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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">X</font>,<font color="Maroon">X</font></span><a href="zfmisc_1.html#K2">:]</a></span>, <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:39"/><i><font color="Green">E29</font></i>: 
(  <a href="eqrel_1.html#K11">SmallestPartition</a> <font color="Maroon">X</font> <a href="hidden.html#R2">in</a>  <a href="taxonom1.html#K2" target="_self">fam_class</a> <font color="Maroon">f</font> &amp; <font color="Maroon">f</font> is <a href="metric_1.html#V4">symmetric</a> &amp; <font color="Maroon">f</font> is <a href="taxonom1.html#V1" target="_self">nonnegative</a> )
 ;<br/>

<a NAME="E2:39"/><i><font color="Green">E30</font></i>: 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a>  <a href="taxonom1.html#K2" target="_self">fam_class</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="taxonom1.html#T2" target="_self">Th2</a>, </i>;<br/>
<a NAME="E3:39"/>
 <a href="taxonom1.html#K2" target="_self">fam_class</a> <font color="Maroon">f</font> is    <a href="taxonom1.html#M1" target="_self">Classification</a> of <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:39"/>
 <a href="taxonom1.html#K2" target="_self">fam_class</a> <font color="Maroon">f</font> is    <a href="taxonom1.html#M2" target="_self">Strong_Classification</a> of <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="taxonom1.html#T2" target="_self">Th2</a>, , </i>;<br/>


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