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

<a NAME="E1:4_1_1"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">n</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ordinal1.html#D13">ORDINAL1:def 13</a></i>;<br/>
<b>thus </b><a NAME="E2:4_1_1"/>
 <a href="turing_1.html#K3" target="_self">SegM</a> <font color="Maroon">n</font> is <a href="finset_1.html#V1">finite</a>
 <b>by </b><i>, <a class="ref" href="cqc_the1.html#T12">CQC_THE1:12</a></i>;<br/>

<a NAME="E3:4_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<a NAME="E4:4_1_1"/><b>then </b>
0 <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">k</font> where <font color="Olive">k</font> is    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  : <font color="Olive">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E5:4_1_1"/>
not  <a href="turing_1.html#K3" target="_self">SegM</a> <font color="Maroon">n</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/>


</div>
