bellman-ford with ghost code

parent 83c63ee3
......@@ -174,7 +174,7 @@ module BellmanFord
forall v: vertex. not (negative_cycle v)
let relax (m: ref distmap) (u v: vertex) (pass: int)
(via: set (vertex, vertex))
(ghost via: set (vertex, vertex))
requires { 1 <= pass /\ mem (u, v) edges /\ not (mem (u, v) via) }
requires { inv1 !m pass via }
ensures { inv1 !m pass (add (u, v) via) }
......@@ -200,7 +200,7 @@ module BellmanFord
while not (S.is_empty es) do
invariant { subset !es edges /\ inv1 !m i (diff edges !es) }
variant { cardinal !es }
let via = diff edges !es in (* ghost *)
let ghost via = diff edges !es in
let (u, v) = S.pop es in
relax m u v i via
done;
......
......@@ -46,14 +46,14 @@
locfile="../bellman_ford.mlw"
loclnum="7" loccnumb="7" loccnume="12"
verified="true"
expanded="false">
expanded="true">
<goal
name="vertices_cardinal_pos"
locfile="../bellman_ford.mlw"
loclnum="30" loccnumb="8" loccnume="29"
sum="01d29c66a68377b45dc43bd759f7e97d"
proved="true"
expanded="false"
expanded="true"
shape="ainfix &gt;acardinalaverticesc0">
<proof
prover="0"
......@@ -70,7 +70,7 @@
loclnum="36" loccnumb="8" loccnume="24"
sum="1f6061670351b6b049563f9c38faaed5"
proved="true"
expanded="false"
expanded="true"
shape="amemV1averticesIapathV0V2V1IamemV0averticesF">
<proof
prover="3"
......@@ -88,7 +88,7 @@
loclnum="60" loccnumb="8" loccnume="39"
sum="bd54a9de471e2d775b04e1bea695ba25"
proved="true"
expanded="false"
expanded="true"
shape="amemV2averticesIamemV2aConsV1V0FINainfix =V0aNilIapathasV0V1F">
<proof
prover="3"
......@@ -106,7 +106,7 @@
loclnum="65" loccnumb="8" loccnume="39"
sum="6d88aa40d8a41b1dc9842acaf6f6776e"
proved="true"
expanded="false"
expanded="true"
shape="ainfix =aConsV1V0ainfix ++V3aConsV2ainfix ++V4aConsV2V5EIainfix &gt;alengthaConsV1V0acardinalaverticesIamemV6averticesIamemV6aConsV1V0FF">
<proof
prover="0"
......@@ -123,7 +123,7 @@
loclnum="72" loccnumb="8" loccnume="39"
sum="b77e62ebd8e059fe801e6f83333d72dd"
proved="true"
expanded="false"
expanded="true"
shape="ainfix =V0ainfix ++V3aConsV2ainfix ++V4aConsV2V5EOainfix =V0ainfix ++V6aConsV1V7EIainfix =aConsV1V0ainfix ++V9aConsV8ainfix ++V10aConsV8V11EF">
<proof
prover="3"
......@@ -141,7 +141,7 @@
loclnum="80" loccnumb="8" loccnume="31"
sum="efda0c80f46786e13f22e1fd23ced756"
proved="true"
expanded="false"
expanded="true"
shape="ainfix =V0ainfix ++V3aConsV2ainfix ++V4aConsV2V5EOainfix =V0ainfix ++V6aConsV1V7EIainfix &gt;=alengthV0acardinalaverticesIapathasV0V1F">
<proof
prover="3"
......@@ -159,7 +159,7 @@
loclnum="87" loccnumb="8" loccnume="19"
sum="7b85b20c1831198b4db28af793735c8a"
proved="true"
expanded="false"
expanded="true"
shape="ainfix &lt;alengthV2acardinalaverticesAapathasV2V0EIapathasV1V0F">
<proof
prover="3"
......@@ -177,7 +177,7 @@
loclnum="108" loccnumb="8" loccnume="19"
sum="bcab9f6e90b33953565b901b7a2cfea6"
proved="true"
expanded="false"
expanded="true"
shape="anegative_cycleV2EIainfix &lt;apath_weightV3V0V1AapathasV3V0EIainfix &gt;=apath_weightV4V0V1Iainfix &lt;alengthV4acardinalaverticesIapathasV4V0FF">
<proof
prover="3"
......@@ -186,7 +186,7 @@
edited="bf_Graph_key_lemma_1_1.v"
obsolete="false"
archived="false">
<result status="valid" time="3.82"/>
<result status="valid" time="4.42"/>
</proof>
</goal>
</theory>
......@@ -200,9 +200,9 @@
name="key_lemma_2"
locfile="../bellman_ford.mlw"
loclnum="172" loccnumb="8" loccnume="19"
sum="007e1cc02aa2c7664dad16261086d2ea"
sum="503a8c63de9b96bf0a98355c4f5a0c3f"
proved="true"
expanded="false"
expanded="true"
shape="Nanegative_cycleV1FIainv2V0aedgesIainv1V0acardinalaverticesaemptyF">
<proof
prover="3"
......@@ -211,7 +211,7 @@
edited="bf_WP_BellmanFord_key_lemma_2_1.v"
obsolete="false"
archived="false">
<result status="valid" time="22.24"/>
<result status="valid" time="25.91"/>
