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

<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:126_1"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/><b>then consider </b><font color="Maroon" title="c2">v</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:126_1"/><i><font color="Green" title="E50">A1</font></i>: 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">v</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="card_2.html#T60" title="CARD_2:th.60">CARD_2:60</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c3">v</font> = <font color="Maroon" title="c2">v</font> as   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font> <b>by </b><i><a class="txt" href="glib_000.html#E3:126_1"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>take </b><font color="Maroon" title="c4">v</font> = <font color="Maroon" title="c3">v</font>;<br/><b>thus </b><a NAME="E5:126_1"/>
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="txt" href="glib_000.html#E3:126_1"><i><font color="Green" title="E50">A1</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon" title="c2">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G</font><b> such that </b><a NAME="E3:126"/><i><font color="Green" title="E50">A2</font></i>: 
 <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 ;<br/>

<b>thus </b><a NAME="E4:126"/>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_000.html#E3:126"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="card_1.html#T79" title="CARD_1:th.79">CARD_1:79</a></i>;<br/>


</div>
