     </pr_pos>
-    <pr_pos name="Append_l_nil" id="3742"
+    <pr_pos name="Append_l_nil" id="3755"
      ip_theory="Append">
      <ip_library name="list"/>
      <ip_qualid name="Append_l_nil"/>
     </pr_pos>
-    <pr_pos name="Append_length" id="3745"
+    <pr_pos name="Append_length" id="3758"
      ip_theory="Append">
      <ip_library name="list"/>
      <ip_qualid name="Append_length"/>
     </pr_pos>
-    <pr_pos name="mem_append" id="3750"
+    <pr_pos name="mem_append" id="3763"
      ip_theory="Append">
      <ip_library name="list"/>
      <ip_qualid name="mem_append"/>
     </pr_pos>
-    <pr_pos name="mem_decomp" id="3757"
+    <pr_pos name="mem_decomp" id="3770"
      ip_theory="Append">
      <ip_library name="list"/>
      <ip_qualid name="mem_decomp"/>
     </pr_pos>
-    <pr_pos name="nth_append_1" id="3767"
+    <pr_pos name="nth_append_1" id="3780"
      ip_theory="NthLengthAppend">
      <ip_library name="list"/>
      <ip_qualid name="nth_append_1"/>
     </pr_pos>
-    <pr_pos name="nth_append_2" id="3774"
+    <pr_pos name="nth_append_2" id="3787"
      ip_theory="NthLengthAppend">
      <ip_library name="list"/>
      <ip_qualid name="nth_append_2"/>
@@ -470,40 +470,40 @@
      <meta_arg_ls id="1469"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="2349"/>
+     <meta_arg_ls id="2362"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="2999"/>
+     <meta_arg_ls id="3012"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="3002"/>
+     <meta_arg_ls id="3015"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="3009"/>
+     <meta_arg_ls id="3022"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="3022"/>
+     <meta_arg_ls id="3035"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="3718"/>
+     <meta_arg_ls id="3731"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="4397"/>
+     <meta_arg_ls id="4410"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="4412"/>
+     <meta_arg_ls id="4425"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="4437"/>
+     <meta_arg_ls id="4450"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="4454"/>
+     <meta_arg_ls id="4467"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="5979"/>
+     <meta_arg_ls id="5992"/>
     </meta>
     <meta name="remove_logic">
-     <meta_arg_ls id="5988"/>
+     <meta_arg_ls id="6001"/>
     </meta>
     <meta name="remove_prop">
      <meta_arg_pr id="1470"/>
@@ -563,43 +563,43 @@
      <meta_arg_pr id="1574"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2342"/>
+     <meta_arg_pr id="2355"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="2345"/>
+     <meta_arg_pr id="2358"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3035"/>
+     <meta_arg_pr id="3048"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3044"/>
+     <meta_arg_pr id="3057"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3644"/>
+     <meta_arg_pr id="3657"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3649"/>
+     <meta_arg_pr id="3662"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3735"/>
+     <meta_arg_pr id="3748"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3742"/>
+     <meta_arg_pr id="3755"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3745"/>
+     <meta_arg_pr id="3758"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3750"/>
+     <meta_arg_pr id="3763"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3757"/>
+     <meta_arg_pr id="3770"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3767"/>
+     <meta_arg_pr id="3780"/>
     </meta>
     <meta name="remove_prop">
