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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E35">Th31</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: WAYBEL11:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L</font> being   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a><br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">L</font> holds <br/> ( <font color="Olive" title="b2">S</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="yellow_6.html#K12" title="YELLOW_6:func.12">ConvergenceSpace</a> <span class="p2">(<span class="default"><a href="waybel11.html#K2" title="WAYBEL11:func.2">Scott-Convergence</a> <font color="Olive" title="b1">L</font></span>)</span></span>)</span> iff ( <font color="Olive" title="b2">S</font> is  <a href="waybel11.html#NV4" title="WAYBEL11:NV.4">inaccessible</a>  &amp; <font color="Olive" title="b2">S</font> is  <a href="waybel_0.html#V13" title="WAYBEL_0:attr.13">upper</a>  ) )</div></div>
