<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">G</font> be  <a href="glib_000.html#V2">finite</a> <a href="glib_003.html#V7">real-weighted</a> <a href="glib_003.html#V9">real-elabeled</a> <a href="glib_003.html#NM4">WEGraph</a>;<br/><b>let </b><font color="Maroon">source</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>;<br/>



<b>set </b><font color="Maroon">CS</font> =  <a href="glib_005.html#K5" target="_self">AP:CompSeq</a> <font color="Maroon">G</font>,<font color="Maroon">source</font>;<br/>
<b>set </b><font color="Maroon">V</font> = <span class="p1">(<span class="default"><a href="glib_005.html#K6" target="_self">AP:FindAugPath</a> <font color="Maroon">G</font>,<font color="Maroon">source</font></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> ;<br/>
<a NAME="E1:51"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K5" target="_self">AP:CompSeq</a> <font color="Maroon">G</font>,<font color="Maroon">source</font></span>)</span> <a href="glib_004.html#K5">.</a> 0</span>)</span> <a href="glib_003.html#K14">.labeledV()</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">source</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i/>;<br/>
<a NAME="E2:51"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">source</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K5" target="_self">AP:CompSeq</a> <font color="Maroon">G</font>,<font color="Maroon">source</font></span>)</span> <a href="glib_004.html#K5">.</a> 0</span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E3:51"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="glib_005.html#K5" target="_self">AP:CompSeq</a> <font color="Maroon">G</font>,<font color="Maroon">source</font></span>)</span> <a href="glib_004.html#K5">.</a> 0</span>)</span> <a href="glib_003.html#K14">.labeledV()</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><a href="glib_005.html#K6" target="_self">AP:FindAugPath</a> <font color="Maroon">G</font>,<font color="Maroon">source</font></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:51"/>
<font color="Maroon">source</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="glib_005.html#K6" target="_self">AP:FindAugPath</a> <font color="Maroon">G</font>,<font color="Maroon">source</font></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E5:51"/>
( <font color="Maroon">G</font> <a href="glib_000.html#R5">==</a>  <a href="glib_005.html#K6" target="_self">AP:FindAugPath</a> <font color="Maroon">G</font>,<font color="Maroon">source</font> &amp;  <a href="glib_003.html#K5">the_Weight_of</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="glib_003.html#K5">the_Weight_of</a> <span class="p1">(<span class="default"><a href="glib_005.html#K6" target="_self">AP:FindAugPath</a> <font color="Maroon">G</font>,<font color="Maroon">source</font></span>)</span> &amp;  <a href="glib_003.html#K6">the_ELabel_of</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a>  <a href="glib_003.html#K6">the_ELabel_of</a> <span class="p1">(<span class="default"><a href="glib_005.html#K6" target="_self">AP:FindAugPath</a> <font color="Maroon">G</font>,<font color="Maroon">source</font></span>)</span> )
 <b>by </b><i/>;<br/>


</div>
