<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="surreal0.html#R4" title="SURREAL0:pred.4">preserves_No_Comparison_on</a> <a onclick="hs(this)" href="javascript:()">SURREAL0:def 11 : <br/></a><span> for <font color="Olive" title="b1">X</font>, <font color="Olive" title="b2">R</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b2">R</font> <a href="surreal0.html#R4" title="SURREAL0:pred.4">preserves_No_Comparison_on</a> <font color="Olive" title="b1">X</font> iff  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">X</font> holds <br/>( <font color="Olive" title="b3">a</font> <a href="surreal0.html#R1" title="SURREAL0:pred.1">&lt;=</a> <font color="Olive" title="b2">R</font>,<font color="Olive" title="b4">b</font> iff (  <a href="surreal0.html#K1" title="SURREAL0:func.1">L_</a> <font color="Olive" title="b3">a</font> <a href="surreal0.html#R3" title="SURREAL0:pred.3">&lt;&lt;</a> <font color="Olive" title="b2">R</font>,<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b4">b</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b3">a</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="surreal0.html#R3" title="SURREAL0:pred.3">&lt;&lt;</a> <font color="Olive" title="b2">R</font>, <a href="surreal0.html#K2" title="SURREAL0:func.2">R_</a> <font color="Olive" title="b4">b</font> ) ) );<br/></span></div>
