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

<b>let </b><font color="Maroon">M</font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/><b>let </b><font color="Maroon">N</font> be   <a href="card_1.html#NM1">Cardinal</a>;<br/><b>let </b><font color="Maroon">phi</font> be   <a href="ordinal2.html#NM1">Ordinal-Sequence</a>;<br/>





<b>assume </b><a NAME="E1:40"/><i><font color="Green">E23</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">phi</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">phi</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">N</font> &amp; <font color="Maroon">M</font> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_5.html#K1" target="_self">cf</a> <font color="Maroon">N</font> )
 ;<br/>

<a NAME="E2:40"/><b>then </b>
(  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">phi</font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">M</font> &amp;  <a href="card_1.html#K1">Card</a> <font color="Maroon">M</font> <a href="hidden.html#R1">=</a> <font color="Maroon">M</font> )
 
<b>by </b><i><a class="ref" href="card_1.html#T28">CARD_1:28</a>, <a class="ref" href="card_1.html#D5">CARD_1:def 5</a></i>;<br/>
<a NAME="E3:40"/><b>then </b>
(  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">phi</font></span>)</span> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_5.html#K1" target="_self">cf</a> <font color="Maroon">N</font> &amp;  <a href="card_3.html#K3">Union</a> <font color="Maroon">phi</font> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">phi</font></span>)</span> &amp;  <a href="ordinal2.html#K4">sup</a> <font color="Maroon">phi</font> <a href="hidden.html#R1">=</a>  <a href="ordinal2.html#K3">sup</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">phi</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="ordinal1.html#T22">ORDINAL1:22</a></i>;<br/>
<b>hence </b><a NAME="E4:40"/>
(  <a href="ordinal2.html#K4">sup</a> <font color="Maroon">phi</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> &amp;  <a href="card_3.html#K3">Union</a> <font color="Maroon">phi</font> <a href="hidden.html#R2">in</a> <font color="Maroon">N</font> )
 <b>by </b><i>, </i>;<br/>


</div>
