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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E10">Th7</font></span>: <a NAME="T7"><span class="comment"><font color="firebrick">:: WAYBEL19:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">T</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#V2" title="PRE_TOPC:attr.2">TopSpace-like</a>   <a href="waybel_9.html#L1" title="WAYBEL_9:struct.1">TopRelStr</a>  holds <br/> ( <font color="Olive" title="b1">T</font> is  <a href="waybel19.html#V1" title="WAYBEL19:attr.1">lower</a>  iff <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Olive" title="b2">F</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a></span>)</span> where <font color="Olive" title="b2">F</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font> : <font color="Olive" title="b2">F</font> is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  </span> } </span>  is   <a href="cantor_1.html#NM1" title="CANTOR_1:NM.1">Basis</a> of <font color="Olive" title="b1">T</font> )</div></div>
