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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E1:29"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:29"/><b>then </b>
<font color="Maroon">c<sub>1</sub></font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E4:29"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="ref" href="ordinal3.html#T30" target="_self">Th30</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>thus </b><a NAME="E5:29"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="ordinal2.html#K10">+^</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="ordinal3.html#E4:29"><i><font color="Green">E17</font></i></a></i>;<br/>

<b>assume </b><a NAME="E6:29"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E7:29"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="ordinal3.html#E4:29"><i><font color="Green">E17</font></i></a>, <a class="ref" href="ordinal2.html#T44">ORDINAL2:44</a></i>;<br/>
<b>hence </b><a NAME="E8:29"/>
contradiction
 <b>by </b><i><a class="txt" href="ordinal3.html#E1:29"><i><font color="Green">E16</font></i></a></i>;<br/>


</div>
