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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="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="108_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:108_1"/><i><font color="Green">E38</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E2:108_1"/>
( <font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> implies  ex <font color="Olive">u</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">u</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> &amp; <font color="Olive">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1" target="_self">.</a> <font color="Olive">u</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="108_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:108_1_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<b>take </b>
<font color="Maroon">e</font>
;<br/>

<b>thus </b><a NAME="E2:108_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span>
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E3:108_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E4:108_1_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1" target="_self">.</a> <font color="Maroon">e</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div><b>given </b><font color="Maroon">u</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E3:108_1"/><i><font color="Green">E40</font></i>: 
( <font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> &amp; <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1" target="_self">.</a> <font color="Maroon">u</font> )
 ;<br/><b>thus </b><a NAME="E4:108_1"/>
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:108"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K6">id</a> <font color="Maroon">X</font></span>)</span> <a href="relat_1.html#K9">.:</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/>


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