</proof>
</goal>
<goal
......@@ -219,54 +219,54 @@
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="VC for relax"
sum="f6c68ab32d14febb247b9e526f273fe0"
sum="e206058616a1f65c0b98caedcabb8969"
proved="true"
expanded="false"
expanded="true"
shape="iainv1V0V3aaddaTuple2V1V2V4ainv1V5V3aaddaTuple2V1V2V4Iainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V6aweightV1V2aFiniteVagetV0V1FCfaInfiniteCtaInfiniteainfix &lt;ainfix +V7aweightV1V2V8aFiniteVagetV0V2aFiniteVagetV0V1Iainv1V0V3V4ANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix &lt;=c1V3F">
<label
name="expl:VC for relax"/>
<transf
name="split_goal"
proved="true"
expanded="false">
expanded="true">
<goal
name="WP_parameter relax.1"
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="1. postcondition"
sum="93fd2cdc76c28f37b14416573617bb82"
sum="ca934cd76a19e6e59009f777a60d8281"
proved="true"
expanded="false"
expanded="true"
shape="postconditionainv1V5V3aaddaTuple2V1V2V4Iainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V6aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V7aweightV1V2V8aFiniteVagetV0V2aFiniteVagetV0V1Iainv1V0V3V4ANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix &lt;=c1V3F">
<label
name="expl:VC for relax"/>
<transf
name="inline_goal"
proved="true"
expanded="false">
expanded="true">
<goal
name="WP_parameter relax.1.1"
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="1. postcondition"
sum="dde1cb7337d770a3d1af6bc7794dd5dd"
sum="424d7e6201a0cf36761acd30e3c2a59f"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix &gt;=ainfix +apath_weightV9V8aweightV8V6V7IamemaTuple2V8V6aaddaTuple2V1V2V4Iainfix &lt;alengthV9V3IapathasV9V8FAainfix &gt;=apath_weightV10V6V7Iainfix &lt;alengthV10V3IapathasV10V6FAainfix =apath_weightV11V6V7AapathasV11V6EaFiniteVainfix &gt;=alengthV13V3IapathasV13V12FIamemaTuple2V12V6aaddaTuple2V1V2V4FAainfix &gt;=alengthV14V3IapathasV14V6FaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V15aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V16aweightV1V2V17aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV21V20aweightV20V18V19IamemaTuple2V20V18V4Iainfix &lt;alengthV21V3IapathasV21V20FAainfix &gt;=apath_weightV22V18V19Iainfix &lt;alengthV22V3IapathasV22V18FAainfix =apath_weightV23V18V19AapathasV23V18EaFiniteVainfix &gt;=alengthV25V3IapathasV25V24FIamemaTuple2V24V18V4FAainfix &gt;=alengthV26V3IapathasV26V18FaInfiniteamixfix []V0V18IamemV18averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
<transf
name="split_goal"
proved="true"
expanded="false">
expanded="true">
<goal
name="WP_parameter relax.1.1.1"
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="1. postcondition"
sum="082bc3db4a78e02c2fcf210a73bf82f0"
sum="9bcbf789d7d8779484589c40944cddc0"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix =apath_weightV8V6V7AapathasV8V6EaFiniteVtaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V9aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V10aweightV1V2V11aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV15V14aweightV14V12V13IamemaTuple2V14V12V4Iainfix &lt;alengthV15V3IapathasV15V14FAainfix &gt;=apath_weightV16V12V13Iainfix &lt;alengthV16V3IapathasV16V12FAainfix =apath_weightV17V12V13AapathasV17V12EaFiniteVainfix &gt;=alengthV19V3IapathasV19V18FIamemaTuple2V18V12V4FAainfix &gt;=alengthV20V3IapathasV20V12FaInfiniteamixfix []V0V12IamemV12averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
......@@ -285,9 +285,9 @@
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="2. postcondition"
sum="281760172216d92e8031b760335dac98"
