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<b>set </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> ;<br/>
<a NAME="E1:43_1_1"/><i><font color="Green">E30</font></i>: 
 <a href="glib_004.html#K7" target="_self">WGraphSelectors</a>  <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="glib_004.html#E36"><i><font color="Green">Lemma29</font></i></a></i>;<br/>
<i><font color="Green">E31</font></i>:  <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#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="subset_1.html#K9">/\</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> 
<b>by </b><i><a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>
<br/>.= 
 <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> 
<b>by </b><i><a class="txt" href="glib_004.html#E1:43_1_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>
;<br/>
<a NAME="E3:43_1_1"/><i><font color="Green">E32</font></i>: 
(  <a href="glib_000.html#K1">VertexSelector</a>  <a href="hidden.html#R2">in</a>  <a href="glib_004.html#K7" target="_self">WGraphSelectors</a>  &amp;  <a href="glib_000.html#K2">EdgeSelector</a>  <a href="hidden.html#R2">in</a>  <a href="glib_004.html#K7" target="_self">WGraphSelectors</a>  &amp;  <a href="glib_000.html#K3">SourceSelector</a>  <a href="hidden.html#R2">in</a>  <a href="glib_004.html#K7" target="_self">WGraphSelectors</a>  &amp;  <a href="glib_000.html#K4">TargetSelector</a>  <a href="hidden.html#R2">in</a>  <a href="glib_004.html#K7" target="_self">WGraphSelectors</a>  &amp;  <a href="glib_003.html#K2">WeightSelector</a>  <a href="hidden.html#R2">in</a>  <a href="glib_004.html#K7" target="_self">WGraphSelectors</a>  )
 
<b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<i><font color="Green">E33</font></i>:  <a href="glib_000.html#K6">the_Vertices_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K1">VertexSelector</a> 

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K1">VertexSelector</a> 
<b>by </b><i><a class="txt" href="glib_004.html#E3:43_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
 <a href="glib_000.html#K6">the_Vertices_of</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<i><font color="Green">E34</font></i>:  <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#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K2">EdgeSelector</a> 

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K2">EdgeSelector</a> 
<b>by </b><i><a class="txt" href="glib_004.html#E3:43_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
 <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<i><font color="Green">E35</font></i>:  <a href="glib_000.html#K8">the_Source_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K3">SourceSelector</a> 

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K3">SourceSelector</a> 
<b>by </b><i><a class="txt" href="glib_004.html#E3:43_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
 <a href="glib_000.html#K10">the_Source_of</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<i><font color="Green">E36</font></i>:  <a href="glib_000.html#K9">the_Target_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K4">TargetSelector</a> 

<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <a href="glib_000.html#K4">TargetSelector</a> 
<b>by </b><i><a class="txt" href="glib_004.html#E3:43_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>
<br/>.= 
 <a href="glib_000.html#K11">the_Target_of</a> <font color="Maroon">c<sub>1</sub></font>

;<br/>
<a NAME="E8:43_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K5">_GraphSelectors</a>  holds <br/><font color="Olive">b<sub>1</sub></font> <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#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a>, <a class="txt" href="glib_004.html#E2:43_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="glib_004.html#E3:43_1_1"><i><font color="Green">E32</font></i></a></i>;<br/>
<a NAME="E9:43_1_1"/><b>then </b>
 <a href="glib_000.html#K5">_GraphSelectors</a>  <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#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E10:43_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a>  is <a href="glib_000.html#V1">[Graph-like]</a>
 <b>by </b><i><a class="txt" href="glib_004.html#E4:43_1_1"><i><font color="Green">E33</font></i></a>, <a class="txt" href="glib_004.html#E5:43_1_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="glib_004.html#E6:43_1_1"><i><font color="Green">E35</font></i></a>, <a class="txt" href="glib_004.html#E7:43_1_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="glib_000.html#T7">GLIB_000:7</a></i>;<br/>

<a NAME="E11:43_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_003.html#K2">WeightSelector</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <a href="glib_003.html#K2">WeightSelector</a> 
 
<b>by </b><i><a class="txt" href="glib_004.html#E3:43_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>
<a NAME="E12:43_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span> <a href="funct_1.html#K1">.</a> <a href="glib_003.html#K2">WeightSelector</a>  is    <a href="pboole.html#M1">ManySortedSet</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#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="glib_004.html#E5:43_1_1"><i><font color="Green">E34</font></i></a>, <a class="ref" href="glib_003.html#D4">GLIB_003:def 4</a></i>;<br/>
<b>hence </b><a NAME="E13:43_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="glib_000.html#K14">.strict</a> <a href="glib_004.html#K7" target="_self">WGraphSelectors</a>  is <a href="glib_003.html#V1">[Weighted]</a>
 <b>by </b><i><a class="txt" href="glib_004.html#E2:43_1_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="glib_004.html#E3:43_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="glib_003.html#D4">GLIB_003:def 4</a></i>;<br/>


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