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<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K36" title="GLIB_000:func.36">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  implies <font color="Maroon" title="c2">v</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a> )</span>
<div class="add"><b>assume </b><a NAME="E1:81_1_1_1"/>
<font color="Maroon" title="c2">v</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K36" title="GLIB_000:func.36">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><a NAME="E2:81_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="glib_000.html#D51" target="_self" title="GLIB_000:def.51">Def51</a></i>;<br/><a NAME="E3:81_1_1_1"/><b>then </b>
( <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K33" title="GLIB_000:func.33">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="ref" href="card_1.html#T47" title="CARD_1:th.47">CARD_1:47</a>, <a class="ref" href="xboole_1.html#T15" title="XBOOLE_1:th.15">XBOOLE_1:15</a></i>;<br/><b>hence </b><a NAME="E4:81_1_1_1"/>
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K36" title="GLIB_000:func.36">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:81_1_1"/>
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K36" title="GLIB_000:func.36">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">v</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a></span><br/>

<a NAME="E3:81_1_1"/><b>then </b>
( <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K33" title="GLIB_000:func.33">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
;<br/>
<a NAME="E4:81_1_1"/><b>then </b>
( <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
;<br/>
<a NAME="E5:81_1_1"/><b>then </b>
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K29" title="GLIB_000:func.29">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<b>hence </b><a NAME="E6:81_1_1"/>
<font color="Maroon" title="c2">v</font> is <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a>
 <b>by </b><i><a class="ref" href="glib_000.html#D51" target="_self" title="GLIB_000:def.51">Def51</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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