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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">T</font>, <font color="Maroon" title="c3">R</font> be   <a href="eqrel_1.html#NM1" title="EQREL_1:NM.1">Tolerance</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><a NAME="E1:49"/><i><font color="Green" title="E24">A1</font></i>: 
 <a href="toler_1.html#K4" title="TOLER_1:func.4">TolClasses</a> <font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="toler_1.html#K4" title="TOLER_1:func.4">TolClasses</a> <font color="Maroon" title="c3">R</font>
 ;<br/>

<a NAME="E2:49"/>
for <font color="Olive" title="b1">Z</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">Z</font> is   <a href="toler_1.html#NM2" title="TOLER_1:NM.2">TolClass</a> of <font color="Maroon" title="c2">T</font> iff <font color="Olive" title="b1">Z</font> is   <a href="toler_1.html#NM2" title="TOLER_1:NM.2">TolClass</a> of <font color="Maroon" title="c3">R</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="49_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">Z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<a NAME="E1:49_1"/>
( <font color="Maroon" title="c4">Z</font> is   <a href="toler_1.html#NM2" title="TOLER_1:NM.2">TolClass</a> of <font color="Maroon" title="c2">T</font> iff <font color="Maroon" title="c4">Z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="toler_1.html#K4" title="TOLER_1:func.4">TolClasses</a> <font color="Maroon" title="c3">R</font> )
 
<b>by </b><i><a class="txt" href="toler_1.html#E1:49"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="toler_1.html#D7" target="_self" title="TOLER_1:def.7">Def7</a></i>;<br/>
<b>hence </b><a NAME="E2:49_1"/>
( <font color="Maroon" title="c4">Z</font> is   <a href="toler_1.html#NM2" title="TOLER_1:NM.2">TolClass</a> of <font color="Maroon" title="c2">T</font> iff <font color="Maroon" title="c4">Z</font> is   <a href="toler_1.html#NM2" title="TOLER_1:NM.2">TolClass</a> of <font color="Maroon" title="c3">R</font> )
 <b>by </b><i><a class="ref" href="toler_1.html#D7" target="_self" title="TOLER_1:def.7">Def7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:49"/>
<font color="Maroon" title="c2">T</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c3">R</font>
 <b>by </b><i><a class="ref" href="toler_1.html#T53" target="_self" title="TOLER_1:th.53">Th53</a></i>;<br/>


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