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Commit c1d0e321 authored by MARCHE Claude's avatar MARCHE Claude
Browse files

update proofs of examples/stdlib

parent c527862b
......@@ -91,7 +91,7 @@ intros a a_WT a1 a2 i j l u h1 (h2,h3) (h4,h5) h6 h7.
destruct h1 as (h11,h12).
destruct h12 as (ha,(hb,(hc,(hd,he)))).
red. repeat split.
(* eq_sub *)
(* eq_sub *)
red. intros. apply he; omega.
assumption. assumption. omega. omega. assumption.
(* permut *)
......@@ -205,4 +205,3 @@ omega.
(* eq_sub *)
red. intros. apply he; omega.
Qed.
......@@ -5,27 +5,28 @@
<prover id="0" name="Alt-Ergo" version="0.99.1" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="1" name="Alt-Ergo" version="1.01" timelimit="6" steplimit="0" memlimit="1000"/>
<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="5" name="Coq" version="8.6" timelimit="6" steplimit="0" memlimit="1000"/>
<file name="../../../modules/array.mlw" expanded="true">
<theory name="Array" sum="285c467dea3cde7aa3a3c699222d37ee">
<goal name="WP_parameter defensive_get" expl="VC for defensive_get">
<proof prover="0"><result status="valid" time="0.01" steps="5"/></proof>
<theory name="Array" sum="970b7405c759ecbe0c07f7a2b552e809">
<goal name="VC defensive_get" expl="VC for defensive_get">
<proof prover="0"><result status="valid" time="0.01" steps="3"/></proof>
<proof prover="4"><result status="valid" time="0.01"/></proof>
</goal>
<goal name="WP_parameter defensive_set" expl="VC for defensive_set">
<proof prover="0"><result status="valid" time="0.02" steps="6"/></proof>
<goal name="VC defensive_set" expl="VC for defensive_set">
<proof prover="0"><result status="valid" time="0.02" steps="5"/></proof>
<proof prover="4"><result status="valid" time="0.01"/></proof>
</goal>
<goal name="WP_parameter fill" expl="VC for fill">
<proof prover="0"><result status="valid" time="0.02" steps="58"/></proof>
<goal name="VC fill" expl="VC for fill">
<proof prover="0"><result status="valid" time="0.02" steps="149"/></proof>
<proof prover="4"><result status="valid" time="0.06"/></proof>
</goal>
<goal name="WP_parameter self_blit" expl="VC for self_blit">
<proof prover="2"><result status="valid" time="0.10" steps="148"/></proof>
<goal name="VC self_blit" expl="VC for self_blit">
<proof prover="2"><result status="valid" time="0.32" steps="605"/></proof>
</goal>
</theory>
<theory name="Init" sum="d41d8cd98f00b204e9800998ecf8427e" expanded="true">
</theory>
<theory name="IntArraySorted" sum="d41d8cd98f00b204e9800998ecf8427e">
</theory>
<theory name="Sorted" sum="d41d8cd98f00b204e9800998ecf8427e">
......@@ -34,20 +35,20 @@
</theory>
<theory name="ArrayExchange" sum="d41d8cd98f00b204e9800998ecf8427e">
</theory>
<theory name="ArrayPermut" sum="c35e6a30805f654f329783c9ec01270c">
<theory name="ArrayPermut" sum="fa43aabf25fea9d71d1310e660ffa972">
<goal name="exchange_permut_sub">
<proof prover="5" edited="array_ArrayPermut_exchange_permut_sub_1.v"><result status="valid" time="1.57"/></proof>
</goal>
<goal name="permut_sub_weakening">
<proof prover="5" 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="0.69"/></proof>
</goal>
<goal name="exchange_permut_all">
<proof prover="4"><result status="valid" time="0.06"/></proof>
</goal>
</theory>
<theory name="ArraySwap" sum="fd8901e039caebc94247a7f0ccc00e16">
<goal name="WP_parameter swap" expl="VC for swap">
<proof prover="0"><result status="valid" time="0.00" steps="13"/></proof>
