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<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="partfun1.html#NM1">PartFunc</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>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:27"/>
( <font color="Maroon">f</font> is <a href="metric_1.html#V2">Reflexive</a> &amp; <font color="Maroon">f</font> is <a href="metric_1.html#V3">discerning</a> )
 ;<br/>

<a NAME="E2:27"/><b>then </b>
<font color="Maroon">f</font> <a href="metric_1.html#K1">.</a> <font color="Maroon">x</font>,<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="metric_1.html#D3">METRIC_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:27"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="taxonom1.html#K1" target="_self">low_toler</a> <font color="Maroon">f</font>,0
 <b>by </b><i/>;<br/>


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