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

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:83_1_1_1"/>
<font color="Maroon" title="c2">v</font> is <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>
 ;<br/><b>then consider </b><font color="Maroon" title="c3">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:83_1_1_1"/><i><font color="Green" title="E36">A1</font></i>: 
( <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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; not <font color="Maroon" title="c3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c1">G</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D53" target="_self" title="GLIB_000:def.53">Def53</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="83_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:83_1_1_1_1_1"/>
( ( <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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) or ( <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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> ) or ( <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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &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>  ) )
 </span><b>by </b><i><a class="txt" href="glib_000.html#E3:83_1_1_1"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T43" title="ZFMISC_1:th.43">ZFMISC_1:43</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="83_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:83_1_1_1_1_1_1"/>
( <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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ;<br/><div class="add"><a NAME="E2:83_1_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E37">A2</font></i>: 
( <font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a>  &amp; <font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">v</font> <a href="glib_000.html#K28" title="GLIB_000:func.28">.edgesOut()</a>  )
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:83_1_1_1_1_1_1"/><b>then </b><i><font color="Green" title="E38">A3</font></i>: 
( <font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E50"><i><font color="Green" title="E31">Lm8</font></i></a></i>;<br/><a NAME="E4:83_1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font>
 <b>by </b><i><a class="txt" href="glib_000.html#E2:83_1_1_1_1_1_1"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="glib_000.html#E51"><i><font color="Green" title="E32">Lm9</font></i></a></i>;<br/><b>hence </b><a NAME="E5:83_1_1_1_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> 1
 <b>by </b><i><a class="txt" href="glib_000.html#E3:83_1_1_1"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="glib_000.html#E3:83_1_1_1_1_1_1"><i><font color="Green" title="E38">A3</font></i></a>, <a class="ref" href="glib_000.html#D15" target="_self" title="GLIB_000:def.15">Def15</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="83_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:83_1_1_1_1_1_2"/>
( <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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:83_1_1_1_1_1_2"/>
<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> 1
 <b>by </b><i><a class="ref" href="card_1.html#T78" title="CARD_1:th.78">CARD_1:78</a>, <a class="ref" href="card_1.html#T79" title="CARD_1:th.79">CARD_1:79</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="83_1_1_1_1_1_3"><b>suppose </b></a><a NAME="E1:83_1_1_1_1_1_3"/>
( <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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &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/><div class="add"><b>hence </b><a NAME="E2:83_1_1_1_1_1_3"/>
<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> 1
 <b>by </b><i><a class="ref" href="card_1.html#T78" title="CARD_1:th.78">CARD_1:78</a>, <a class="ref" href="card_1.html#T79" title="CARD_1:th.79">CARD_1:79</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E5:83_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> 1
 ;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:83_1_1"/><i><font color="Green" title="E36">A4</font></i>: 
<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> 1
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1_1_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="83_1_1_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:83_1_1_2_1"/>
(  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="83_1_1_2_1_1"><b>suppose </b></a><a NAME="E1:83_1_1_2_1_1"/><i><font color="Green" title="E37">A5</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><a NAME="E2:83_1_1_2_1_1"/><b>then </b><i><font color="Green" title="E38">A6</font></i>: 
<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> 
 <b>by </b><i><a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/><b>consider </b><font color="Maroon" title="c3">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E4:83_1_1_2_1_1"/><i><font color="Green" title="E39">A7</font></i>: 
<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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_000.html#E2:83_1_1"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="glib_000.html#E1:83_1_1_2_1_1"><i><font color="Green" title="E37">A5</font></i></a>, <a class="ref" href="card_2.html#T60" title="CARD_2:th.60">CARD_2:60</a></i>;<br/><a NAME="E5:83_1_1_2_1_1"/><i><font color="Green" title="E40">A8</font></i>: 
