<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="realalg1.html#K4" title="REALALG1:func.4">OrdRel</a> <a onclick="hs(this)" href="javascript:()">REALALG1:def 19 : <br/></a><span> for <font color="Olive" title="b1">R</font> being   <a href="realalg1.html#V13" title="REALALG1:attr.13">preordered</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">P</font> being   <a href="realalg1.html#NM1" title="REALALG1:NM.1">Preordering</a> of <font color="Olive" title="b1">R</font> holds   <a href="realalg1.html#K4" title="REALALG1:func.4">OrdRel</a> <font color="Olive" title="b2">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Olive" title="b3">a</font>,<font color="Olive" title="b4">b</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> where <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">R</font> : <font color="Olive" title="b3">a</font> <a href="realalg1.html#R1" title="REALALG1:pred.1">&lt;=</a> <font color="Olive" title="b2">P</font>,<font color="Olive" title="b4">b</font> </span> } </span> ;<br/></span></div>
