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<b>consider </b><font color="Maroon" title="c2">W</font> being    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G</font>;<br/>
<b>set </b><font color="Maroon" title="c3">G2</font> = <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font>;<br/>
<b>consider </b><font color="Maroon" title="c4">E</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>
<b>set </b><font color="Maroon" title="c5">G3</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font>;<br/>
<b>consider </b><font color="Maroon" title="c6">V</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font></span>)</span>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>
<b>set </b><font color="Maroon" title="c7">G4</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c6">V</font>;<br/>
<a NAME="E4:34_1_1"/>
( <font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font> &amp; <font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c6">V</font> )
 
<b>by </b><i><a class="txt" href="glib_003.html#E14"><i><font color="Green" title="E7">Lm3</font></i></a></i>;<br/>
<a NAME="E5:34_1_1"/><b>then </b><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T88" title="GLIB_000:th.88">GLIB_000:88</a></i>;<br/>
<a NAME="E6:34_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c6">V</font>
 
<b>by </b><i><a class="txt" href="glib_003.html#E14"><i><font color="Green" title="E7">Lm3</font></i></a></i>;<br/>
<a NAME="E7:34_1_1"/><b>then </b>
<font color="Maroon" title="c1">G</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c6">V</font>
 
<b>by </b><i><a class="txt" href="glib_003.html#E5:34_1_1"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="glib_000.html#T88" title="GLIB_000:th.88">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" title="c1">G</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K2" title="GLIB_003:func.2">WeightSelector</a> ,<font color="Maroon" title="c2">W</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K3" title="GLIB_003:func.3">ELabelSelector</a> ,<font color="Maroon" title="c4">E</font></span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> <a href="glib_003.html#K4" title="GLIB_003:func.4">VLabelSelector</a> ,<font color="Maroon" title="c6">V</font> is    <a href="glib_000.html#M2" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="glib_000.html#T90" title="GLIB_000:th.90">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" title="GLIB_000:mode.2">Subgraph</a> of <font color="Maroon" title="c1">G</font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="glib_003.html#V1" title="GLIB_003:attr.1">[Weighted]</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="glib_003.html#V2" title="GLIB_003:attr.2">[ELabeled]</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="glib_003.html#V3" title="GLIB_003:attr.3">[VLabeled]</a> )
 ;<br/>


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