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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E42">Th57</font></span>: <a NAME="T57"><span class="comment"><font color="firebrick">:: KURATO_1:57</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font>, <font color="Olive" title="b2">G</font> being   <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>   <a href="setfam_1.html#V3" title="SETFAM_1:attr.3">with_proper_subsets</a>  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <a href="topmetr.html#K3" title="TOPMETR:func.3">R^1</a>  st <font color="Olive" title="b1">F</font> is  <a href="tops_2.html#V1" title="TOPS_2:attr.1">open</a>  &amp; <font color="Olive" title="b2">G</font> is  <a href="tops_2.html#V2" title="TOPS_2:attr.2">closed</a>  holds <br/><font color="Olive" title="b1">F</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">G</font></div></div>
