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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A1</font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">X</font>;<br/>



<b>assume </b><a NAME="E1:74"/>
<font color="Maroon">A1</font> is <a href="prob_1.html#V2">non-increasing</a>
 ;<br/>

<a NAME="E2:74"/><b>then </b><i><font color="Green">E28</font></i>: 
(  <a href="kurato_2.html#K5">lim_sup</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a>  <a href="prob_1.html#K4">Intersection</a> <font color="Maroon">A1</font> &amp;  <a href="kurato_2.html#K4">lim_inf</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a>  <a href="prob_1.html#K4">Intersection</a> <font color="Maroon">A1</font> )
 
<b>by </b><i>, <a class="ref" href="setlim_1.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E3:74"/>
<font color="Maroon">A1</font> is <a href="kurato_2.html#V3">convergent</a>
 <b>by </b><i><a class="ref" href="kurato_2.html#D7">KURATO_2:def 7</a></i>;<br/>

<b>hence </b><a NAME="E4:74"/>
 <a href="setlim_1.html#K3" target="_self">lim</a> <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a>  <a href="prob_1.html#K4">Intersection</a> <font color="Maroon">A1</font>
 <b>by </b><i><a class="ref" href="setlim_1.html#T12" target="_self">Th12</a>, <a class="ref" href="setlim_1.html#T8" target="_self">Th8</a></i>;<br/>


</div>
