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

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:82_1_1_1"/>
<font color="Maroon">v</font> is <a href="glib_000.html#V10" target="_self">isolated</a>
 ;<br/><a NAME="E2:82_1_1_1"/><b>then </b>
<font color="Maroon">v</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/>;<br/><a NAME="E3:82_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E4:82_1_1_1"/><b>then </b>
(  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> </span>)</span> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> </span>)</span> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="ref" href="card_1.html#T78">CARD_1:78</a>, <a class="ref" href="xboole_1.html#T15">XBOOLE_1:15</a></i>;<br/><a NAME="E5:82_1_1_1"/><b>then </b>
( <font color="Maroon">v</font> <a href="glib_000.html#K33" target="_self">.inDegree()</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">v</font> <a href="glib_000.html#K34" target="_self">.outDegree()</a>  <a href="hidden.html#R1">=</a> 0 )
 ;<br/><a NAME="E6:82_1_1_1"/><b>then </b>
<font color="Maroon">v</font> <a href="glib_000.html#K36" target="_self">.degree()</a>  <a href="hidden.html#R1">=</a> 0 <a href="nat_1.html#K1">+</a> 0
 ;<br/><b>hence </b><a NAME="E7:82_1_1_1"/>
<font color="Maroon">v</font> <a href="glib_000.html#K36" target="_self">.degree()</a>  <a href="hidden.html#R1">=</a> 0
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:82_1_1"/>
<font color="Maroon">v</font> <a href="glib_000.html#K36" target="_self">.degree()</a>  <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E3:82_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="glib_000.html#K33" target="_self">.inDegree()</a> </span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="glib_000.html#K34" target="_self">.outDegree()</a> </span>)</span> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E4:82_1_1"/><b>then </b>
( <font color="Maroon">v</font> <a href="glib_000.html#K33" target="_self">.inDegree()</a>  <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">v</font> <a href="glib_000.html#K34" target="_self">.outDegree()</a>  <a href="hidden.html#R1">=</a> 0 )
 
<b>by </b><i><a class="ref" href="nat_1.html#T23">NAT_1:23</a></i>;<br/>
<a NAME="E5:82_1_1"/><b>then </b>
(  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a> </span>)</span> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><font color="Maroon">v</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a> </span>)</span> <a href="hidden.html#R1">=</a> 0 )
 
;<br/>
<a NAME="E6:82_1_1"/><b>then </b><i><font color="Green">E28</font></i>: 
( <font color="Maroon">v</font> <a href="glib_000.html#K27" target="_self">.edgesIn()</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">v</font> <a href="glib_000.html#K28" target="_self">.edgesOut()</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="ref" href="card_2.html#T59">CARD_2:59</a></i>;<br/>
<a NAME="E7:82_1_1"/>
<font color="Maroon">v</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/>;<br/>
<b>hence </b><a NAME="E8:82_1_1"/>
<font color="Maroon">v</font> is <a href="glib_000.html#V10" target="_self">isolated</a>
 <b>by </b><i/>;<br/>


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