sum="fe15c375a540a43473effc7abfaa7fc7"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix &gt;=apath_weightV8V6V7Iainfix &lt;alengthV8V3IapathasV8V6FaFiniteVtaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V9aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V10aweightV1V2V11aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV15V14aweightV14V12V13IamemaTuple2V14V12V4Iainfix &lt;alengthV15V3IapathasV15V14FAainfix &gt;=apath_weightV16V12V13Iainfix &lt;alengthV16V3IapathasV16V12FAainfix =apath_weightV17V12V13AapathasV17V12EaFiniteVainfix &gt;=alengthV19V3IapathasV19V18FIamemaTuple2V18V12V4FAainfix &gt;=alengthV20V3IapathasV20V12FaInfiniteamixfix []V0V12IamemV12averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
......@@ -305,9 +305,9 @@
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="3. postcondition"
sum="f732015b314ef2a3d4aa767547f92011"
sum="8663bfda26c1a20601e7f4e090b07f77"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix &gt;=ainfix +apath_weightV9V8aweightV8V6V7IamemaTuple2V8V6aaddaTuple2V1V2V4Iainfix &lt;alengthV9V3IapathasV9V8FaFiniteVtaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V10aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V11aweightV1V2V12aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV16V15aweightV15V13V14IamemaTuple2V15V13V4Iainfix &lt;alengthV16V3IapathasV16V15FAainfix &gt;=apath_weightV17V13V14Iainfix &lt;alengthV17V3IapathasV17V13FAainfix =apath_weightV18V13V14AapathasV18V13EaFiniteVainfix &gt;=alengthV20V3IapathasV20V19FIamemaTuple2V19V13V4FAainfix &gt;=alengthV21V3IapathasV21V13FaInfiniteamixfix []V0V13IamemV13averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
......@@ -325,9 +325,9 @@
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="4. postcondition"
sum="1e3e365e4f3a11962845029371b76fad"
sum="e54dcf3cbda7184518e92c93d0c5d979"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCtaFiniteVainfix &gt;=alengthV8V3IapathasV8V6FaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V9aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V10aweightV1V2V11aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV15V14aweightV14V12V13IamemaTuple2V14V12V4Iainfix &lt;alengthV15V3IapathasV15V14FAainfix &gt;=apath_weightV16V12V13Iainfix &lt;alengthV16V3IapathasV16V12FAainfix =apath_weightV17V12V13AapathasV17V12EaFiniteVainfix &gt;=alengthV19V3IapathasV19V18FIamemaTuple2V18V12V4FAainfix &gt;=alengthV20V3IapathasV20V12FaInfiniteamixfix []V0V12IamemV12averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
......@@ -337,7 +337,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="0.72"/>
<result status="valid" time="0.89"/>
</proof>
<proof
prover="1"
......@@ -353,9 +353,9 @@
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="5. postcondition"
sum="b8f5461c98a17a702098298bcf4b8a74"
sum="6c75438b8804cfb8dcb54c3ee8cf3f63"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCtaFiniteVainfix &gt;=alengthV9V3IapathasV9V8FIamemaTuple2V8V6aaddaTuple2V1V2V4FaInfiniteamixfix []V5V6IamemV6averticesFIainfix =V5asetV0V2CaInfiniteaInfiniteaFiniteainfix +V10aweightV1V2aFiniteVagetV0V1FICfaInfiniteCtaInfiniteainfix &lt;ainfix +V11aweightV1V2V12aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV16V15aweightV15V13V14IamemaTuple2V15V13V4Iainfix &lt;alengthV16V3IapathasV16V15FAainfix &gt;=apath_weightV17V13V14Iainfix &lt;alengthV17V3IapathasV17V13FAainfix =apath_weightV18V13V14AapathasV18V13EaFiniteVainfix &gt;=alengthV20V3IapathasV20V19FIamemaTuple2V19V13V4FAainfix &gt;=alengthV21V3IapathasV21V13FaInfiniteamixfix []V0V13IamemV13averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
......@@ -377,39 +377,39 @@
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="2. postcondition"
sum="7cda7556ea30a001851b7265fa44d7bf"
sum="0e44806ab1409efe0e70df1ad5fc2bb8"
proved="true"
expanded="false"
expanded="true"
shape="postconditionainv1V0V3aaddaTuple2V1V2V4INCfaInfiniteCtaInfiniteainfix &lt;ainfix +V5aweightV1V2V6aFiniteVagetV0V2aFiniteVagetV0V1Iainv1V0V3V4ANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix &lt;=c1V3F">
