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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E3">Th1</font></span>: <a NAME="T1"><span class="comment"><font color="firebrick">:: WAYBEL22:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <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/>  for <font color="Olive" title="b2">F</font> being   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#K1" title="YELLOW_1:func.1">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K8" title="WAYBEL_0:func.8">Filt</a> <font color="Olive" title="b1">L</font></span>)</span></span>)</span> holds   <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Olive" title="b2">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="Olive" title="b2">F</font></div></div>
