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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="metric_1.html#V6">Reflexive</a> <a href="metric_1.html#V8">symmetric</a>  <a href="metric_1.html#L1">MetrStruct</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="relset_1.html#M2">Relation</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:43"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="taxonom1.html#K3" target="_self">dist_toler</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 ;<br/>

<a NAME="E2:43"/><i><font color="Green">E37</font></i>: 
the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="metric_1.html#V4">symmetric</a>
 
<b>by </b><i><a class="ref" href="metric_1.html#D9">METRIC_1:def 9</a></i>;<br/>
<a NAME="E3:43"/><i><font color="Green">E38</font></i>: 
the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font> is <a href="metric_1.html#V2">Reflexive</a>
 
<b>by </b><i><a class="ref" href="metric_1.html#D7">METRIC_1:def 7</a></i>;<br/>
<a NAME="E4:43"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="taxonom1.html#K1" target="_self">low_toler</a> the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="taxonom1.html#E1:43"><i><font color="Green">E36</font></i></a>, <a class="ref" href="taxonom1.html#T33" target="_self">Th33</a></i>;<br/>
<b>hence </b><a NAME="E5:43"/>
<font color="Maroon">c<sub>3</sub></font> is   <a href="eqrel_1.html#NM1">Tolerance</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="taxonom1.html#E1:43"><i><font color="Green">E36</font></i></a>, <a class="txt" href="taxonom1.html#E2:43"><i><font color="Green">E37</font></i></a>, <a class="txt" href="taxonom1.html#E3:43"><i><font color="Green">E38</font></i></a>, <a class="ref" href="taxonom1.html#T18" target="_self">Th18</a></i>;<br/>


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