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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E27">Th37</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: WAYBEL14:37</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="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>  <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a><br/>  for <font color="Olive" title="b2">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font>  st (  for <font color="Olive" title="b3">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">L</font>  ex <font color="Olive" title="b4">B</font> being   <a href="yellow_8.html#NM1" title="YELLOW_8:NM.1">Basis</a> of <font color="Olive" title="b3">x</font> st <br/> for <font color="Olive" title="b5">Y</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L</font>  st <font color="Olive" title="b5">Y</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">B</font> holds <br/>( <font color="Olive" title="b5">Y</font> is  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>  &amp; <font color="Olive" title="b5">Y</font> is  <a href="waybel_0.html#V2" title="WAYBEL_0:attr.2">filtered</a>  ) ) &amp;  <a href="yellow_1.html#K1" title="YELLOW_1:func.1">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Olive" title="b1">L</font></span>)</span> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  holds <br/><font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> (<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Olive" title="b3">X</font></span>)</span> where <font color="Olive" title="b3">X</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L</font> : ( <font color="Olive" title="b2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">X</font> &amp; <font color="Olive" title="b3">X</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Olive" title="b1">L</font> ) </span> } </span> ,<font color="Olive" title="b1">L</font>)</div></div>
