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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: FINTOPO6:42</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">C</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="orders_2.html#V3" title="ORDERS_2:attr.3">filled</a>  &amp; <font color="Olive" title="b1">FT</font> is  <a href="fin_topo.html#V1" title="FIN_TOPO:attr.1">symmetric</a>  &amp; <font color="Olive" title="b2">C</font> is  <a href="fin_topo.html#V4" title="FIN_TOPO:attr.4">connected</a>  holds <br/> for <font color="Olive" title="b3">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">FT</font>  holds <br/>(  not <font color="Olive" title="b3">S</font> <a href="fintopo6.html#R1" title="FINTOPO6:pred.1">is_a_component_of</a> <font color="Olive" title="b1">FT</font> or <font color="Olive" title="b2">C</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b3">S</font> or <font color="Olive" title="b2">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b3">S</font> )</div></div>