<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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_000.html#E2:83_1_1_2_1_1"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="glib_000.html#E4:83_1_1_2_1_1"><i><font color="Green" title="E39">A7</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1_1_2_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:83_1_1_2_1_1_1"/>
<font color="Maroon" title="c3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c1">G</font>
 ;<br/><a NAME="E2:83_1_1_2_1_1_1"/><b>then </b>
( <font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D15" target="_self" title="GLIB_000:def.15">Def15</a></i>;<br/><b>hence </b><a NAME="E3:83_1_1_2_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_000.html#E2:83_1_1_2_1_1"><i><font color="Green" title="E38">A6</font></i></a>, <a class="txt" href="glib_000.html#E50"><i><font color="Green" title="E31">Lm8</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:83_1_1_2_1_1"/>
<font color="Maroon" title="c2">v</font> is <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>
 <b>by </b><i><a class="txt" href="glib_000.html#E5:83_1_1_2_1_1"><i><font color="Green" title="E40">A8</font></i></a>, <a class="ref" href="glib_000.html#D53" target="_self" title="GLIB_000:def.53">Def53</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="83_1_1_2_1_2"><b>suppose </b></a><a NAME="E1:83_1_1_2_1_2"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ;<br/><div class="add"><a NAME="E2:83_1_1_2_1_2"/><b>then </b>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T3" title="NAT_1:th.3">NAT_1:3</a></i>;<br/><a NAME="E3:83_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E37">A9</font></i>: 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E4:83_1_1_2_1_2"/>
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 1
 <b>by </b><i><a class="txt" href="glib_000.html#E2:83_1_1"><i><font color="Green" title="E36">A4</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E5:83_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E38">A10</font></i>: 
 <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">v</font> <a href="glib_000.html#K27" title="GLIB_000:func.27">.edgesIn()</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="txt" href="glib_000.html#E3:83_1_1_2_1_2"><i><font color="Green" title="E37">A9</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><b>then consider </b><font color="Maroon" title="c3">e</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:83_1_1_2_1_2"/><i><font color="Green" title="E39">A11</font></i>: 
<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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="card_2.html#T60" title="CARD_2:th.60">CARD_2:60</a></i>;<br/><a NAME="E8:83_1_1_2_1_2"/><i><font color="Green" title="E40">A12</font></i>: 
<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> 
 <b>by </b><i><a class="txt" href="glib_000.html#E2:83_1_1"><i><font color="Green" title="E36">A4</font></i></a>, <a class="txt" href="glib_000.html#E5:83_1_1_2_1_2"><i><font color="Green" title="E38">A10</font></i></a>, <a class="ref" href="card_2.html#T59" title="CARD_2:th.59">CARD_2:59</a></i>;<br/><a NAME="E9:83_1_1_2_1_2"/><b>then </b><i><font color="Green" title="E41">A13</font></i>: 
<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> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">e</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="glib_000.html#E7:83_1_1_2_1_2"><i><font color="Green" title="E39">A11</font></i></a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1_1_2_1_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:83_1_1_2_1_2_1"/>
<font color="Maroon" title="c3">e</font> <a href="glib_000.html#R1" title="GLIB_000:pred.1">Joins</a> <font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c2">v</font>,<font color="Maroon" title="c1">G</font>
 ;<br/><a NAME="E2:83_1_1_2_1_2_1"/><b>then </b>
( <font color="Maroon" title="c3">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" title="GLIB_000:func.10">the_Source_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" title="GLIB_000:func.11">the_Target_of</a> <font color="Maroon" title="c1">G</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> )
 <b>by </b><i><a class="ref" href="glib_000.html#D15" target="_self" title="GLIB_000:def.15">Def15</a></i>;<br/><b>hence </b><a NAME="E3:83_1_1_2_1_2_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_000.html#E8:83_1_1_2_1_2"><i><font color="Green" title="E40">A12</font></i></a>, <a class="txt" href="glib_000.html#E51"><i><font color="Green" title="E32">Lm9</font></i></a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E11:83_1_1_2_1_2"/>
<font color="Maroon" title="c2">v</font> is <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>
 <b>by </b><i><a class="txt" href="glib_000.html#E9:83_1_1_2_1_2"><i><font color="Green" title="E41">A13</font></i></a>, <a class="ref" href="glib_000.html#D53" target="_self" title="GLIB_000:def.53">Def53</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:83_1_1"/>
<font color="Maroon" title="c2">v</font> is <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>
 ;<br/>


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