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

<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">A1</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>thus </b><a NAME="E1:34"/>
 <a href="setlim_1.html#K1" title="SETLIM_1:func.1">inferior_setsequence</a> <font color="Maroon" title="c2">A1</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>proof </b></a><div class="add">

<a NAME="E1:34_1"/>
 <a href="setlim_1.html#K1" title="SETLIM_1:func.1">inferior_setsequence</a> <font color="Maroon" title="c2">A1</font> is <a href="prob_1.html#V3" title="PROB_1:attr.3">non-decreasing</a>
 
<b>by </b><i><a class="ref" href="setlim_1.html#T28" target="_self" title="SETLIM_1:th.28">Th28</a></i>;<br/>
<b>hence </b><a NAME="E2:34_1"/>
 <a href="setlim_1.html#K1" title="SETLIM_1:func.1">inferior_setsequence</a> <font color="Maroon" title="c2">A1</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a>
 <b>by </b><i><a class="ref" href="setlim_1.html#D1" target="_self" title="SETLIM_1:def.1">Def1</a></i>;<br/>


</div><b>end;</b></div>

<a NAME="E2:34"/>
 <a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font> is <a href="prob_1.html#V2" title="PROB_1:attr.2">non-increasing</a>
 
<b>by </b><i><a class="ref" href="setlim_1.html#T29" target="_self" title="SETLIM_1:th.29">Th29</a></i>;<br/>
<b>hence </b><a NAME="E3:34"/>
 <a href="setlim_1.html#K2" title="SETLIM_1:func.2">superior_setsequence</a> <font color="Maroon" title="c2">A1</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a>
 <b>by </b><i><a class="ref" href="setlim_1.html#D1" target="_self" title="SETLIM_1:def.1">Def1</a></i>;<br/>


</div>
