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<b>let </b><font color="Maroon">G1</font> be   <a href="glib_000.html#NM2">_Graph</a>;<br/><b>let </b><font color="Maroon">G2</font> be    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">v1</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G1</font>;<br/><b>let </b><font color="Maroon">v2</font> be   <a href="glib_000.html#NM10">Vertex</a> of <font color="Maroon">G2</font>;<br/>







<b>assume </b><a NAME="E1:177"/><i><font color="Green">E28</font></i>: 
( <font color="Maroon">v1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v2</font> &amp; <font color="Maroon">v1</font> is <a href="glib_000.html#V11" target="_self">endvertex</a> )
 ;<br/>

<a NAME="E2:177"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">v2</font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">v1</font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a> 
 
<b>by </b><i/>;<br/>
<b>consider </b><font color="Maroon">e</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:177"/><i><font color="Green">E30</font></i>: 
( <font color="Maroon">v1</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">e</font></span><a href="tarski.html#K1">}</a></span> &amp; not <font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">v1</font>,<font color="Maroon">v1</font>,<font color="Maroon">G1</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D29" target="_self">Def29</a>, </i>;<br/>
<a NAME="E5:177"/><i><font color="Green">E41</font></i>: 
( <font color="Maroon">v2</font> <a href="glib_000.html#K29" target="_self">.edgesInOut()</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">v2</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">e</font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="glib_000.html#D32" target="_self">Def32</a>, <a class="ref" href="glib_000.html#D33" target="_self">Def33</a>, <a class="ref" href="zfmisc_1.html#T39">ZFMISC_1:39</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="177_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:177_1"/><i><font color="Green">E42</font></i>: 
not <font color="Maroon">v2</font> is <a href="glib_000.html#V10" target="_self">isolated</a>
 ;<br/><a NAME="E2:177_1"/>
not <font color="Maroon">e</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Maroon">v2</font>,<font color="Maroon">v2</font>,<font color="Maroon">G2</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D29" target="_self">Def29</a>, <a class="ref" href="glib_000.html#D33" target="_self">Def33</a>, </i>;<br/><b>hence </b><a NAME="E3:177_1"/>
<font color="Maroon">v2</font> is <a href="glib_000.html#V11" target="_self">endvertex</a>
 <b>by </b><i>, , , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:177"/>
( <font color="Maroon">v2</font> is <a href="glib_000.html#V11" target="_self">endvertex</a> or <font color="Maroon">v2</font> is <a href="glib_000.html#V10" target="_self">isolated</a> )
 ;<br/>


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