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<b>let </b><font color="Maroon">S</font> be  <a href="compts_1.html#V2">compact</a> <a href="compts_1.html#V3">Hausdorff</a> <a href="waybel_9.html#NM1">TopLattice</a>;<br/>

<b>assume </b><a NAME="E1:99"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> holds  <font color="Olive">x</font> <a href="waybel_1.html#K4">"/\"</a>  is <a href="pre_topc.html#V5">continuous</a>
 ;<br/>

<a NAME="E2:99"/><b>then </b>
for <font color="Olive">N</font> being  <a href="waybel_0.html#NM2">net</a> of <font color="Maroon">S</font>  st <font color="Olive">N</font> is <a href="waybel_0.html#V10">eventually-directed</a> holds <br/>(  <a href="waybel_9.html#R1" target="_self">ex_sup_of</a> <font color="Olive">N</font> &amp;  <a href="waybel_2.html#K1">sup</a> <font color="Olive">N</font> <a href="hidden.html#R2">in</a>  <a href="yellow_6.html#K11">Lim</a> <font color="Olive">N</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:99"/>
<font color="Maroon">S</font> is <a href="waybel_2.html#V2">meet-continuous</a>
 <b>by </b><i>, </i>;<br/>


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