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<b>let </b><font color="Maroon" title="c1">L</font> be  <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L</font></span>)</span> is <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</a> iff (  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L</font></span>)</span> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> &amp; <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> ) )</span><br/>

<a NAME="E1:47"/>
 <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">L</font>
 
<b>by </b><i><a class="ref" href="waybel14.html#T23" target="_self" title="WAYBEL14:th.23">Th23</a></i>;<br/>
<b>hence </b><a NAME="E2:47"/>
(  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L</font></span>)</span> is <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</a> iff (  <a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L</font></span>)</span> is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> &amp; <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel11.html#K5" title="WAYBEL11:func.5">sigma</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> ) )
 <b>by </b><i><a class="ref" href="waybel_6.html#T39" title="WAYBEL_6:th.39">WAYBEL_6:39</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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