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

<b>let </b><font color="Maroon">E</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">E</font>;<br/>



<b>thus </b><a NAME="E1:36"/>
( <font color="Maroon">A</font> <a href="subset_1.html#K3" target="_self">`</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> implies <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="subset_1.html#K2" target="_self">[#]</a> <font color="Maroon">E</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:36_1"/>
<font color="Maroon">A</font> <a href="subset_1.html#K3" target="_self">`</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 ;<br/>

<b>hence </b><font color="Maroon">A</font> = 
<font color="Maroon">A</font> <a href="subset_1.html#K4" target="_self">\/</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3" target="_self">`</a> </span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
<br/>.= 
 <a href="subset_1.html#K2" target="_self">[#]</a> <font color="Maroon">E</font>
<b>by </b><i/>
;<br/><br/>


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

<b>assume </b><a NAME="E2:36"/>
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="subset_1.html#K2" target="_self">[#]</a> <font color="Maroon">E</font>
 ;<br/>

<a NAME="E3:36"/><b>then </b>
<font color="Maroon">A</font> <a href="subset_1.html#K3" target="_self">`</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T37">XBOOLE_1:37</a></i>;<br/>
<b>hence </b><a NAME="E4:36"/>
<font color="Maroon">A</font> <a href="subset_1.html#K3" target="_self">`</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>


</div>