<theory name="ArraySwap" sum="7f838d1eeb430063a79b41c547f5a161">
<goal name="VC swap" expl="VC for swap">
<proof prover="0"><result status="valid" time="0.00" steps="20"/></proof>
<proof prover="4"><result status="valid" time="0.04"/></proof>
</goal>
</theory>
......@@ -57,41 +58,41 @@
</theory>
<theory name="NumOfEq" sum="d41d8cd98f00b204e9800998ecf8427e">
</theory>
<theory name="ToList" sum="b7bcfe4954496ee8ce9bf8d36ab68113">
<goal name="WP_parameter to_list_append" expl="VC for to_list_append">
<proof prover="2"><result status="valid" time="0.01" steps="34"/></proof>
<theory name="ToList" sum="1cfde67ed2807856253ce564c8a87788">
<goal name="VC to_list" expl="VC for to_list">
<proof prover="2"><result status="valid" time="0.00" steps="5"/></proof>
</goal>
<goal name="VC to_list_append" expl="VC for to_list_append">
<proof prover="2"><result status="valid" time="0.03" steps="118"/></proof>
</goal>
</theory>
<theory name="ToSeq" sum="972d3973679c1b19bf79339fb847c382">
<goal name="WP_parameter to_seq_length" expl="VC for to_seq_length">
<theory name="ToSeq" sum="92110e2d9bcac82fcbe10442f737b359">
<goal name="VC to_seq" expl="VC for to_seq">
<proof prover="2"><result status="valid" time="0.00" steps="5"/></proof>
</goal>
<goal name="VC to_seq_length" expl="VC for to_seq_length">
<transf name="split_goal_wp">
<goal name="WP_parameter to_seq_length.1" expl="1. variant decrease">
<proof prover="1"><result status="valid" time="0.00" steps="5"/></proof>
<goal name="VC to_seq_length.1" expl="1. variant decrease">
<proof prover="1"><result status="valid" time="0.00" steps="4"/></proof>
</goal>
<goal name="WP_parameter to_seq_length.2" expl="2. precondition">
<proof prover="1"><result status="valid" time="0.00" steps="5"/></proof>
<goal name="VC to_seq_length.2" expl="2. precondition">
<proof prover="1"><result status="valid" time="0.00" steps="4"/></proof>
</goal>
<goal name="WP_parameter to_seq_length.3" expl="3. postcondition">
<proof prover="1"><result status="valid" time="0.00" steps="13"/></proof>
</goal>
<goal name="WP_parameter to_seq_length.4" expl="4. postcondition">
<proof prover="1"><result status="valid" time="0.00" steps="8"/></proof>
<goal name="VC to_seq_length.3" expl="3. postcondition">
<proof prover="1"><result status="valid" time="0.00" steps="14"/></proof>
</goal>
</transf>
</goal>
<goal name="WP_parameter to_seq_nth" expl="VC for to_seq_nth">
<goal name="VC to_seq_nth" expl="VC for to_seq_nth">
<transf name="split_goal_wp">
<goal name="WP_parameter to_seq_nth.1" expl="1. variant decrease">
<proof prover="1"><result status="valid" time="0.00" steps="6"/></proof>
</goal>
<goal name="WP_parameter to_seq_nth.2" expl="2. precondition">
<proof prover="1"><result status="valid" time="0.00" steps="6"/></proof>
<goal name="VC to_seq_nth.1" expl="1. variant decrease">
<proof prover="1"><result status="valid" time="0.00" steps="5"/></proof>
</goal>
<goal name="WP_parameter to_seq_nth.3" expl="3. postcondition">
<proof prover="1"><result status="valid" time="0.01" steps="20"/></proof>
<goal name="VC to_seq_nth.2" expl="2. precondition">
<proof prover="1"><result status="valid" time="0.00" steps="5"/></proof>
</goal>
<goal name="WP_parameter to_seq_nth.4" expl="4. postcondition">
<proof prover="3"><result status="valid" time="0.02"/></proof>
<goal name="VC to_seq_nth.3" expl="3. postcondition">
<proof prover="1"><result status="valid" time="0.01" steps="26"/></proof>
</goal>
</transf>
</goal>
......
