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<div><span class="kw">theorem </span><a NAME="T10"><span class="comment"><font color="firebrick">:: TOPGEN_2:10</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#NM1" title="PRE_TOPC:NM.1">TopSpace</a><br/>  for <font color="Olive" title="b2">A</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">T</font><br/>  for <font color="Olive" title="b3">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">T</font> holds <br/> ( <font color="Olive" title="b3">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b2">A</font> iff  ex <font color="Olive" title="b4">B</font> being   <a href="yellow_8.html#NM1" title="YELLOW_8:NM.1">Basis</a> of <font color="Olive" title="b3">x</font> st <br/> for <font color="Olive" title="b5">U</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b5">U</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b4">B</font> holds <br/><font color="Olive" title="b5">U</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Olive" title="b2">A</font> )</div></div>