<label
name="expl:VC for relax"/>
<transf
name="inline_goal"
proved="true"
expanded="false">
expanded="true">
<goal
name="WP_parameter relax.2.1"
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="1. postcondition"
sum="f8962b48c0ddcb65929e40712c113a56"
sum="4675baf798c711d4e9efadee9bf84c96"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix &gt;=ainfix +apath_weightV8V7aweightV7V5V6IamemaTuple2V7V5aaddaTuple2V1V2V4Iainfix &lt;alengthV8V3IapathasV8V7FAainfix &gt;=apath_weightV9V5V6Iainfix &lt;alengthV9V3IapathasV9V5FAainfix =apath_weightV10V5V6AapathasV10V5EaFiniteVainfix &gt;=alengthV12V3IapathasV12V11FIamemaTuple2V11V5aaddaTuple2V1V2V4FAainfix &gt;=alengthV13V3IapathasV13V5FaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V14aweightV1V2V15aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV19V18aweightV18V16V17IamemaTuple2V18V16V4Iainfix &lt;alengthV19V3IapathasV19V18FAainfix &gt;=apath_weightV20V16V17Iainfix &lt;alengthV20V3IapathasV20V16FAainfix =apath_weightV21V16V17AapathasV21V16EaFiniteVainfix &gt;=alengthV23V3IapathasV23V22FIamemaTuple2V22V16V4FAainfix &gt;=alengthV24V3IapathasV24V16FaInfiniteamixfix []V0V16IamemV16averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
<transf
name="split_goal"
proved="true"
expanded="false">
expanded="true">
<goal
name="WP_parameter relax.2.1.1"
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="1. postcondition"
sum="6832dcd7ffca14f301344cc08a3f98f8"
sum="0a20cec996399f5f7ceba948e2f1814d"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix =apath_weightV7V5V6AapathasV7V5EaFiniteVtaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V8aweightV1V2V9aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV13V12aweightV12V10V11IamemaTuple2V12V10V4Iainfix &lt;alengthV13V3IapathasV13V12FAainfix &gt;=apath_weightV14V10V11Iainfix &lt;alengthV14V3IapathasV14V10FAainfix =apath_weightV15V10V11AapathasV15V10EaFiniteVainfix &gt;=alengthV17V3IapathasV17V16FIamemaTuple2V16V10V4FAainfix &gt;=alengthV18V3IapathasV18V10FaInfiniteamixfix []V0V10IamemV10averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
......@@ -435,9 +435,9 @@
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="2. postcondition"
sum="fd088b2c3b2d2224aab26ace73083de8"
sum="3f1dd00a604deaadb8e104ac6b3838c0"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix &gt;=apath_weightV7V5V6Iainfix &lt;alengthV7V3IapathasV7V5FaFiniteVtaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V8aweightV1V2V9aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV13V12aweightV12V10V11IamemaTuple2V12V10V4Iainfix &lt;alengthV13V3IapathasV13V12FAainfix &gt;=apath_weightV14V10V11Iainfix &lt;alengthV14V3IapathasV14V10FAainfix =apath_weightV15V10V11AapathasV15V10EaFiniteVainfix &gt;=alengthV17V3IapathasV17V16FIamemaTuple2V16V10V4FAainfix &gt;=alengthV18V3IapathasV18V10FaInfiniteamixfix []V0V10IamemV10averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
......@@ -463,9 +463,9 @@
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="3. postcondition"
sum="21aeec1b908fdd3096ae04420d9ad5c6"
sum="35f1f437a72b7d8c69bea93b4ea475a8"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix &gt;=ainfix +apath_weightV8V7aweightV7V5V6IamemaTuple2V7V5aaddaTuple2V1V2V4Iainfix &lt;alengthV8V3IapathasV8V7FaFiniteVtaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V9aweightV1V2V10aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV14V13aweightV13V11V12IamemaTuple2V13V11V4Iainfix &lt;alengthV14V3IapathasV14V13FAainfix &gt;=apath_weightV15V11V12Iainfix &lt;alengthV15V3IapathasV15V11FAainfix =apath_weightV16V11V12AapathasV16V11EaFiniteVainfix &gt;=alengthV18V3IapathasV18V17FIamemaTuple2V17V11V4FAainfix &gt;=alengthV19V3IapathasV19V11FaInfiniteamixfix []V0V11IamemV11averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
