<?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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B</font> being  <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font> holds <br/> (  <a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Olive" title="b1">B</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a> &amp;  <a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Olive" title="b1">B</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a> )</span><br/><b>let </b><font color="Maroon" title="c2">B</font> be   <a href="prob_1.html#NM2" title="PROB_1:NM.2">SetSequence</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Maroon" title="c2">B</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a> &amp;  <a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c2">B</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a> )</span><br/>



<b>thus </b><a NAME="E1:32"/>
 <a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Maroon" title="c2">B</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c2">B</font> is <a href="setlim_1.html#V1" title="SETLIM_1:attr.1">monotone</a></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1"><b>proof </b></a><div class="add">

<a NAME="E1:32_1"/>
 <a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Maroon" title="c2">B</font> is <a href="prob_1.html#V3" title="PROB_1:attr.3">non-descending</a>
 
<b>by </b><i><a class="ref" href="setlim_1.html#T23" target="_self" title="SETLIM_1:th.23">Th25</a></i>;<br/>
<b>hence </b><a NAME="E2:32_1"/>
 <a href="setlim_1.html#K2" title="SETLIM_1:func.2">inferior_setsequence</a> <font color="Maroon" title="c2">B</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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

<a NAME="E2:32"/>
 <a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c2">B</font> is <a href="prob_1.html#V2" title="PROB_1:attr.2">non-ascending</a>
 
<b>by </b><i><a class="ref" href="setlim_1.html#T24" target="_self" title="SETLIM_1:th.24">Th26</a></i>;<br/>
<b>hence </b><a NAME="E3:32"/>
 <a href="setlim_1.html#K4" title="SETLIM_1:func.4">superior_setsequence</a> <font color="Maroon" title="c2">B</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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
