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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="waybel25.html#V1" target="_self">monotone-convergence</a> <a href="t_0topsp.html#NM1">T_0-TopSpace</a>;<br/>

<a NAME="E1:64"/>
for <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Olive">b<sub>1</sub></font>, <a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="waybel25.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E2:64"/>
 <a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V24">up-complete</a>
 <b>by </b><i><a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a></i>;<br/>


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