<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="eqrel_1.html#NM1">Tolerance</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:49"/><i><font color="Green">E24</font></i>: 
 <a href="toler_1.html#K4" target="_self">TolClasses</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="toler_1.html#K4" target="_self">TolClasses</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:49"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>1</sub></font> is   <a href="toler_1.html#NM2">TolClass</a> of <font color="Maroon">c<sub>2</sub></font> iff <font color="Olive">b<sub>1</sub></font> is   <a href="toler_1.html#NM2">TolClass</a> of <font color="Maroon">c<sub>3</sub></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">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<a NAME="E1:49_1"/>
( <font color="Maroon">c<sub>4</sub></font> is   <a href="toler_1.html#NM2">TolClass</a> of <font color="Maroon">c<sub>2</sub></font> iff <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="toler_1.html#K4" target="_self">TolClasses</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="txt" href="toler_1.html#E1:49"><i><font color="Green">E24</font></i></a>, <a class="ref" href="toler_1.html#D7" target="_self">Def7</a></i>;<br/>
<b>hence </b><a NAME="E2:49_1"/>
( <font color="Maroon">c<sub>4</sub></font> is   <a href="toler_1.html#NM2">TolClass</a> of <font color="Maroon">c<sub>2</sub></font> iff <font color="Maroon">c<sub>4</sub></font> is   <a href="toler_1.html#NM2">TolClass</a> of <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="ref" href="toler_1.html#D7" target="_self">Def7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:49"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="toler_1.html#T53" target="_self">Th53</a></i>;<br/>


</div>