......@@ -2,21 +2,25 @@
<!DOCTYPE why3session PUBLIC "-//Why3//proof session v5//EN"
"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="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="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="Alt-Ergo" version="1.30" timelimit="5" steplimit="0" memlimit="1000"/>
<prover id="7" name="Coq" version="8.6" timelimit="5" steplimit="0" memlimit="4000"/>
<file name="../../../theories/list.why">
<theory name="List" sum="d41d8cd98f00b204e9800998ecf8427e">
<file name="../../../theories/list.why" expanded="true">
<theory name="List" sum="0837e0e504ae2d2a2dc07ff388fab3e5">
<goal name="VC is_nil" expl="VC for is_nil">
<proof prover="6"><result status="valid" time="0.00" steps="7"/></proof>
</goal>
</theory>
<theory name="Length" sum="05caecc0d3ea8074e1ba80a75530a754">
<theory name="Length" sum="c836170b4eda4e34d46c7076259ef108">
<goal name="VC length" expl="VC for length">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
<goal name="Length_nonnegative">
<transf name="induction_ty_lex">
<goal name="Length_nonnegative.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="4"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="5"/></proof>
</goal>
</transf>
</goal>
......@@ -27,71 +31,94 @@
<proof prover="4"><result status="valid" time="0.01"/></proof>
</goal>
<goal name="Length_nil.2" expl="2.">
<proof prover="0"><result status="valid" time="0.00" steps="3"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="4"/></proof>
</goal>
</transf>
</goal>
</theory>
<theory name="Quant" sum="cbe49ff1e6c76878e96cfcfaac826ecd">
<goal name="VC for_all" expl="VC for for_all">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
<goal name="VC for_some" expl="VC for for_some">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
<goal name="VC mem" expl="VC for mem">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
</theory>
<theory name="Mem" sum="d41d8cd98f00b204e9800998ecf8427e">
</theory>
<theory name="Elements" sum="8bdd844429293cfd31fd0f17ecbc15a7">
<theory name="Elements" sum="26546cc0b3612c14b51d5935ff3a45f9">
<goal name="elements_mem">
<transf name="induction_ty_lex">
<goal name="elements_mem.1" expl="1.">
<proof prover="5"><result status="valid" time="0.00" steps="57"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="50"/></proof>
</goal>
</transf>
</goal>
</theory>
<theory name="Nth" sum="d41d8cd98f00b204e9800998ecf8427e">
<theory name="Nth" sum="47a0a8b24dfb020f9c4bf623590c6125">
<goal name="VC nth" expl="VC for nth">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
</theory>
<theory name="NthNoOpt" sum="d41d8cd98f00b204e9800998ecf8427e">
</theory>
<theory name="NthLength" sum="9df36b3cf6313d38366bfd7427521f0d">
<theory name="NthLength" sum="88b9cc7ba70744fcb32e3989c12b15e7">
<goal name="nth_none_1">
<transf name="induction_ty_lex">
<goal name="nth_none_1.1" expl="1.">
<proof prover="0"><result status="valid" time="0.02" steps="19"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="22"/></proof>
</goal>
</transf>
</goal>
<goal name="nth_none_2">
<transf name="induction_ty_lex">
<goal name="nth_none_2.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="21"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="22"/></proof>
</goal>
</transf>
</goal>
<goal name="nth_none_3">
<transf name="induction_ty_lex">
<goal name="nth_none_3.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="26"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="23"/></proof>
</goal>
</transf>
</goal>
</theory>
<theory name="HdTl" sum="d41d8cd98f00b204e9800998ecf8427e">
<theory name="HdTl" sum="6a7bb36d89529a0f0ca85a317461a161">
<goal name="VC hd" expl="VC for hd">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
<goal name="VC tl" expl="VC for tl">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
</theory>
<theory name="HdTlNoOpt" sum="d41d8cd98f00b204e9800998ecf8427e">
</theory>
<theory name="NthHdTl" sum="605b4f2f29860acc4d58392b8e6b8e95">
<theory name="NthHdTl" sum="3d14df5fb64a9db0c86e94f99cbc6759">
<goal name="Nth_tl">
<proof prover="0"><result status="valid" time="0.01" steps="19"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="21"/></proof>
