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

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ] <b>means </b>for <font color="Olive">G</font> being <a href="glib_000.html#V2" target="_self">finite</a> <a href="glib_000.html#NM2">_Graph</a>  st <font color="Olive">G</font> <a href="glib_000.html#K16" target="_self">.order()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> holds <br/><font color="Maroon">P<sub>1</sub></font>[<font color="Olive">G</font>];<br/>
<a NAME="E1:37_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[1]
 
<b>by </b><i/>;<br/>
<a NAME="E2:37_1"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">k</font> being non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font> <a href="nat_1.html#K1">+</a> 1]
 
<b>by </b><i><a class="ref" href="glib_000.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E3:37_1"/><i><font color="Green">E42</font></i>: 
for <font color="Olive">k</font> being non <a href="xboole_0.html#V1">empty</a>  <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">k</font>]
 
<b>from </b><i><a class="ref" href="binarith.html#S1">BINARITH:sch 1</a>(, );<br/></i>
<b>let </b><font color="Maroon">G</font> be  <a href="glib_000.html#V2" target="_self">finite</a> <a href="glib_000.html#NM2">_Graph</a>;<br/>

<a NAME="E4:37_1"/>
<font color="Maroon">G</font> <a href="glib_000.html#K16" target="_self">.order()</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">G</font> <a href="glib_000.html#K16" target="_self">.order()</a> 
 
;<br/>
<b>hence </b><a NAME="E5:37_1"/>
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">G</font>]
 <b>by </b><i/>;<br/>


</div>
