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<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="glib_000.html#K12" target="_self">createGraph</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E1:28_1_1"/><i><font color="Green">E19</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> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</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> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="glib_000.html#E14"><i><font color="Green">Lemma4</font></i></a></i>;<br/>
<a NAME="E2:28_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>(  not <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> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></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> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</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> <span class="p2">(<span class="default"><a href="glib_000.html#K12" target="_self">createGraph</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></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/>
<a NAME="E3:28_1_1"/><b>then </b><i><font color="Green">E20</font></i>: 
 <a href="glib_000.html#K12" target="_self">createGraph</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> is <a href="glib_000.html#V3" target="_self">loopless</a>
 
<b>by </b><i><a class="ref" href="glib_000.html#D20" target="_self">Def20</a></i>;<br/>
<a NAME="E4:28_1_1"/>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>, <a href="glib_000.html#K12" target="_self">createGraph</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="glib_000.html#R1" target="_self">Joins</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>, <a href="glib_000.html#K12" target="_self">createGraph</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> holds <br/><font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="glib_000.html#E1:28_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="glib_000.html#D15" target="_self">Def15</a></i>;<br/>
<a NAME="E5:28_1_1"/><b>then </b>
 <a href="glib_000.html#K12" target="_self">createGraph</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> is <a href="glib_000.html#V5" target="_self">non-multi</a>
 
<b>by </b><i><a class="ref" href="glib_000.html#D22" target="_self">Def22</a></i>;<br/>
<b>hence </b><a NAME="E6:28_1_1"/>
 <a href="glib_000.html#K12" target="_self">createGraph</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> is <a href="glib_000.html#V7" target="_self">simple</a>
 <b>by </b><i><a class="txt" href="glib_000.html#E3:28_1_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="glib_000.html#D24" target="_self">Def24</a></i>;<br/>


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