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

<b>let </b><font color="Maroon">X</font> be   <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:45"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">X</font> is <a href="seq_4.html#V1">bounded_above</a>
 <b>and </b><br/><a NAME="E2:45"/><i><font color="Green">E34</font></i>: 
not  <a href="pscomp_1.html#K2">sup</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:45"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E5:45"/>
<font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="pscomp_1.html#K2">sup</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E2:45"><i><font color="Green">E34</font></i></a>, , <a class="ref" href="seq_4.html#D4">SEQ_4:def 4</a></i>;<br/>
<a NAME="E6:45"/><b>then </b>
<font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;</a>  <a href="pscomp_1.html#K2">sup</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="txt" href="rcomp_3.html#E1:45"><i><font color="Green">E33</font></i></a>, <a class="txt" href="rcomp_3.html#E2:45"><i><font color="Green">E34</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<b>hence </b><a NAME="E7:45"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="limfunc1.html#NK2" target="_self">left_open_halfline</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K2">sup</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i><a class="ref" href="borsuk_5.html#T17">BORSUK_5:17</a></i>;<br/>


</div>