......@@ -483,9 +483,9 @@
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="4. postcondition"
sum="26e9f8b5f3ad36b23fef49c9bbea1ed2"
sum="63528c0fd05379ce22919b5accc78591"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCtaFiniteVainfix &gt;=alengthV7V3IapathasV7V5FaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V8aweightV1V2V9aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV13V12aweightV12V10V11IamemaTuple2V12V10V4Iainfix &lt;alengthV13V3IapathasV13V12FAainfix &gt;=apath_weightV14V10V11Iainfix &lt;alengthV14V3IapathasV14V10FAainfix =apath_weightV15V10V11AapathasV15V10EaFiniteVainfix &gt;=alengthV17V3IapathasV17V16FIamemaTuple2V16V10V4FAainfix &gt;=alengthV18V3IapathasV18V10FaInfiniteamixfix []V0V10IamemV10averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
......@@ -511,9 +511,9 @@
locfile="../bellman_ford.mlw"
loclnum="176" loccnumb="6" loccnume="11"
expl="5. postcondition"
sum="9e2afcc88a84df5844029885e5cf698c"
sum="3bb40e27d5c4df58131d8984b43dfad7"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCtaFiniteVainfix &gt;=alengthV8V3IapathasV8V7FIamemaTuple2V7V5aaddaTuple2V1V2V4FaInfiniteamixfix []V0V5IamemV5averticesFINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V9aweightV1V2V10aFiniteVagetV0V2aFiniteVagetV0V1ICainfix &gt;=ainfix +apath_weightV14V13aweightV13V11V12IamemaTuple2V13V11V4Iainfix &lt;alengthV14V3IapathasV14V13FAainfix &gt;=apath_weightV15V11V12Iainfix &lt;alengthV15V3IapathasV15V11FAainfix =apath_weightV16V11V12AapathasV16V11EaFiniteVainfix &gt;=alengthV18V3IapathasV18V17FIamemaTuple2V17V11V4FAainfix &gt;=alengthV19V3IapathasV19V11FaInfiniteamixfix []V0V11IamemV11averticesFANamemaTuple2V1V2V4AamemaTuple2V1V2aedgesAainfix =c1V3Oainfix &lt;c1V3F">
<label
name="expl:VC for relax"/>
......@@ -537,7 +537,7 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="VC for bellman_ford"
sum="737dd12183387bbdc8d8c15a199900b0"
sum="e90e4889bc06dc12d93e9748eedc1c2f"
proved="true"
expanded="true"
shape="iCainfix &gt;=apath_weightV7V5V6IapathasV7V5FAainfix =apath_weightV8V5V6AapathasV8V5EaFiniteVNapathasV9V5FaInfiniteagetV1V5IamemV5averticesFAainv2V1aedgesiainfix &lt;acardinalV10acardinalV3Aainfix &lt;=c0acardinalV3Aainv2V1adiffaedgesV10AasubsetV10aedgesanegative_cycleV14ECfaInfiniteCtaInfiniteainfix &lt;ainfix +V15aweightV11V12V16aFiniteVagetV1V12aFiniteVagetV1V11Iainfix =V10aremoveV13V3AamemV13V3LaTuple2V11V12FFANais_emptyV3Nainfix =V4aTrueIais_emptyV3qainfix =V4aTrueFIainv2V1adiffaedgesV3AasubsetV3aedgesFAainv2V1adiffaedgesV2AasubsetV2aedgesIainfix =V2aedgesFAainv1V1acardinalaverticesaemptyIainv1V1ainfix +V0c1aemptyAiainv1V20ainfix +V17c1aemptyAainv1V20V17aedgesainfix &lt;acardinalV23acardinalV19Aainfix &lt;=c0acardinalV19Aainv1V27V17adiffaedgesV23AasubsetV23aedgesIainv1V27V17aaddaTuple2V24V25V22FAainv1V20V17V22ANamemaTuple2V24V25V22AamemaTuple2V24V25aedgesAainfix &lt;=c1V17Iainfix =V23aremoveV26V19AamemV26V19LaTuple2V24V25FFANais_emptyV19LadiffaedgesV19Nainfix =V21aTrueIais_emptyV19qainfix =V21aTrueFIainv1V20V17adiffaedgesV19AasubsetV19aedgesFAainv1V1V17adiffaedgesV18AasubsetV18aedgesIainfix =V18aedgesFIainv1V1V17aemptyIainfix &lt;=V17V0Aainfix &lt;=c1V17FFAainv1ainitialize_single_sourceasc1aemptyIainfix &lt;=c1V0AiCainfix &gt;=apath_weightV33V31V32IapathasV33V31FAainfix =apath_weightV34V31V32AapathasV34V31EaFiniteVNapathasV35V31FaInfiniteagetainitialize_single_sourceasV31IamemV31averticesFAainv2ainitialize_single_sourceasaedgesiainfix &lt;acardinalV36acardinalV29Aainfix &lt;=c0acardinalV29Aainv2ainitialize_single_sourceasadiffaedgesV36AasubsetV36aedgesanegative_cycleV40ECfaInfiniteCtaInfiniteainfix &lt;ainfix +V41aweightV37V38V42aFiniteVagetainitialize_single_sourceasV38aFiniteVagetainitialize_single_sourceasV37Iainfix =V36aremoveV39V29AamemV39V29LaTuple2V37V38FFANais_emptyV29Nainfix =V30aTrueIais_emptyV29qainfix =V30aTrueFIainv2ainitialize_single_sourceasadiffaedgesV29AasubsetV29aedgesFAainv2ainitialize_single_sourceasadiffaedgesV28AasubsetV28aedgesIainfix =V28aedgesFAainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