</goal>
<goal name="Nth0_head">
<proof prover="4"><result status="valid" time="0.01"/></proof>
</goal>
</theory>
<theory name="Append" sum="23c9caac5f459c7810a5c31001d09327">
<theory name="Append" sum="cd9221d7e491d871dece8021cb6c5451">
<goal name="VC infix ++" expl="VC for infix ++">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
<goal name="Append_assoc">
<transf name="induction_ty_lex">
<goal name="Append_assoc.1" expl="1.">
<transf name="split_goal_wp">
<goal name="Append_assoc.1.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="3"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="3"/></proof>
</goal>
<goal name="Append_assoc.1.2" expl="2.">
<proof prover="0"><result status="valid" time="0.00" steps="5"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="5"/></proof>
</goal>
</transf>
</goal>
......@@ -100,21 +127,21 @@
<goal name="Append_l_nil">
<transf name="induction_ty_lex">
<goal name="Append_l_nil.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="7"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="5"/></proof>
</goal>
</transf>
</goal>
<goal name="Append_length">
<transf name="induction_ty_lex">
<goal name="Append_length.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="24"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="23"/></proof>
</goal>
</transf>
</goal>
<goal name="mem_append">
<transf name="induction_ty_lex">
<goal name="mem_append.1" expl="1.">
<proof prover="0"><result status="valid" time="0.06" steps="184"/></proof>
<proof prover="6"><result status="valid" time="0.06" steps="272"/></proof>
</goal>
</transf>
</goal>
......@@ -123,121 +150,130 @@
<goal name="mem_decomp.1" expl="1.">
<transf name="split_goal_wp">
<goal name="mem_decomp.1.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="2"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="3"/></proof>
</goal>
<goal name="mem_decomp.1.2" expl="2.">
<proof prover="3"><result status="valid" time="0.31"/></proof>
<proof prover="3"><result status="valid" time="0.83"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</theory>
<theory name="NthLengthAppend" sum="f3c686209d40076fa7f8e64ec02f92be">
<theory name="NthLengthAppend" sum="7318e3e7234e906a5e0115e643b4b46e">
<goal name="nth_append_1">
<transf name="induction_ty_lex">
<goal name="nth_append_1.1" expl="1.">
<proof prover="0"><result status="valid" time="0.03" steps="64"/></proof>
<proof prover="6"><result status="valid" time="0.02" steps="61"/></proof>
</goal>
</transf>
</goal>
<goal name="nth_append_2">
<transf name="induction_ty_lex">
<goal name="nth_append_2.1" expl="1.">
<proof prover="0"><result status="valid" time="0.11" steps="42"/></proof>
<proof prover="6"><result status="valid" time="0.02" steps="44"/></proof>
</goal>
</transf>
</goal>
</theory>
<theory name="Reverse" sum="bc1b8b026b77ef2c52577c6ef9cc53d0">
<theory name="Reverse" sum="b03b90e920b1f860b0f941f5922fccec">
<goal name="VC reverse" expl="VC for reverse">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
<goal name="reverse_append">
<transf name="induction_ty_lex">
<goal name="reverse_append.1" expl="1.">
<proof prover="0"><result status="valid" time="0.29" steps="254"/></proof>
<proof prover="6"><result status="valid" time="0.09" steps="240"/></proof>
</goal>
</transf>
</goal>
<goal name="reverse_cons">
<proof prover="0"><result status="valid" time="0.01" steps="14"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="2"/></proof>
</goal>
<goal name="cons_reverse">
<transf name="induction_ty_lex">
<goal name="cons_reverse.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="42"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="35"/></proof>
</goal>
</transf>
</goal>
<goal name="reverse_reverse">
<transf name="induction_ty_lex">
<goal name="reverse_reverse.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="12"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="12"/></proof>
</goal>
</transf>
</goal>
<goal name="reverse_mem">
<transf name="induction_ty_lex">
<goal name="reverse_mem.1" expl="1.">
<proof prover="0"><result status="valid" time="0.08" steps="191"/></proof>
