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

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K6">ExtREAL</a> ;<br/><b>let </b><font color="Maroon">x</font> be   <a href="supinf_1.html#NM3">R_eal</a>;<br/>



<b>assume </b><a NAME="E1:53"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 ;<br/>

<a NAME="E2:53"/>
 <a href="supinf_1.html#K6" target="_self">sup</a> <font color="Maroon">X</font> is    <a href="supinf_1.html#M1" target="_self">majorant</a> of <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:53"/>
<font color="Maroon">x</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="supinf_1.html#K6" target="_self">sup</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="supinf_1.html#T33" target="_self">Th33</a>, </i>;<br/>


</div>