......@@ -552,7 +552,7 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="1. assertion"
sum="ba5ee770856ab121589c3a75651e03e7"
sum="ae86e50b9e9853afe542ea70cda28d0e"
proved="true"
expanded="true"
shape="assertionainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
......@@ -567,7 +567,7 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="1. assertion"
sum="3c76c8c631ad63db9ddc0d938a2835eb"
sum="ac729c45e7a56ab5adafbc4d093bfa26"
proved="true"
expanded="true"
shape="assertionCainfix &gt;=ainfix +apath_weightV4V3aweightV3V1V2IamemaTuple2V3V1aemptyIainfix &lt;alengthV4acardinalaverticesIapathasV4V3FAainfix &gt;=apath_weightV5V1V2Iainfix &lt;alengthV5acardinalaverticesIapathasV5V1FAainfix =apath_weightV6V1V2AapathasV6V1EaFiniteVainfix &gt;=alengthV8acardinalaverticesIapathasV8V7FIamemaTuple2V7V1aemptyFAainfix &gt;=alengthV9acardinalaverticesIapathasV9V1FaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
......@@ -582,7 +582,7 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="1. assertion"
sum="c496ab0405f78fd2c2a0dc1bff2404d5"
sum="93aba822cd26236d9102876c3c4a57c1"
proved="true"
expanded="true"
shape="assertionCainfix =apath_weightV3V1V2AapathasV3V1EaFiniteVtaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
......@@ -618,9 +618,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="2. assertion"
sum="52b70975898e178ccdbc03d0f98b0bfc"
sum="d7b91b3242375f0c541765167c1e82c4"
proved="true"
expanded="false"
expanded="true"
shape="assertionCainfix &gt;=apath_weightV3V1V2Iainfix &lt;alengthV3acardinalaverticesIapathasV3V1FaFiniteVtaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -638,9 +638,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="3. assertion"
sum="eeb311f9548a057a14e607465affce80"
sum="e6fa40d3e7020cbf5136a39afa401c60"
proved="true"
expanded="false"
expanded="true"
shape="assertionCainfix &gt;=ainfix +apath_weightV4V3aweightV3V1V2IamemaTuple2V3V1aemptyIainfix &lt;alengthV4acardinalaverticesIapathasV4V3FaFiniteVtaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -658,9 +658,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="4. assertion"
sum="75fac407d46fa0e412bade027d956932"
sum="0cb146b4e4b73b58b0702f30b2393660"
proved="true"
expanded="false"
expanded="true"
shape="assertionCtaFiniteVainfix &gt;=alengthV3acardinalaverticesIapathasV3V1FaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -678,9 +678,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="5. assertion"
sum="8afe2bce0995b7f0d2d8b6c1d391d656"
sum="844c3362ead02b1ed7c18195b4b49f7b"
proved="true"
expanded="false"
expanded="true"
shape="assertionCtaFiniteVainfix &gt;=alengthV4acardinalaverticesIapathasV4V3FIamemaTuple2V3V1aemptyFaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix &lt;V0c1Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -702,9 +702,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="2. loop invariant init"
sum="bb0628e5315041a46f4c2885093e5bec"
sum="77046b7fedaa61d93354c84e2de746b1"
proved="true"
expanded="false"
expanded="true"
shape="loop invariant initainv2ainitialize_single_sourceasadiffaedgesV1AasubsetV1aedgesIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -722,9 +722,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="3. precondition"
sum="14744173cda170395cf7ddc69266545b"
sum="1ffaad7b1476187ebc023a4a0e13690b"
proved="true"
expanded="false"
expanded="true"
