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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E22">Th23</font></span>: <a NAME="T23"><span class="comment"><font color="firebrick">:: WAYBEL31:23</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">L1</font> being   <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>   <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  <a href="waybel_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a><br/>  for <font color="Olive" title="b2">T</font> being   <a href="waybel11.html#V4" title="WAYBEL11:attr.4">Scott</a>   <a href="yellow_9.html#M1" title="YELLOW_9:mode.1">TopAugmentation</a> of <font color="Olive" title="b1">L1</font><br/>  for <font color="Olive" title="b3">B1</font> being   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <font color="Olive" title="b2">T</font>  st <font color="Olive" title="b3">B1</font> is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a>  holds <br/><span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Olive" title="b4">u</font></span>)</span> where <font color="Olive" title="b4">u</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b2">T</font> : <font color="Olive" title="b4">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">B1</font> </span> } </span>  is  <a href="finset_1.html#NV2" title="FINSET_1:NV.2">infinite</a> </div></div>
