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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">x1</font> be    <a href="subset_1.html#M1" target="_self">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x2</font> be    <a href="subset_1.html#M1" target="_self">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x3</font> be    <a href="subset_1.html#M1" target="_self">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x4</font> be    <a href="subset_1.html#M1" target="_self">Element</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x5</font> be    <a href="subset_1.html#M1" target="_self">Element</a> of <font color="Maroon">X</font>;<br/>











<b>assume </b><a NAME="E1:54"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">X</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:54"/>
<span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font>,<font color="Maroon">x3</font>,<font color="Maroon">x4</font>,<font color="Maroon">x5</font></span><a href="enumset1.html#K3">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:54_1"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font>,<font color="Maroon">x3</font>,<font color="Maroon">x4</font>,<font color="Maroon">x5</font></span><a href="enumset1.html#K3">}</a></span>
 ;<br/>

<a NAME="E2:54_1"/>
(  not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font>,<font color="Maroon">x3</font>,<font color="Maroon">x4</font>,<font color="Maroon">x5</font></span><a href="enumset1.html#K3">}</a></span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x3</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x4</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x5</font> )
 
<b>by </b><i><a class="ref" href="enumset1.html#D3">ENUMSET1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E3:54_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>
<a NAME="E3:54"/><b>then </b>
<span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font>,<font color="Maroon">x3</font>,<font color="Maroon">x4</font>,<font color="Maroon">x5</font></span><a href="enumset1.html#K3">}</a></span> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D1">ZFMISC_1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:54"/>
<span class="p1"><a href="enumset1.html#K3">{</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font>,<font color="Maroon">x3</font>,<font color="Maroon">x4</font>,<font color="Maroon">x5</font></span><a href="enumset1.html#K3">}</a></span> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>


</div>
