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<div><span class="kw">theorem </span><a NAME="T7"><span class="comment"><font color="firebrick">:: FINTOPO4:7</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">FT</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> <br/>  for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">FT</font>  st <font color="Olive" title="b1">FT</font> is  <a href="fin_topo.html#V1" title="FIN_TOPO:attr.1">symmetric</a>  holds <br/>( <font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">B</font> <a href="fintopo4.html#R1" title="FINTOPO4:pred.1">are_separated</a>  iff ( <font color="Olive" title="b2">A</font> <a href="fin_topo.html#K12" title="FIN_TOPO:func.12">^f</a>  <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">B</font> &amp; <font color="Olive" title="b2">A</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">B</font> <a href="fin_topo.html#K12" title="FIN_TOPO:func.12">^f</a>  ) ) <span class="kw">by</span> <span class="lab"><a class="ref" href="fin_topo.html#T12" onmouseover="rs('fin_topo/T12')" onmouseout="rh()">FIN_TOPO:12</a></span>;<br/></div></div>
