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<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="yellow_0.html#V2" title="YELLOW_0:attr.2">upper-bounded</a> <a href="waybel_0.html#NM6" title="WAYBEL_0:NM.6">Semilattice</a>;<br/><b>let </b><font color="Maroon" title="c2">F</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <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="waybel_0.html#K8" title="WAYBEL_0:func.8">Filt</a> <font color="Maroon" title="c1">L</font></span>)</span></span>)</span>;<br/>



<a NAME="E1:3"/>
 <a href="waybel_0.html#K8" title="WAYBEL_0:func.8">Filt</a> <font color="Maroon" title="c1">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="waybel16.html#T7" title="WAYBEL16:th.7">WAYBEL16:7</a></i>;<br/>
<b>hence </b><a NAME="E2:3"/>
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c2">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tarski.html#K3" title="TARSKI:func.3">union</a> <font color="Maroon" title="c2">F</font>
 <b>by </b><i><a class="ref" href="waybel13.html#T9" title="WAYBEL13:th.9">WAYBEL13:9</a></i>;<br/>


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