-     <meta_arg_pr id="3774"/>
+     <meta_arg_pr id="3787"/>
     </meta>
     <meta name="remove_type">
      <meta_arg_ts id="2"/>
@@ -617,10 +617,10 @@
      <meta_arg_ts id="68"/>
     </meta>
     <meta name="remove_type">
-     <meta_arg_ts id="4389"/>
+     <meta_arg_ts id="4402"/>
     </meta>
     <meta name="remove_type">
-     <meta_arg_ts id="5965"/>
+     <meta_arg_ts id="5978"/>
     </meta>
     <goal name="WP_parameter pop.6.7" expl="VC for pop">
     <transf name="eliminate_builtin">
@@ -643,7 +643,7 @@
    <proof prover="5" timelimit="5" memlimit="1000"><result status="valid" time="0.01" steps="18"/></proof>
    </goal>
    <goal name="WP_parameter pop.8.2" expl="VC for pop">
-   <proof prover="0" edited="vstte12_ring_buffer_RingBuffer_WP_parameter_pop_2.v"><result status="valid" time="0.52"/></proof>
+   <proof prover="2" edited="vstte12_ring_buffer_RingBuffer_WP_parameter_pop_2.v"><result status="valid" time="0.80"/></proof>
    </goal>
    <goal name="WP_parameter pop.8.3" expl="VC for pop">
    <proof prover="5" timelimit="5" memlimit="1000"><result status="valid" time="0.02" steps="24"/></proof>
diff --git a/examples/vstte12_tree_reconstruction/why3session.xml b/examples/vstte12_tree_reconstruction/why3session.xml
index 580d7161520e61b6e5e2629ea8d1c1817df0d2c8..d70da6e934a735ec3784887cd0518c5095449605 100644
--- a/examples/vstte12_tree_reconstruction/why3session.xml
+++ b/examples/vstte12_tree_reconstruction/why3session.xml
@@ -2,10 +2,10 @@
 <!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
 "http://why3.lri.fr/why3session.dtd">
 <why3session shape_version="4">
-<prover id="0" name="Coq" version="8.6.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="2" name="Alt-Ergo" version="1.30" timelimit="2" steplimit="0" memlimit="1000"/>
 <prover id="3" name="CVC4" version="1.4" timelimit="1" steplimit="0" memlimit="1000"/>
+<prover id="4" name="Coq" version="8.7.1" timelimit="10" steplimit="0" memlimit="0"/>
 <prover id="6" name="Z3" version="4.4.1" timelimit="1" steplimit="0" memlimit="1000"/>
 <file name="../vstte12_tree_reconstruction.mlw" expanded="true">
 <theory name="Tree" sum="94da36b854220cd722a2d451bd7b45a0">
@@ -74,10 +74,10 @@
   <proof prover="2"><result status="valid" time="0.01" steps="18"/></proof>
   </goal>
   <goal name="WP_parameter build_rec.7" expl="exceptional postcondition">
-  <proof prover="0" edited="vstte12_tree_reconstruction_WP_TreeReconstruction_WP_parameter_build_rec_3.v"><result status="valid" time="0.50"/></proof>
+  <proof prover="4" edited="vstte12_tree_reconstruction_WP_TreeReconstruction_WP_parameter_build_rec_3.v"><result status="valid" time="0.50"/></proof>
   </goal>
   <goal name="WP_parameter build_rec.8" expl="exceptional postcondition">
-  <proof prover="0" edited="vstte12_tree_reconstruction_WP_TreeReconstruction_WP_parameter_build_rec_4.v"><result status="valid" time="0.37"/></proof>
+  <proof prover="4" edited="vstte12_tree_reconstruction_WP_TreeReconstruction_WP_parameter_build_rec_4.v"><result status="valid" time="0.37"/></proof>
   </goal>
  </transf>
  </goal>
@@ -99,15 +99,15 @@
  <goal name="WP_parameter harness" expl="VC for harness">
  <transf name="split_goal_wp">
   <goal name="WP_parameter harness.1" expl="postcondition">
-  <proof prover="0" edited="vstte12_tree_reconstruction_WP_Harness_WP_parameter_harness_3.v"><result status="valid" time="0.31"/></proof>
+  <proof prover="4" edited="vstte12_tree_reconstruction_WP_Harness_WP_parameter_harness_3.v"><result status="valid" time="0.31"/></proof>
   </goal>
