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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">Th30</font></span>: <a NAME="T30"><span class="comment"><font color="firebrick">:: TAXONOM1:30</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><br/>  for <font color="Olive" title="b2">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><font color="Olive" title="b1">X</font>,<font color="Olive" title="b1">X</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  st <font color="Olive" title="b2">f</font> is  <a href="metric_1.html#V4" title="METRIC_1:attr.4">symmetric</a>  &amp; <font color="Olive" title="b2">f</font> is  <a href="taxonom1.html#V1" title="TAXONOM1:attr.1">nonnegative</a>  holds <br/><span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b1">X</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="taxonom1.html#K2" title="TAXONOM1:func.2">fam_class</a> <font color="Olive" title="b2">f</font></div></div>
