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

<b>let </b><font color="Maroon">C</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">xi</font> be   <a href="ordinal2.html#NM1">Ordinal-Sequence</a>;<br/>





<a NAME="E1:20"/><i><font color="Green">E37</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">xi</font></span>)</span> <a href="ordinal1.html#K2">|</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">xi</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">A</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">xi</font> <a href="ordinal1.html#K2">|</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">xi</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">A</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">xi</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">xi</font> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="ordinal3.html#K1">+^</a> <span class="p2">(<span class="default"><font color="Maroon">xi</font> <a href="ordinal1.html#K2">|</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">xi</font> <a href="ordinal1.html#K2">|</a> <font color="Maroon">A</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="ordinal3.html#D2">ORDINAL3:def 2</a>, <a class="ref" href="relat_1.html#T90">RELAT_1:90</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">e</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:20_1"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">xi</font></span>)</span> <a href="ordinal1.html#K2">|</a> <font color="Maroon">A</font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">a</font> = <font color="Maroon">e</font> as   <a href="ordinal1.html#NM2">Ordinal</a> <b>by </b><i><a class="ref" href="ordinal1.html#T23">ORDINAL1:23</a></i>;<br/><a NAME="E3:20_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">e</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">xi</font>
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">C</font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">xi</font></span>)</span> <a href="ordinal1.html#K2">|</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font> = 
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">xi</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<font color="Maroon">C</font> <a href="ordinal2.html#K10">+^</a> <span class="p1">(<span class="default"><font color="Maroon">xi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, <a class="ref" href="ordinal3.html#D2">ORDINAL3:def 2</a></i>
<br/>.= 
<font color="Maroon">C</font> <a href="ordinal2.html#K10">+^</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">xi</font> <a href="ordinal1.html#K2">|</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="ordinal3.html#K1">+^</a> <span class="p2">(<span class="default"><font color="Maroon">xi</font> <a href="ordinal1.html#K2">|</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">e</font>
<b>by </b><i>, , <a class="ref" href="ordinal3.html#D2">ORDINAL3:def 2</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20"/>
<span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">xi</font></span>)</span> <a href="ordinal1.html#K2">|</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">C</font> <a href="ordinal3.html#K1">+^</a> <span class="p1">(<span class="default"><font color="Maroon">xi</font> <a href="ordinal1.html#K2">|</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