   <goal name="WP_parameter harness.2" expl="VC for harness">
-  <proof prover="0" edited="vstte12_tree_reconstruction_WP_Harness_WP_parameter_harness_4.v"><result status="valid" time="0.29"/></proof>
+  <proof prover="4" edited="vstte12_tree_reconstruction_WP_Harness_WP_parameter_harness_4.v"><result status="valid" time="0.29"/></proof>
   </goal>
  </transf>
  </goal>
  <goal name="WP_parameter harness2" expl="VC for harness2">
- <proof prover="0" edited="vstte12_tree_reconstruction_WP_Harness_WP_parameter_harness2_2.v"><result status="valid" time="0.38"/></proof>
+ <proof prover="4" edited="vstte12_tree_reconstruction_WP_Harness_WP_parameter_harness2_2.v"><result status="valid" time="0.38"/></proof>
  </goal>
 </theory>
 <theory name="ZipperBasedTermination" sum="68cebb9857482610e9524fbc061fb285">
@@ -133,13 +133,13 @@
 </theory>
 <theory name="ZipperBased" sum="3445bf6bce561868d94ea5facd4b83d1">
  <goal name="forest_depths_append" expl="">
- <proof prover="0" edited="vstte12_tree_reconstruction_WP_ZipperBased_forest_depths_append_1.v"><result status="valid" time="0.48"/></proof>
+ <proof prover="4" edited="vstte12_tree_reconstruction_WP_ZipperBased_forest_depths_append_1.v"><result status="valid" time="0.48"/></proof>
  </goal>
  <goal name="g_append" expl="">
- <proof prover="0" timelimit="20" edited="vstte12_tree_reconstruction_WP_ZipperBased_g_append_1.v"><result status="valid" time="0.97"/></proof>
+ <proof prover="4" timelimit="20" edited="vstte12_tree_reconstruction_WP_ZipperBased_g_append_1.v"><result status="valid" time="0.97"/></proof>
  </goal>
  <goal name="right_nil" expl="">
- <proof prover="0" timelimit="29" edited="vstte12_tree_reconstruction_WP_ZipperBased_right_nil_1.v"><result status="valid" time="2.67"/></proof>
+ <proof prover="4" timelimit="29" edited="vstte12_tree_reconstruction_WP_ZipperBased_right_nil_1.v"><result status="valid" time="2.67"/></proof>
  </goal>
  <goal name="main_lemma" expl="">
  <proof prover="2"><result status="valid" time="0.02" steps="107"/></proof>
diff --git a/examples/warshall_algorithm/why3session.xml b/examples/warshall_algorithm/why3session.xml
index c849fb204e66e7f0b16513443a6049b107bfa681..fa57e0b929e66376a3164e4e161efa6d83a0f97e 100644
--- a/examples/warshall_algorithm/why3session.xml
+++ b/examples/warshall_algorithm/why3session.xml
@@ -4,14 +4,14 @@
 <why3session shape_version="4">
 <prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
 <prover id="1" name="CVC3" version="2.4.1" timelimit="5" steplimit="0" memlimit="1000"/>
-<prover id="2" name="Coq" version="8.6.1" timelimit="6" steplimit="0" memlimit="1000"/>
+<prover id="3" name="Coq" version="8.7.1" timelimit="6" steplimit="0" memlimit="1000"/>
 <file name="../warshall_algorithm.mlw" expanded="true">
 <theory name="WarshallAlgorithm" sum="11d2805532fb81964a21c2cc08777290" expanded="true">
  <goal name="weakening" expl="" expanded="true">
- <proof prover="2" edited="warshall_algorithm_WarshallAlgorithm_weakening_1.v"><result status="valid" time="0.33"/></proof>
+ <proof prover="3" edited="warshall_algorithm_WarshallAlgorithm_weakening_1.v"><result status="valid" time="0.33"/></proof>
  </goal>
  <goal name="decomposition" expl="" expanded="true">
- <proof prover="2" edited="warshall_algorithm_WarshallAlgorithm_decomposition_1.v"><result status="valid" time="0.89"/></proof>
+ <proof prover="3" edited="warshall_algorithm_WarshallAlgorithm_decomposition_1.v"><result status="valid" time="0.89"/></proof>
  </goal>
  <goal name="WP_parameter transitive_closure" expl="VC for transitive_closure">
  <transf name="split_goal_wp">