<?xml version="1.0"?>
<div class="add">

<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_005.html#R3" target="_self">is_forward_labeling_in</a> <font color="Maroon">G</font> or <font color="Maroon">a<sub>1</sub></font> <a href="glib_005.html#R4" target="_self">is_backward_labeling_in</a> <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">the_Edges_of</a> <font color="Maroon">G</font></span>)</span><b> such that </b><br/><a NAME="E2:35_1_1"/><i><font color="Green">E37</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">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="E3:35_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/>;<br/>

<b>assume </b><a NAME="E4:35_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">e</font>]
 ;<br/>

<a NAME="E5:35_1_1"/><b>then </b>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="glib_000.html#K7">the_Edges_of</a> <font color="Maroon">G</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:35_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">IT</font>
 <b>by </b><i>, </i>;<br/>


</div>
