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

<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="glib_003.html#V7" title="GLIB_003:attr.7">real-weighted</a> <a href="glib_003.html#NM1" title="GLIB_003:NM.1">WGraph</a>;<br/>

<b>set </b><font color="Maroon" title="c2">G2</font> =  <a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:Init</a> <font color="Maroon" title="c1">G</font>;<br/>
<b>set </b><font color="Maroon" title="c3">X</font> = <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1;<br/>
<a NAME="E1:63"/><i><font color="Green" title="E39">A1</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="glib_003.html#T8" title="GLIB_003:th.8">GLIB_003:8</a></i>;<br/>
<a NAME="E2:63"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p3">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:Init</a> <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="glib_003.html#T8" title="GLIB_003:th.8">GLIB_003:8</a></i>;<br/>
<b>hence </b><a NAME="E3:63"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a>  <a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:Init</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="txt" href="glib_004.html#E1:63"><i><font color="Green" title="E39">A1</font></i></a>, <a class="ref" href="glib_000.html#T88" title="GLIB_000:th.88">GLIB_000:88</a></i>;<br/>

<b>thus </b> <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p1">(<span class="default"><a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:Init</a> <font color="Maroon" title="c1">G</font></span>)</span> = 
 <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="glib_000.html#T12" title="GLIB_000:th.12">GLIB_000:12</a></i>
<br/>.= 
 <a href="glib_003.html#K5" title="GLIB_003:func.5">the_Weight_of</a> <font color="Maroon" title="c1">G</font>
<b>by </b><i><a class="ref" href="glib_000.html#T12" title="GLIB_000:th.12">GLIB_000:12</a></i>
;<br/>

<b>thus </b><a NAME="E5:63"/>
 <a href="glib_003.html#K6" title="GLIB_003:func.6">the_ELabel_of</a> <span class="p1">(<span class="default"><a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:Init</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="glib_000.html#T11" title="GLIB_000:th.11">GLIB_000:11</a></i>;<br/>

 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:Init</a> <font color="Maroon" title="c1">G</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p4">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> 
<b>by </b><i><a class="ref" href="glib_000.html#T12" title="GLIB_000:th.12">GLIB_000:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1
<b>by </b><i><a class="ref" href="glib_000.html#T11" title="GLIB_000:th.11">GLIB_000:11</a></i>
;<br/>
<b>hence </b><a NAME="E7:63"/>
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><a href="glib_004.html#K12" title="GLIB_004:func.12">PRIM:Init</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="subset_1.html#K10" title="SUBSET_1:func.10">choose</a> <span class="p2">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font></span>)</span></span>)</span> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> 1
 ;<br/>


</div>
