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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">Th12</font></span>: <a NAME="T12"><span class="comment"><font color="firebrick">:: OPENLATT:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattices.html#NM2" title="LATTICES:NM.2">D_Lattice</a><br/>  for <font color="Olive" title="b2">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font><br/>  for <font color="Olive" title="b3">x</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds <br/> ( <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="openlatt.html#K8" title="OPENLATT:func.8">StoneH</a> <font color="Olive" title="b1">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">a</font> iff  ex <font color="Olive" title="b4">F</font> being   <a href="filter_0.html#NM1" title="FILTER_0:NM.1">Filter</a> of <font color="Olive" title="b1">L</font> st <br/>( <font color="Olive" title="b4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">x</font> &amp; <font color="Olive" title="b4">F</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">L</font> &amp; <font color="Olive" title="b4">F</font> is  <a href="filter_0.html#V2" title="FILTER_0:attr.2">prime</a>  &amp; <font color="Olive" title="b2">a</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">F</font> ) )</div></div>
