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<b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="glib_000.html#M2" target="_self">Subgraph</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="45_1_1_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E1:45_1_1_1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K26" target="_self">the_Edges_of</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</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>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/><a NAME="E2:45_1_1_1"/>
( <span class="p1">(<span class="default"><a href="glib_000.html#K10" target="_self">the_Source_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</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="Maroon">c<sub>3</sub></font> &amp; <span class="p1">(<span class="default"><a href="glib_000.html#K11" target="_self">the_Target_of</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</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="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="glib_000.html#E1:45_1_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="glib_000.html#D34" target="_self">Def34</a></i>;<br/><b>hence </b><a NAME="E3:45_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="glib_000.html#E1:45_1_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="glib_000.html#D20" target="_self">Def20</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:45_1_1"/>
<font color="Maroon">c<sub>2</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/>


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