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<b>let </b><font color="Maroon">G</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">v</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="190_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:190_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K1" target="_self">.walkOf</a> <font color="Maroon">v</font></span>)</span> <a href="glib_001.html#K13" target="_self">.vertices()</a> 
 ;<br/><b>then consider </b><font color="Maroon">n</font> being  <a href="abian.html#V1">odd</a>  <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E3:190_1_1"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K1" target="_self">.walkOf</a> <font color="Maroon">v</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K1" target="_self">.walkOf</a> <font color="Maroon">v</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 <b>by </b><i/>;<br/><a NAME="E4:190_1_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">n</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="ref" href="glib_001.html#D24" target="_self">Def24</a>, </i>;<br/><a NAME="E5:190_1_1"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a></i>;<br/><a NAME="E6:190_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K1" target="_self">.walkOf</a> <font color="Maroon">v</font></span>)</span> <a href="funct_1.html#K1">.</a> 1
 <b>by </b><i><a class="ref" href="glib_001.html#D24" target="_self">Def24</a>, <a class="ref" href="glib_001.html#D25" target="_self">Def25</a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/><a NAME="E7:190_1_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E8:190_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</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="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:190_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</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="E3:190_1"/><b>then </b><i><font color="Green">E42</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:190_1"/><i><font color="Green">E43</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K1" target="_self">.walkOf</a> <font color="Maroon">v</font></span>)</span> &amp; not 1 is <a href="abian.html#V1">even</a> )
 <b>by </b><i><a class="ref" href="heyting3.html#T1">HEYTING3:1</a>, <a class="ref" href="jordan12.html#T3">JORDAN12:3</a></i>;<br/><a NAME="E5:190_1"/>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K1" target="_self">.walkOf</a> <font color="Maroon">v</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">v</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E6:190_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K1" target="_self">.walkOf</a> <font color="Maroon">v</font></span>)</span> <a href="glib_001.html#K13" target="_self">.vertices()</a> 
 <b>by </b><i><a class="ref" href="glib_001.html#D24" target="_self">Def24</a>, <a class="ref" href="glib_001.html#D25" target="_self">Def25</a>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:190"/>
<span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="glib_001.html#K1" target="_self">.walkOf</a> <font color="Maroon">v</font></span>)</span> <a href="glib_001.html#K13" target="_self">.vertices()</a>  <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="tarski.html#T2">TARSKI:2</a></i>;<br/>


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