<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="roughs_4.html#V2" title="ROUGHS_4:attr.2">cap-closed</a> <a onclick="hs(this)" href="javascript:()">ROUGHS_4:def 2 : <br/></a><span> 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">F</font> being   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Olive" title="b1">X</font> holds <br/> ( <font color="Olive" title="b2">F</font> is  <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">cap-closed</a>  iff  for <font color="Olive" title="b3">a</font>, <font color="Olive" title="b4">b</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b3">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">F</font> &amp; <font color="Olive" title="b4">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">F</font> holds <br/><font color="Olive" title="b3">a</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Olive" title="b4">b</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">F</font> );<br/></span></div>
