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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="subset_1.html#M1">Element</a> of  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="xboole_0.html#K1">{}</a> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></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#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</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">c<sub>6</sub></font> =  <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<a NAME="E3:41_1_1"/>
(  <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#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</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#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 
<b>by </b><i><a class="txt" href="glib_000.html#E14"><i><font color="Green">Lemma4</font></i></a></i>;<br/>
<a NAME="E4:41_1_1"/><b>then </b><i><font color="Green">E24</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#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K6" target="_self">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font> &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#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<a NAME="E5:41_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></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#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> holds <br/>( <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#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> &amp; <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#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></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> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> )
 
<b>by </b><i><a class="txt" href="glib_000.html#E14"><i><font color="Green">Lemma4</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> =  <a href="glib_000.html#K12" target="_self">createGraph</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K6">}</a></span>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>5</sub></font> as    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="glib_000.html#E4:41_1_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self">Def34</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<b>thus </b><a NAME="E7:41_1_1"/>
( <font color="Maroon">c<sub>7</sub></font> is <a href="glib_000.html#V4" target="_self">trivial</a> &amp; <font color="Maroon">c<sub>7</sub></font> is <a href="glib_000.html#V7" target="_self">simple</a> )
 ;<br/>


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