<proof prover="6"><result status="valid" time="0.03" steps="192"/></proof>
</goal>
</transf>
</goal>
<goal name="Reverse_length">
<transf name="induction_ty_lex">
<goal name="Reverse_length.1" expl="1.">
<proof prover="0"><result status="valid" time="0.02" steps="34"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="28"/></proof>
</goal>
</transf>
</goal>
</theory>
<theory name="RevAppend" sum="9da10df4b75652aa79e575c6cf846dc2">
<theory name="RevAppend" sum="7e7c0334da40a0255ac15033d4dd86f2">
<goal name="VC rev_append" expl="VC for rev_append">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
<goal name="rev_append_append_l">
<transf name="induction_ty_lex">
<goal name="rev_append_append_l.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="24"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="17"/></proof>
</goal>
</transf>
</goal>
<goal name="rev_append_length">
<transf name="induction_ty_lex">
<goal name="rev_append_length.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="24"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="23"/></proof>
</goal>
</transf>
</goal>
<goal name="rev_append_def">
<transf name="induction_ty_lex">
<goal name="rev_append_def.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="30"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="31"/></proof>
</goal>
</transf>
</goal>
<goal name="rev_append_append_r">
<proof prover="0"><result status="valid" time="0.03" steps="42"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="40"/></proof>
</goal>
</theory>
<theory name="Combine" sum="d41d8cd98f00b204e9800998ecf8427e">
<theory name="Combine" sum="fd1c76819779fd0bd76baa52457d5ac3">
<goal name="VC combine" expl="VC for combine">
<proof prover="6"><result status="valid" time="0.00" steps="1"/></proof>
</goal>
</theory>
<theory name="Sorted" sum="aedc51a4d5f32e1722b9b8d9b080a402">
<theory name="Sorted" sum="7ec0006f0f77f4b6679680c6ad677646">
<goal name="sorted_mem">
<transf name="split_goal_wp">
<goal name="sorted_mem.1" expl="1.">
<proof prover="0"><result status="valid" time="0.07" steps="41"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="51"/></proof>
</goal>
<goal name="sorted_mem.2" expl="2.">
<transf name="induction_pr">
<goal name="sorted_mem.2.1" expl="1.">
<proof prover="2"><result status="valid" time="0.00"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="5"/></proof>
</goal>
<goal name="sorted_mem.2.2" expl="2.">
<proof prover="2"><result status="valid" time="0.01"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="13"/></proof>
</goal>
<goal name="sorted_mem.2.3" expl="3.">
<proof prover="1"><result status="valid" time="0.05"/></proof>
<proof prover="6"><result status="valid" time="0.03" steps="116"/></proof>
</goal>
</transf>
</goal>
<goal name="sorted_mem.3" expl="3.">
<proof prover="0"><result status="valid" time="0.01" steps="16"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="18"/></proof>
</goal>
</transf>
</goal>
......@@ -246,73 +282,73 @@
<goal name="sorted_append.1" expl="1.">
<transf name="split_goal_wp">
<goal name="sorted_append.1.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="6"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="6"/></proof>
</goal>
<goal name="sorted_append.1.2" expl="2.">
<proof prover="0"><result status="valid" time="0.01" steps="3"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="4"/></proof>
</goal>
<goal name="sorted_append.1.3" expl="3.">
<proof prover="0"><result status="valid" time="0.01" steps="6"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="5"/></proof>
</goal>
<goal name="sorted_append.1.4" expl="4.">
<proof prover="0"><result status="valid" time="0.00" steps="10"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="7"/></proof>
</goal>
<goal name="sorted_append.1.5" expl="5.">
<proof prover="2"><result status="valid" time="0.16"/></proof>
<proof prover="6"><result status="valid" time="0.11" steps="373"/></proof>
</goal>
<goal name="sorted_append.1.6" expl="6.">
<proof prover="2"><result status="valid" time="1.87"/></proof>
<proof prover="6"><result status="valid" time="0.12" steps="406"/></proof>