shape="preconditionNais_emptyV2INainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -742,9 +742,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="4. exceptional postcondition"
sum="e53370849cacd7c589fd8d66f4e7b8a3"
sum="e5f6b2e380eb7a0cb7e48a94a737a81c"
proved="true"
expanded="false"
expanded="true"
shape="exceptional postconditionanegative_cycleV8EICfaInfiniteCtaInfiniteainfix &lt;ainfix +V9aweightV5V6V10aFiniteVagetainitialize_single_sourceasV6aFiniteVagetainitialize_single_sourceasV5Iainfix =V4aremoveV7V2AamemV7V2LaTuple2V5V6FFINais_emptyV2INainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -755,7 +755,7 @@
edited="bf_WP_BellmanFord_WP_parameter_bellman_ford_20.v"
obsolete="false"
archived="false">
<result status="valid" time="2.31"/>
<result status="valid" time="2.68"/>
</proof>
</goal>
<goal
......@@ -763,9 +763,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="5. loop invariant preservation"
sum="0d95c45112d02068bf40f81c33421c86"
sum="4ff773e0f5e089f20c2dda88d39da847"
proved="true"
expanded="false"
expanded="true"
shape="loop invariant preservationainv2ainitialize_single_sourceasadiffaedgesV4AasubsetV4aedgesINCfaInfiniteCtaInfiniteainfix &lt;ainfix +V8aweightV5V6V9aFiniteVagetainitialize_single_sourceasV6aFiniteVagetainitialize_single_sourceasV5Iainfix =V4aremoveV7V2AamemV7V2LaTuple2V5V6FFINais_emptyV2INainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -775,7 +775,7 @@
memlimit="0"
obsolete="false"
archived="false">
<result status="valid" time="3.19"/>
<result status="valid" time="3.89"/>
</proof>
</goal>
<goal
......@@ -783,9 +783,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="6. loop variant decrease"
sum="412c30a04647ff866789d31244cb48be"
sum="7e1336731bb9dcee45b34af677c90e58"
proved="true"
expanded="false"
expanded="true"
shape="loop variant decreaseainfix &lt;acardinalV4acardinalV2Aainfix &lt;=c0acardinalV2INCfaInfiniteCtaInfiniteainfix &lt;ainfix +V8aweightV5V6V9aFiniteVagetainitialize_single_sourceasV6aFiniteVagetainitialize_single_sourceasV5Iainfix =V4aremoveV7V2AamemV7V2LaTuple2V5V6FFINais_emptyV2INainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -803,9 +803,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="7. assertion"
sum="3bd134e92c57cb1850d4274fd14b11a8"
sum="954de816de079d477d17ac8b881f1609"
proved="true"
expanded="false"
expanded="true"
shape="assertionainv2ainitialize_single_sourceasaedgesINNainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -823,24 +823,24 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="8. postcondition"
sum="d643ed3a30832ef9678372cdf9adc347"
sum="b36fae4bb3fc060f0a1401dba94ee12f"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix &gt;=apath_weightV6V4V5IapathasV6V4FAainfix =apath_weightV7V4V5AapathasV7V4EaFiniteVNapathasV8V4FaInfiniteagetainitialize_single_sourceasV4IamemV4averticesFIainv2ainitialize_single_sourceasaedgesINNainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
<transf
name="split_goal"
proved="true"
expanded="false">
expanded="true">
<goal
name="WP_parameter bellman_ford.8.1"
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="1. postcondition"
sum="16ac405c4e0e751627a2770f853fedf7"
sum="c8fb18bf05429af718fc3f009edbab7b"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix =apath_weightV6V4V5AapathasV6V4EaFiniteVtaInfiniteagetainitialize_single_sourceasV4IamemV4averticesFIainv2ainitialize_single_sourceasaedgesINNainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -874,9 +874,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="2. postcondition"
sum="2efcbd71fff030f3e0c5d1264d37e7cf"
sum="13f514fcffd9b7623a7d440892bb407a"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCainfix &gt;=apath_weightV6V4V5IapathasV6V4FaFiniteVtaInfiniteagetainitialize_single_sourceasV4IamemV4averticesFIainv2ainitialize_single_sourceasaedgesINNainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -894,9 +894,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="3. postcondition"
