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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">ThC</font></span>: <a NAME="T3"><span class="comment"><font color="firebrick">:: LATSTONE:3</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a><br/>  for <font color="Olive" title="b2">I</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="lattice4.html#NM2" title="LATTICE4:NM.2">ClosedSubset</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b1">L</font> is  <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a>  &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Olive" title="b1">L</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">I</font> holds <br/>(  <a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Olive" title="b1">L</font>,<font color="Olive" title="b2">I</font>) is  <a href="lattices.html#V14" title="LATTICES:attr.14">upper-bounded</a>  &amp;  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <span class="p1">(<span class="default"><a href="filter_2.html#K10" title="FILTER_2:func.10">latt</a> (<font color="Olive" title="b1">L</font>,<font color="Olive" title="b2">I</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#K6" title="LATTICES:func.6">Top</a> <font color="Olive" title="b1">L</font> )</div></div>
