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

<b>let </b><font color="Maroon">e</font> be   <a href="rpr_1.html#NM1">El_ev</a> of <font color="Maroon">E</font>;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="4_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:4_1_1_1"/>
( <font color="Maroon">e</font> is <a href="xboole_0.html#V1">empty</a> or  ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">x</font></span><a href="tarski.html#K1">}</a></span> )
 </span><b>by </b><i><a class="ref" href="realset1.html#D4">REALSET1:def 4</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="4_1_1_1_1"><b>suppose </b></a><a NAME="E1:4_1_1_1_1"/>
<font color="Maroon">e</font> is <a href="xboole_0.html#V1">empty</a>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">T</font> = <font color="Maroon">e</font> as  <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  ;<br/><a NAME="E3:4_1_1_1_1"/>
<font color="Maroon">T</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/><b>hence </b><a NAME="E4:4_1_1_1_1"/>
<font color="Maroon">e</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="4_1_1_1_2"><b>suppose </b></a><a NAME="E1:4_1_1_1_2"/>
 ex <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Olive">x</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:4_1_1_1_2"/>
<font color="Maroon">e</font> is <a href="finset_1.html#V1">finite</a>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
