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

<b>let </b><font color="Maroon">r</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>let </b><font color="Maroon">s</font> be   <a href="real_1.html#NM1">Real</a>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:9_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="jordan1h.html#K1" target="_self">RealOrd</a> 
 ;<br/><b>then consider </b><font color="Maroon">r1</font> being   <a href="real_1.html#NM1">Real</a>, <font color="Maroon">s1</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E3:9_1"/><i><font color="Green">E59</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">r1</font>,<font color="Maroon">s1</font></span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E4:9_1"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">r1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s1</font>
 ;<br/><a NAME="E5:9_1"/>
( <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">r1</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s1</font> )
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><b>hence </b><a NAME="E6:9_1"/>
<font color="Maroon">r</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">s</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>


</div>
