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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E41">Th37</font></span>: <a NAME="T37"><span class="comment"><font color="firebrick">:: WAYBEL_9:37</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">S</font> being   <a href="compts_1.html#NV4" title="COMPTS_1:NV.4">Hausdorff</a>  <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a>  st (  for <font color="Olive" title="b2">N</font> being   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Olive" title="b1">S</font>  st <font color="Olive" title="b2">N</font> is  <a href="waybel_0.html#V10" title="WAYBEL_0:attr.10">eventually-directed</a>  holds <br/>(  <a href="waybel_9.html#R1" title="WAYBEL_9:pred.1">ex_sup_of</a> <font color="Olive" title="b2">N</font> &amp;  <a href="waybel_2.html#K1" title="WAYBEL_2:func.1">sup</a> <font color="Olive" title="b2">N</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="yellow_6.html#K9" title="YELLOW_6:func.9">Lim</a> <font color="Olive" title="b2">N</font> ) ) &amp; (  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">S</font> holds  <font color="Olive" title="b2">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a>  is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  ) holds <br/><font color="Olive" title="b1">S</font> is  <a href="waybel_2.html#V2" title="WAYBEL_2:attr.2">meet-continuous</a> </div></div>
