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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">E</font> be   <a href="eqrel_1.html#NM1">Tolerance</a> of <font color="Maroon">X</font>;<br/>





<b>thus </b><a NAME="E1:18"/>
( <font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K2" target="_self">CohSp</a> <font color="Maroon">E</font> implies <font color="Maroon">a</font> is    <a href="toler_1.html#M1">TolSet</a> of <font color="Maroon">E</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:18_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K2" target="_self">CohSp</a> <font color="Maroon">E</font>
 ;<br/>

<a NAME="E2:18_1"/><b>then </b>
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:18_1"/>
<font color="Maroon">a</font> is    <a href="toler_1.html#M1">TolSet</a> of <font color="Maroon">E</font>
 <b>by </b><i><a class="ref" href="toler_1.html#D3">TOLER_1:def 3</a></i>;<br/>


</div><b>end;</b></div>

<b>assume </b><a NAME="E2:18"/>
<font color="Maroon">a</font> is    <a href="toler_1.html#M1">TolSet</a> of <font color="Maroon">E</font>
 ;<br/>

<a NAME="E3:18"/><b>then </b>
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> &amp; <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">a</font> holds <br/><span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">E</font>
 
<b>by </b><i><a class="ref" href="toler_1.html#D3">TOLER_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E4:18"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="coh_sp.html#K2" target="_self">CohSp</a> <font color="Maroon">E</font>
 <b>by </b><i/>;<br/>


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