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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th18</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: WAYBEL33:18</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="waybel33.html#V1" title="WAYBEL33:attr.1">lim-inf</a>  <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a><br/>  for <font color="Olive" title="b2">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</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">A</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>  iff  for <font color="Olive" title="b3">F</font> being   <a href="waybel_7.html#V3" title="WAYBEL_7:attr.3">ultra</a>  <a href="waybel_0.html#NM4" title="WAYBEL_0:NM.4">Filter</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">BoolePoset</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Olive" title="b1">L</font></span>)</span></span>)</span>  st <font color="Olive" title="b2">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">F</font> holds <br/> <a href="waybel33.html#K1" title="WAYBEL33:func.1">lim_inf</a> <font color="Olive" title="b3">F</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">A</font> )</div></div>