sum="66897d12b0e74f00a6c36fc8fd4de9c7"
sum="6cab34c3a16e0f82525f7bf72901b030"
proved="true"
expanded="false"
expanded="true"
shape="postconditionCtaFiniteVNapathasV6V4FaInfiniteagetainitialize_single_sourceasV4IamemV4averticesFIainv2ainitialize_single_sourceasaedgesINNainfix =V3aTrueIais_emptyV2qainfix =V3aTrueFIainv2ainitialize_single_sourceasadiffaedgesV2AasubsetV2aedgesFIainfix =V1aedgesFIainv1ainitialize_single_sourceasacardinalaverticesaemptyIainfix &gt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -932,7 +932,7 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="9. loop invariant init"
sum="3037730b4268534b952c0a041c5e6481"
sum="f02428b65a75aacce76163e1289eb49e"
proved="true"
expanded="true"
shape="loop invariant initainv1ainitialize_single_sourceasc1aemptyIainfix &lt;=c1V0Lainfix -acardinalaverticesc1">
......@@ -947,7 +947,7 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="1. loop invariant init"
sum="65f025a56fb7c4556828542bc7728ac4"
sum="f2700140dfcc56be949fd3d25f17ce3a"
proved="true"
expanded="true"
shape="loop invariant initCainfix &gt;=ainfix +apath_weightV4V3aweightV3V1V2IamemaTuple2V3V1aemptyIainfix &lt;alengthV4c1IapathasV4V3FAainfix &gt;=apath_weightV5V1V2Iainfix &lt;alengthV5c1IapathasV5V1FAainfix =apath_weightV6V1V2AapathasV6V1EaFiniteVainfix &gt;=alengthV8c1IapathasV8V7FIamemaTuple2V7V1aemptyFAainfix &gt;=alengthV9c1IapathasV9V1FaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix =c1V0Oainfix &lt;c1V0Lainfix -acardinalaverticesc1">
......@@ -962,7 +962,7 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="1. loop invariant init"
sum="b3ab76af721b9bb1d8bfef917b62d069"
sum="a68d9f9265b3a531a51f70e948f4b126"
proved="true"
expanded="true"
shape="loop invariant initCainfix =apath_weightV3V1V2AapathasV3V1EaFiniteVtaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix =c1V0Oainfix &lt;c1V0Lainfix -acardinalaverticesc1">
......@@ -976,14 +976,6 @@
archived="false">
<result status="valid" time="0.12"/>
</proof>
<proof
prover="5"
timelimit="5"
memlimit="1000"
obsolete="false"
archived="false">
<result status="valid" time="2.28"/>
</proof>
<proof
prover="6"
timelimit="5"
......@@ -998,9 +990,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="2. loop invariant init"
sum="071d2f5ed2ac69d1d0c2b5df30c494e3"
sum="2ad0baacdd272cbe9ab49045350a6b34"
proved="true"
expanded="false"
expanded="true"
shape="loop invariant initCainfix &gt;=apath_weightV3V1V2Iainfix &lt;alengthV3c1IapathasV3V1FaFiniteVtaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix =c1V0Oainfix &lt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -1018,9 +1010,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="3. loop invariant init"
sum="a6e4de6c33329d8d180687ece3e4869d"
sum="0ffa3ccdb178e88040c3e9617c6444be"
proved="true"
expanded="false"
expanded="true"
shape="loop invariant initCainfix &gt;=ainfix +apath_weightV4V3aweightV3V1V2IamemaTuple2V3V1aemptyIainfix &lt;alengthV4c1IapathasV4V3FaFiniteVtaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix =c1V0Oainfix &lt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -1038,9 +1030,9 @@
locfile="../bellman_ford.mlw"
loclnum="186" loccnumb="6" loccnume="18"
expl="4. loop invariant init"
sum="5f3c48edb06f684422ab7843265209c7"
sum="daf8fe80c16ce2b04ac306589c162915"
proved="true"
expanded="false"
expanded="true"
shape="loop invariant initCtaFiniteVainfix &gt;=alengthV3c1IapathasV3V1FaInfiniteamixfix []ainitialize_single_sourceasV1IamemV1averticesFIainfix =c1V0Oainfix &lt;c1V0Lainfix -acardinalaverticesc1">
<label
name="expl:VC for bellman_ford"/>
......@@ -1058,9 +1050,9 @@