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<b>let </b><font color="Maroon" title="c1">S</font> be  <a href="compts_1.html#NV4" title="COMPTS_1:NV.4">Hausdorff</a> <a href="compts_1.html#V1" title="COMPTS_1:attr.1">compact</a> <a href="waybel_9.html#NM1" title="WAYBEL_9:NM.1">TopLattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Olive" title="b1">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> ) implies <font color="Maroon" title="c1">S</font> is <a href="waybel_2.html#V2" title="WAYBEL_2:attr.2">meet-continuous</a> )</span><br/>

<b>assume </b><a NAME="E1:98"/><i><font color="Green" title="E48">A1</font></i>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font> holds  <font color="Olive" title="b1">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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">S</font> is <a href="waybel_2.html#V2" title="WAYBEL_2:attr.2">meet-continuous</a></span><br/>

<a NAME="E2:98"/><b>then </b>
for <font color="Olive" title="b1">N</font> being  <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">S</font>  st <font color="Olive" title="b1">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="b1">N</font> &amp;  <a href="waybel_2.html#K1" title="WAYBEL_2:func.1">sup</a> <font color="Olive" title="b1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <font color="Olive" title="b1">N</font> )
 
<b>by </b><i><a class="ref" href="waybel_9.html#T38" target="_self" title="WAYBEL_9:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E3:98"/>
<font color="Maroon" title="c1">S</font> is <a href="waybel_2.html#V2" title="WAYBEL_2:attr.2">meet-continuous</a>
 <b>by </b><i><a class="txt" href="#E1:98"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="waybel_9.html#T37" target="_self" title="WAYBEL_9:th.37">Th37</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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