</goal>
<goal name="sorted_append.1.7" expl="7.">
<proof prover="0"><result status="valid" time="0.03" steps="80"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="49"/></proof>
</goal>
<goal name="sorted_append.1.8" expl="8.">
<proof prover="1"><result status="valid" time="1.84"/></proof>
<proof prover="6"><result status="valid" time="1.31" steps="3142"/></proof>
</goal>
</transf>
</goal>
</transf>
</goal>
</theory>
<theory name="SortedInt" sum="06ce40f504085478e9252d4d73c60488">
<theory name="SortedInt" sum="d364ac24e753ef3281f6f98fe0bdd059">
<goal name="Transitive.Trans">
<proof prover="0"><result status="valid" time="0.00" steps="2"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="3"/></proof>
</goal>
</theory>
<theory name="RevSorted" sum="19294c1c9d872edacfaf8b426b74d395">
<theory name="RevSorted" sum="b379759278409cf4a274452ce863435e">
<goal name="Incr.Transitive.Trans">
<proof prover="0"><result status="valid" time="0.01" steps="4"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="4"/></proof>
</goal>
<goal name="Decr.Transitive.Trans">
<proof prover="0"><result status="valid" time="0.01" steps="5"/></proof>
<proof prover="6"><result status="valid" time="0.00" steps="5"/></proof>
</goal>
<goal name="rev_append_sorted_incr">
<transf name="induction_ty_lex">
<goal name="rev_append_sorted_incr.1" expl="1.">
<transf name="split_goal_wp">
<goal name="rev_append_sorted_incr.1.1" expl="1.">
<proof prover="0"><result status="valid" time="0.02" steps="4"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="5"/></proof>
</goal>
<goal name="rev_append_sorted_incr.1.2" expl="2.">
<proof prover="0"><result status="valid" time="0.02" steps="8"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="6"/></proof>
</goal>
<goal name="rev_append_sorted_incr.1.3" expl="3.">
<proof prover="0"><result status="valid" time="0.02" steps="38"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="25"/></proof>
</goal>
<goal name="rev_append_sorted_incr.1.4" expl="4.">
<proof prover="0"><result status="valid" time="0.02" steps="9"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="8"/></proof>
</goal>
<goal name="rev_append_sorted_incr.1.5" expl="5.">
<proof prover="2"><result status="valid" time="0.07"/></proof>
</goal>
<goal name="rev_append_sorted_incr.1.6" expl="6.">
<proof prover="0"><result status="valid" time="0.15" steps="142"/></proof>
<proof prover="6"><result status="valid" time="0.03" steps="63"/></proof>
</goal>
<goal name="rev_append_sorted_incr.1.7" expl="7.">
<proof prover="4"><result status="valid" time="0.54"/></proof>
<proof prover="6"><result status="valid" time="1.58" steps="2697"/></proof>
</goal>
<goal name="rev_append_sorted_incr.1.8" expl="8.">
<proof prover="4"><result status="valid" time="1.20"/></proof>
<proof prover="4"><result status="valid" time="1.59"/></proof>
</goal>
</transf>
</goal>
......@@ -323,30 +359,25 @@
<goal name="rev_append_sorted_decr.1" expl="1.">
<transf name="split_goal_wp">
<goal name="rev_append_sorted_decr.1.1" expl="1.">
<proof prover="0"><result status="valid" time="0.01" steps="4"/></proof>
<proof prover="2"><result status="valid" time="0.00"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="5"/></proof>
</goal>
<goal name="rev_append_sorted_decr.1.2" expl="2.">
<proof prover="0"><result status="valid" time="0.02" steps="8"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="6"/></proof>
</goal>
<goal name="rev_append_sorted_decr.1.3" expl="3.">
<proof prover="0"><result status="valid" time="0.05" steps="53"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="25"/></proof>
</goal>
<goal name="rev_append_sorted_decr.1.4" expl="4.">
<proof prover="0"><result status="valid" time="0.01" steps="9"/></proof>
<proof prover="2"><result status="valid" time="0.02"/></proof>
<proof prover="6"><result status="valid" time="0.01" steps="8"/></proof>
</goal>
<goal name="rev_append_sorted_decr.1.5" expl="5.">
<proof prover="2"><result status="valid" time="0.05"/></proof>
</goal>
<goal name="rev_append_sorted_decr.1.6" expl="6.">
<proof prover="0"><result status="valid" time="0.22" steps="216"/></proof>