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

<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ;<br/><b>let </b><font color="Maroon" title="c2">X'</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c3">x</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/>





<b>assume </b><a NAME="E1:54"/><i><font color="Green" title="E45">A1</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">X'</font> &amp; <font color="Maroon" title="c2">X'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 ;<br/>

<a NAME="E2:54"/><b>then </b>
( <font color="Maroon" title="c2">X'</font> is <a href="seq_4.html#V1" title="SEQ_4:attr.1">bounded_above</a> &amp; <font color="Maroon" title="c2">X'</font> is <a href="seq_4.html#V2" title="SEQ_4:attr.2">bounded_below</a> )
 
<b>by </b><i><a class="ref" href="borsuk_4.html#T50" target="_self" title="BORSUK_4:th.50">Th50</a></i>;<br/>
<b>hence </b><a NAME="E3:54"/>
(  <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">inf</a> <font color="Maroon" title="c2">X'</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c3">x</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="pscomp_1.html#K2" title="PSCOMP_1:func.2">sup</a> <font color="Maroon" title="c2">X'</font> )
 <b>by </b><i><a class="txt" href="borsuk_4.html#E1:54"><i><font color="Green" title="E45">A1</font></i></a>, <a class="ref" href="seq_4.html#D4" title="SEQ_4:def.4">SEQ_4:def 4</a>, <a class="ref" href="seq_4.html#D5" title="SEQ_4:def.5">SEQ_4:def 5</a></i>;<br/>


</div>
