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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="prob_1.html#M1">SetSequence</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:104"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="setlim_1.html#V1" target="_self">monotone</a>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="104_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:104_1"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="prob_1.html#V2">non-increasing</a> or <font color="Maroon">c<sub>3</sub></font> is <a href="prob_1.html#V3">non-decreasing</a> )
 </span><b>by </b><i><a class="txt" href="setlim_1.html#E1:104"><i><font color="Green">E70</font></i></a>, <a class="ref" href="setlim_1.html#D1" target="_self">Def1</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="104_1_1"><b>suppose </b></a><a NAME="E1:104_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="prob_1.html#V2">non-increasing</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:104_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="setlim_1.html#V3" target="_self">convergent</a>
 <b>by </b><i><a class="ref" href="setlim_1.html#T91" target="_self">Th91</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="104_1_2"><b>suppose </b></a><a NAME="E1:104_1_2"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="prob_1.html#V3">non-decreasing</a>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:104_1_2"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="setlim_1.html#V3" target="_self">convergent</a>
 <b>by </b><i><a class="ref" href="setlim_1.html#T88" target="_self">Th88</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
