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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">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>





<b>set </b><font color="Maroon">T</font> =  <a href="taxonom1.html#K1" target="_self">low_toler</a> <font color="Maroon">f</font>,<font color="Maroon">a</font>;<br/>
<b>assume </b><a NAME="E1:23"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">a</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 &amp; <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#V4">symmetric</a> )
 ;<br/>

<a NAME="E2:23"/><b>then </b><i><font color="Green">E30</font></i>: 
 <a href="taxonom1.html#K1" target="_self">low_toler</a> <font color="Maroon">f</font>,<font color="Maroon">a</font> <a href="relat_2.html#R1">is_reflexive_in</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:23"/><b>then </b><i><font color="Green">E31</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K1" target="_self">low_toler</a> <font color="Maroon">f</font>,<font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<b>then </b><i><font color="Green">E32</font></i>:  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K1" target="_self">low_toler</a> <font color="Maroon">f</font>,<font color="Maroon">a</font></span>)</span> = 
<font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p2">(<span class="default"><a href="taxonom1.html#K1" target="_self">low_toler</a> <font color="Maroon">f</font>,<font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#D6">RELAT_1:def 6</a></i>
<br/>.= 
<font color="Maroon">X</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/>
<a NAME="E5:23"/><b>then </b>
 <a href="taxonom1.html#K1" target="_self">low_toler</a> <font color="Maroon">f</font>,<font color="Maroon">a</font> <a href="relat_2.html#R3">is_symmetric_in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="taxonom1.html#K1" target="_self">low_toler</a> <font color="Maroon">f</font>,<font color="Maroon">a</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:23"/>
 <a href="taxonom1.html#K1" target="_self">low_toler</a> <font color="Maroon">f</font>,<font color="Maroon">a</font> is   <a href="eqrel_1.html#NM1">Tolerance</a> of <font color="Maroon">X</font>
 <b>by </b><i>, , , <a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a>, <a class="ref" href="relat_2.html#D9">RELAT_2:def 9</a>, <a class="ref" href="relat_2.html#D11">RELAT_2:def 11</a></i>;<br/>


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