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

<a NAME="E1:39"/>
 <a href="xboole_0.html#K1">{}</a>  is <a href="card_1.html#V1" target="_self">cardinal</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>take </b>
 <a href="xboole_0.html#K1">{}</a> 
; <i><font color="Red">:: according to </font></i><a class="ref" href="card_1.html#D1" target="_self">CARD_1:def 1</a><br/>

<b>thus </b><a NAME="E1:39_1"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>

<b>assume </b><a NAME="E2:39_1"/>
<font color="Maroon">c<sub>1</sub></font>, <a href="xboole_0.html#K1">{}</a>  <a href="wellord2.html#R2">are_equipotent</a> 
 ;<br/>

<b>thus </b><a NAME="E3:39_1"/>
 <a href="xboole_0.html#K1">{}</a>  <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>1</sub></font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="card_1.html#NM1">Cardinal</a> ;<br/>
<a NAME="E3:39"/>
 <a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c<sub>1</sub></font> <a href="wellord2.html#R2">are_equipotent</a> 
 
;<br/>
<b>hence </b><a NAME="E4:39"/>
 <a href="card_1.html#K1" target="_self">Card</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="card_1.html#D5" target="_self">Def5</a></i>;<br/>


</div>
