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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">a<sub>1</sub></font> <a href="glib_000.html#R3" target="_self">SJoins</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">G</font>;<br/>
<b>consider </b><font color="Maroon">IT</font> being   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G</font></span>)</span><b> such that </b><br/><a NAME="E2:36_1_1"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">e</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> iff ( <font color="Olive">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">e</font>] ) )
 <b>from </b><i><a class="ref" href="subset_1.html#S1">SUBSET_1:sch 1</a>();<br/></i>
<b>take </b>
<font color="Maroon">IT</font>
;<br/>

<b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>thus </b><a NAME="E3:36_1_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font> implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">e</font>] )
 <b>by </b><i><a class="ref" href="glib_000.html#D1" target="_self">Def1</a></i>;<br/>

<b>assume </b><a NAME="E4:36_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">e</font> <a href="glib_000.html#R3" target="_self">SJoins</a> <font color="Maroon">X</font>,<font color="Maroon">Y</font>,<font color="Maroon">G</font>
 ;<br/>

<a NAME="E5:36_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7" target="_self">the_Edges_of</a> <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:36_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 <b>by </b><i><a class="ref" href="glib_000.html#D1" target="_self">Def1</a>, </i>;<br/>


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