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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:190"/><i><font color="Green">E79</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#R5" target="_self">==</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:190_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="glib_000.html#V10" target="_self">isolated</a>
 ;<br/><a NAME="E2:190_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="glib_000.html#D51" target="_self">Def51</a></i>;<br/><a NAME="E3:190_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="glib_000.html#E1:190"><i><font color="Green">E79</font></i></a>, <a class="ref" href="glib_000.html#T99" target="_self">Th99</a></i>;<br/><b>hence </b><a NAME="E4:190_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="glib_000.html#V10" target="_self">isolated</a>
 <b>by </b><i><a class="ref" href="glib_000.html#D51" target="_self">Def51</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:190"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="glib_000.html#V11" target="_self">endvertex</a>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:190"/><i><font color="Green">E80</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D53" target="_self">Def53</a></i>;<br/>
<a NAME="E6:190"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K1">}</a></span> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="glib_000.html#E1:190"><i><font color="Green">E79</font></i></a>, <a class="txt" href="glib_000.html#E5:190"><i><font color="Green">E80</font></i></a>, <a class="ref" href="glib_000.html#T91" target="_self">Th91</a>, <a class="ref" href="glib_000.html#T99" target="_self">Th99</a></i>;<br/>
<b>hence </b><a NAME="E7:190"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="glib_000.html#V11" target="_self">endvertex</a>
 <b>by </b><i><a class="ref" href="glib_000.html#D53" target="_self">Def53</a></i>;<br/>


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