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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being    <a href="pboole.html#M1">ManySortedSet</a> of  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<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/>
<b>consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="partfun1.html#NM1">PartFunc</a> of  <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>, <a href="numbers.html#K1">REAL</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <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="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="partfun1.html#NM1">PartFunc</a> of  <a href="glib_000.html#K6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<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="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font></span>)</span>, <a href="numbers.html#K1">REAL</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<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="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K4" target="_self">VLabelSelector</a> ,<font color="Maroon">c<sub>6</sub></font>;<br/>
<a NAME="E4:34_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> &amp; <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> <a href="glib_000.html#R5">==</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> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font> &amp; <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="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#R5">==</a> <span class="p1">(<span class="default"><span class="p2">(<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="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K4" target="_self">VLabelSelector</a> ,<font color="Maroon">c<sub>6</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="E5:34_1_1"/><b>then </b><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#R5">==</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> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T88">GLIB_000:88</a></i>;<br/>
<a NAME="E6:34_1_1"/>
<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="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font> <a href="glib_000.html#R5">==</a> <span class="p1">(<span class="default"><span class="p2">(<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="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K4" target="_self">VLabelSelector</a> ,<font color="Maroon">c<sub>6</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="E7:34_1_1"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#R5">==</a> <span class="p1">(<span class="default"><span class="p2">(<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="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K4" target="_self">VLabelSelector</a> ,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="glib_003.html#E5:34_1_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="glib_000.html#T88">GLIB_000:88</a></i>;<br/>
<a NAME="E8:34_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<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="glib_000.html#K13">.set</a> <a href="glib_003.html#K3" target="_self">ELabelSelector</a> ,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="glib_000.html#K13">.set</a> <a href="glib_003.html#K4" target="_self">VLabelSelector</a> ,<font color="Maroon">c<sub>6</sub></font> is    <a href="glib_000.html#M2">Subgraph</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T90">GLIB_000:90</a></i>;<br/>
<b>hence </b><a NAME="E9:34_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="glib_000.html#M2">Subgraph</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="glib_003.html#V1" target="_self">[Weighted]</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="glib_003.html#V2" target="_self">[ELabeled]</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="glib_003.html#V3" target="_self">[VLabeled]</a> )
 ;<br/>


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