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<div><span class="kw">theorem </span><a NAME="T39"><span class="comment"><font color="firebrick">:: WAYBEL30:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">N</font> being   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>   <a href="waybel19.html#V2" title="WAYBEL19:attr.2">Lawson</a>   <a href="waybel_2.html#V2" title="WAYBEL_2:attr.2">meet-continuous</a>  <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a> holds <br/> ( <font color="Olive" title="b1">N</font> is  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  iff  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">N</font> holds  <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">V</font></span>)</span> where <font color="Olive" title="b3">V</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">N</font> : ( <font color="Olive" title="b2">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">V</font> &amp; <font color="Olive" title="b3">V</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="waybel19.html#K2" title="WAYBEL19:func.2">lambda</a> <font color="Olive" title="b1">N</font> ) </span> } </span> ,<font color="Olive" title="b1">N</font>) )</div></div>
