<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E39">Th65</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: PROOFS_1:24</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">R</font> being   <a href="proofs_1.html#NM2" title="PROOFS_1:NM.2">Rule</a><br/>  for <font color="Olive" title="b3">a</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a>  holds <br/> ( <font color="Olive" title="b1">X</font>,<font color="Olive" title="b2">R</font> <a href="proofs_1.html#R2" title="PROOFS_1:pred.2">|-</a> <font color="Olive" title="b3">a</font> iff  for <font color="Olive" title="b4">Y</font> being  <font color="Olive">b<sub>1</sub></font> <a href="proofs_1.html#V6" title="PROOFS_1:attr.6">-extending</a>  <font color="Olive">b<sub>2</sub></font> <a href="proofs_1.html#V18" title="PROOFS_1:attr.18">-closed</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <font color="Olive" title="b3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">Y</font> )</div></div>
