<?xml version="1.0"?>
<div><span class="kw">theorem </span><a NAME="T44"><span class="comment"><font color="firebrick">:: SURREAL0:44</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a><br/>  for <font color="Olive" title="b3">X1</font>, <font color="Olive" title="b4">X2</font>, <font color="Olive" title="b5">Y1</font>, <font color="Olive" title="b6">Y2</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st (  for <font color="Olive" title="b7">x</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st <font color="Olive" title="b7">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">X1</font> holds <br/> ex <font color="Olive" title="b8">y</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> st <br/>( <font color="Olive" title="b8">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">X2</font> &amp; <font color="Olive" title="b7">x</font> <a href="surreal0.html#R5" title="SURREAL0:pred.5">&lt;=</a> <font color="Olive" title="b8">y</font> ) ) &amp; (  for <font color="Olive" title="b7">x</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a>  st <font color="Olive" title="b7">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b6">Y2</font> holds <br/> ex <font color="Olive" title="b8">y</font> being   <a href="surreal0.html#NM1" title="SURREAL0:NM.1">Surreal</a> st <br/>( <font color="Olive" title="b8">y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b5">Y1</font> &amp; <font color="Olive" title="b8">y</font> <a href="surreal0.html#R5" title="SURREAL0:pred.5">&lt;=</a> <font color="Olive" title="b7">x</font> ) ) &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">X1</font>,<font color="Olive" title="b5">Y1</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">X2</font>,<font color="Olive" title="b6">Y2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> holds <br/><font color="Olive" title="b1">x</font> <a href="surreal0.html#R5" title="SURREAL0:pred.5">&lt;=</a> <font color="Olive" title="b2">y</font></div></div>
