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<b>let </b><font color="Maroon">G</font> be  <a href="glib_000.html#V2" target="_self">finite</a> <a href="glib_000.html#NM2">_Graph</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:127_1"/>
<font color="Maroon">G</font> <a href="glib_000.html#K16" target="_self">.order()</a>  <a href="hidden.html#R1">=</a> 1
 ;<br/><a NAME="E2:127_1"/><b>then </b>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 ;<br/><b>then consider </b><font color="Maroon">v</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:127_1"/><i><font color="Green">E28</font></i>: 
 <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">v</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="card_2.html#T60">CARD_2:60</a></i>;<br/><b>reconsider </b><font color="Maroon">v</font> = <font color="Maroon">v</font> as   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font> <b>by </b><i><a class="ref" href="glib_000.html#D20" target="_self">Def20</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>take </b><font color="Maroon">v</font> = <font color="Maroon">v</font>;<br/><b>thus </b><a NAME="E6:127_1"/>
 <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="glib_000.html#D20" target="_self">Def20</a></i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">v</font> being   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font><b> such that </b><a NAME="E2:127"/><i><font color="Green">E29</font></i>: 
 <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">v</font></span><a href="domain_1.html#K6">}</a></span>
 ;<br/>

<a NAME="E3:127"/>
 <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">G</font></span>)</span> <a href="hidden.html#R1">=</a> 1
 
<b>by </b><i><a class="ref" href="card_1.html#T79">CARD_1:79</a>, <a class="ref" href="glib_000.html#D20" target="_self">Def20</a></i>;<br/>
<b>hence </b><a NAME="E4:127"/>
<font color="Maroon">G</font> <a href="glib_000.html#K16" target="_self">.order()</a>  <a href="hidden.html#R1">=</a> 1
 ;<br/>


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