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<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.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"><span class="kw">assume </span><a NAME="E1:82_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.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="E2:82_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A1</font></span>: 
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D51" target="_self" title="GLIB_000:def.51">Def51</a></span>;<br/><a NAME="E3:82_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K32" title="GLIB_000:func.32">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><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></span>;<br/><span class="kw">hence </span><a NAME="E4:82_1_1_1"/>
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:82_1_1_1"><span class="lab"><font color="Green" title="E34">A1</font></span></a>, <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></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:82_1_1"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K35" title="GLIB_000:func.35">.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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E3:82_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</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="E4:82_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesInOut()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:82_1_1"><span class="lab"><font color="Green" title="E34">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:82_1_1"/>
<font color="Maroon" title="c2">v</font> is  <a href="glib_000.html#V10" title="GLIB_000:attr.10">isolated</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D51" target="_self" title="GLIB_000:def.51">Def51</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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