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

<b>set </b><font color="Maroon">V</font> = <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>;<br/>
<b>set </b><font color="Maroon">E</font> =  <a href="xboole_0.html#K1">{}</a> ;<br/>
<b>reconsider </b><font color="Maroon">S</font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="funct_2.html#NM1">Function</a> of  <a href="xboole_0.html#K1">{}</a> ,<span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span> <b>by </b><i><a class="ref" href="funct_2.html#T55">FUNCT_2:55</a>, <a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>;<br/>
<b>set </b><font color="Maroon">G</font> =  <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font>;<br/>
<b>take </b>
 <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font>
;<br/>

<a NAME="E2:24_2_1"/><i><font color="Green">E30</font></i>: 
(  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span> &amp;  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:24_2_1"/>
 <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font> is <a href="glib_000.html#V2" target="_self">finite</a>
 <b>by </b><i/>;<br/>

<a NAME="E4:24_2_1"/>
for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>   holds <br/>(  not <font color="Olive">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <span class="p1">(<span class="default"><a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p2"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font></span>)</span> or  not <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">e</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E5:24_2_1"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font> is <a href="glib_000.html#V3" target="_self">loopless</a>
 
<b>by </b><i/>;<br/>
<a NAME="E6:24_2_1"/>
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <span class="p2">(<span class="default"><a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p3"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 1
 
<b>by </b><i>, <a class="ref" href="card_2.html#T76">CARD_2:76</a></i>;<br/>
<b>hence </b><a NAME="E7:24_2_1"/>
not  <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font> is <a href="glib_000.html#V4" target="_self">trivial</a>
 <b>by </b><i/>;<br/>

<a NAME="E8:24_2_1"/>
for <font color="Olive">e1</font>, <font color="Olive">e2</font>, <font color="Olive">v1</font>, <font color="Olive">v2</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">e1</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Olive">v1</font>,<font color="Olive">v2</font>, <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font> &amp; <font color="Olive">e2</font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Olive">v1</font>,<font color="Olive">v2</font>, <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font> holds <br/><font color="Olive">e1</font> <a href="hidden.html#R1">=</a> <font color="Olive">e2</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:24_2_1"/><b>then </b>
 <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font> is <a href="glib_000.html#V5" target="_self">non-multi</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E10:24_2_1"/>
 <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default">1,2</span><a href="domain_1.html#K7">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">S</font>,<font color="Maroon">S</font> is <a href="glib_000.html#V7" target="_self">simple</a>
 <b>by </b><i>, </i>;<br/>


</div>
