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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E25">Th24</font></span>: <a NAME="T24"><span class="comment"><font color="firebrick">:: TAXONOM1:24</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="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">f</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</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><br/>  for <font color="Olive" title="b3">R</font> being   <a href="eqrel_1.html#NM2" title="EQREL_1:NM.2">Equivalence_Relation</a> of <font color="Olive" title="b1">X</font>  st <font color="Olive" title="b3">R</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K1" title="TAXONOM1:func.1">low_toler</a> (<font color="Olive" title="b2">f</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)</span>)</span> <a href="lang1.html#K13" title="LANG1:func.13">[*]</a>  &amp; <font color="Olive" title="b2">f</font> is  <a href="taxonom1.html#V1" title="TAXONOM1:attr.1">nonnegative</a>  &amp; <font color="Olive" title="b2">f</font> is  <a href="metric_1.html#V2" title="METRIC_1:attr.2">Reflexive</a>  &amp; <font color="Olive" title="b2">f</font> is  <a href="metric_1.html#V3" title="METRIC_1:attr.3">discerning</a>  holds <br/><font color="Olive" title="b3">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K4" title="RELAT_1:func.4">id</a> <font color="Olive" title="b1">X</font></div></div>
