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<b>let </b><font color="Maroon" title="c1">M</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="metric_1.html#V6" title="METRIC_1:attr.6">Reflexive</a> <a href="metric_1.html#V8" title="METRIC_1:attr.8">symmetric</a>  <a href="metric_1.html#L1" title="METRIC_1:struct.1">MetrStruct</a> ;<br/><b>let </b><font color="Maroon" title="c2">a</font> be  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ;<br/><b>let </b><font color="Maroon" title="c3">T</font> be    <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>;<br/>





<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E36">A1</font></i>: 
( <font color="Maroon" title="c3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="taxonom1.html#K3" title="TAXONOM1:func.3">dist_toler</a> <font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c2">a</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> 0 )
 ;<br/>

<a NAME="E2:43"/><i><font color="Green" title="E37">A2</font></i>: 
the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <font color="Maroon" title="c1">M</font> is <a href="metric_1.html#V4" title="METRIC_1:attr.4">symmetric</a>
 
<b>by </b><i><a class="ref" href="metric_1.html#D9" title="METRIC_1:def.9">METRIC_1:def 9</a></i>;<br/>
<a NAME="E3:43"/><i><font color="Green" title="E38">A3</font></i>: 
the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <font color="Maroon" title="c1">M</font> is <a href="metric_1.html#V2" title="METRIC_1:attr.2">Reflexive</a>
 
<b>by </b><i><a class="ref" href="metric_1.html#D7" title="METRIC_1:def.7">METRIC_1:def 7</a></i>;<br/>
<a NAME="E4:43"/>
<font color="Maroon" title="c3">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="taxonom1.html#K1" title="TAXONOM1:func.1">low_toler</a> the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <font color="Maroon" title="c1">M</font>,<font color="Maroon" title="c2">a</font>
 
<b>by </b><i><a class="txt" href="taxonom1.html#E1:43"><i><font color="Green" title="E36">A1</font></i></a>, <a class="ref" href="taxonom1.html#T33" target="_self" title="TAXONOM1:th.33">Th33</a></i>;<br/>
<b>hence </b><a NAME="E5:43"/>
<font color="Maroon" title="c3">T</font> is   <a href="eqrel_1.html#NM1" title="EQREL_1:NM.1">Tolerance</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">M</font>
 <b>by </b><i><a class="txt" href="taxonom1.html#E1:43"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="taxonom1.html#E2:43"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="taxonom1.html#E3:43"><i><font color="Green" title="E38">A3</font></i></a>, <a class="ref" href="taxonom1.html#T18" target="_self" title="TAXONOM1:th.18">Th18</a></i>;<br/>


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