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<div><span class="kw">theorem </span><a NAME="T31"><span class="comment"><font color="firebrick">:: WAYBEL23:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="waybel_0.html#NM6" title="WAYBEL_0:NM.6">Semilattice</a><br/>  for <font color="Olive" title="b2">S</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L</font> holds <br/> ( <font color="Olive" title="b2">S</font> is   <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <font color="Olive" title="b1">L</font> iff <font color="Olive" title="b2">S</font> is  <a href="waybel23.html#V1" title="WAYBEL23:attr.1">meet-closed</a>  ) <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T63" onmouseover="rs('waybel_0/T63')" onmouseout="rh()">WAYBEL_0:63</a></span>;<br/></div></div>
