<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="roughs_4.html#V3" title="ROUGHS_4:attr.3">union-closed</a> <a onclick="hs(this)" href="javascript:()">ROUGHS_4:def 3 : <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="roughs_4.html#V3" title="ROUGHS_4:attr.3">union-closed</a>  iff  for <font color="Olive" title="b3">a</font> being   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b3">a</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">F</font> holds <br/> <a href="setfam_1.html#K5" title="SETFAM_1:func.5">union</a> <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> );<br/></span></div>
