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<b>set </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K2" target="_self">WeightSelector</a> ,<font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E1:27_1_1"/><i><font color="Green">E8</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K2" target="_self">WeightSelector</a> ,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T11">FUNCT_4:11</a></i>;<br/>
<a NAME="E2:27_1_1"/>
 <a href="glib_003.html#K3" target="_self">ELabelSelector</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="glib_003.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E3:27_1_1"/>
 <a href="glib_003.html#K3" target="_self">ELabelSelector</a>  <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K2" target="_self">WeightSelector</a> ,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="glib_003.html#E1:27_1_1"><i><font color="Green">E8</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="glib_003.html#D5" target="_self">GLIB_003:def 5</a><br/>

<a NAME="E4:27_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#R5">==</a> <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K2" target="_self">WeightSelector</a> ,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="glib_003.html#E14"><i><font color="Green">Lemma7</font></i></a></i>;<br/>
<a NAME="E5:27_1_1"/><b>then </b><i><font color="Green">E9</font></i>: 
 <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="glib_000.html#K7">the_Edges_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K2" target="_self">WeightSelector</a> ,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="glib_000.html#D36">GLIB_000:def 36</a></i>;<br/>
<i><font color="Green">E10</font></i>: <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K2" target="_self">WeightSelector</a> ,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a>  = 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> 
<b>by </b><i><a class="ref" href="glib_000.html#T12">GLIB_000:12</a></i>
<br/>.= 
 <a href="glib_003.html#K6" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<a NAME="E7:27_1_1"/>
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K6" target="_self">the_ELabel_of</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="glib_003.html#E12"><i><font color="Green">Lemma5</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:27_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="funct_1.html#NM1">Function</a> st <br/>( <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K2" target="_self">WeightSelector</a> ,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a>  <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="glib_000.html#K7">the_Edges_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K2" target="_self">WeightSelector</a> ,<font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="glib_003.html#E5:27_1_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="glib_003.html#E6:27_1_1"><i><font color="Green">E10</font></i></a></i>;<br/>


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