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

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







<b>assume </b><b>that </b><br/><a NAME="E1:9"/><i><font color="Green">E13</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">psi</font>
 <b>and </b><br/><a NAME="E2:9"/><i><font color="Green">E25</font></i>: 
( ( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  ex <font color="Olive">A1</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">A1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> &amp; ( for <font color="Olive">C</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">A1</font> <a href="ordinal1.html#R1">c=</a> <font color="Olive">C</font> &amp; <font color="Olive">C</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> holds <br/><font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">C</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) ) ) or ( <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; ( for <font color="Olive">A1</font>, <font color="Olive">C</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">A1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Olive">C</font> holds <br/> ex <font color="Olive">D</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">D</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> &amp; ( for <font color="Olive">E</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">D</font> <a href="ordinal1.html#R1">c=</a> <font color="Olive">E</font> &amp; <font color="Olive">E</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> holds <br/>( <font color="Olive">A1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">E</font> &amp; <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">E</font> <a href="hidden.html#R2">in</a> <font color="Olive">C</font> ) ) ) ) ) )
 <b>and </b><br/><a NAME="E3:9"/><i><font color="Green">E26</font></i>: 
( ( <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  ex <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">B</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">psi</font> &amp; ( for <font color="Olive">A1</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">B</font> <a href="ordinal1.html#R1">c=</a> <font color="Olive">A1</font> &amp; <font color="Olive">A1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">psi</font> holds <br/><font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A1</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) ) ) or ( <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; ( for <font color="Olive">B</font>, <font color="Olive">A1</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <font color="Olive">A1</font> holds <br/> ex <font color="Olive">D</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">D</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">psi</font> &amp; ( for <font color="Olive">E</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">D</font> <a href="ordinal1.html#R1">c=</a> <font color="Olive">E</font> &amp; <font color="Olive">E</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">psi</font> holds <br/>( <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">E</font> &amp; <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">E</font> <a href="hidden.html#R2">in</a> <font color="Olive">A1</font> ) ) ) ) ) )
 <b>and </b><br/><a NAME="E4:9"/><i><font color="Green">E27</font></i>: 
( for <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> holds <br/><font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> or for <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> holds <br/><font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ordinal2.html#D13">ORDINAL2:def 13</a><br/>

<div><i><font color="Green">E28</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">A</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>assume </b><a NAME="E1:9_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font>
 ;<br/><b>reconsider </b><font color="Maroon">A1</font> = <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font>, <font color="Maroon">A2</font> = <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font> as   <a href="ordinal1.html#NM2">Ordinal</a> ;<br/><a NAME="E3:9_1"/>
( <font color="Maroon">A1</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">A2</font> or <font color="Maroon">A1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A2</font> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E4:9_1"/>
<font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_2"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_2_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:9_2_1"/>
( ( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) or ( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  ) or ( <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) or ( <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_2_1_1"><b>suppose </b></a><a NAME="E1:9_2_1_1"/>
( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/><div class="add"><b>hence </b><a NAME="E2:9_2_1_1"/>
<font color="Maroon">B</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">C</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_2_1_2"><b>suppose </b></a><a NAME="E1:9_2_1_2"/>
( <font color="Maroon">B</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/><div class="add"><a NAME="E2:9_2_1_2"/><b>then </b>
<font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="ordinal3.html#T10">ORDINAL3:10</a></i>;<br/><b>hence </b><a NAME="E3:9_2_1_2"/>
<font color="Maroon">B</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">C</font>
 <b>by </b><i><a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_2_1_3"><b>suppose </b></a><a NAME="E1:9_2_1_3"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">A1</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E3:9_2_1_3"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">A1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">psi</font> &amp; ( for <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Maroon">A1</font> <a href="ordinal1.html#R1">c=</a> <font color="Olive">A</font> &amp; <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">psi</font> holds <br/><font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) )
 <b>by </b><i/>;<br/><a NAME="E4:9_2_1_3"/>
(  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">B</font> )
 <b>by </b><i>, <a class="ref" href="ordinal1.html#T10">ORDINAL1:10</a>, <a class="ref" href="ordinal3.html#T10">ORDINAL3:10</a></i>;<br/><b>then consider </b><font color="Maroon">A2</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E6:9_2_1_3"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">A2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> &amp; ( for <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Maroon">A2</font> <a href="ordinal1.html#R1">c=</a> <font color="Olive">A</font> &amp; <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> holds <br/>(  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> &amp; <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">B</font> ) ) )
 <b>by </b><i/>;<br/><a NAME="E7:9_2_1_3"/>
( <font color="Maroon">A1</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font> &amp; <font color="Maroon">A2</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font> &amp; ( <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font> or <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font> ) )
 <b>by </b><i><a class="ref" href="ordinal3.html#T15">ORDINAL3:15</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E8:9_2_1_3"/><b>then </b>
( <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font></span>)</span> &amp; <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font></span>)</span> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font></span>)</span> )
 <b>by </b><i>, , <a class="txt" href="ordinal4.html#E1:9"><i><font color="Green">E13</font></i></a>, </i>;<br/><b>hence </b><a NAME="E9:9_2_1_3"/>
<font color="Maroon">B</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">C</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="9_2_1_4"><b>suppose </b></a><a NAME="E1:9_2_1_4"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">C</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/><div class="add"><b>assume </b><a NAME="E2:9_2_1_4"/>
not <font color="Maroon">B</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">C</font>
 ;<br/><a NAME="E3:9_2_1_4"/><b>then </b>
( <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">B</font> )
 <b>by </b><i><a class="ref" href="ordinal1.html#T10">ORDINAL1:10</a>, <a class="ref" href="ordinal1.html#T26">ORDINAL1:26</a></i>;<br/><b>then consider </b><font color="Maroon">A1</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E5:9_2_1_4"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">A1</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> &amp; ( for <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Maroon">A1</font> <a href="ordinal1.html#R1">c=</a> <font color="Olive">A</font> &amp; <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">fi</font> holds <br/>( <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> &amp; <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">B</font> ) ) )
 <b>by </b><i/>;<br/><a NAME="E6:9_2_1_4"/>
(  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">C</font> )
 <b>by </b><i>, <a class="ref" href="ordinal1.html#T10">ORDINAL1:10</a>, <a class="ref" href="ordinal3.html#T10">ORDINAL3:10</a></i>;<br/><b>then consider </b><font color="Maroon">A2</font> being   <a href="ordinal1.html#NM2">Ordinal</a><b> such that </b><br/><a NAME="E8:9_2_1_4"/><i><font color="Green">E46</font></i>: 
( <font color="Maroon">A2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">psi</font> &amp; ( for <font color="Olive">A</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Maroon">A2</font> <a href="ordinal1.html#R1">c=</a> <font color="Olive">A</font> &amp; <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">psi</font> holds <br/>(  <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> &amp; <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <font color="Olive">A</font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">C</font> ) ) )
 <b>by </b><i/>;<br/><a NAME="E9:9_2_1_4"/>
( <font color="Maroon">A1</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font> &amp; <font color="Maroon">A2</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font> &amp; ( <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A1</font> or <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font> ) )
 <b>by </b><i><a class="ref" href="ordinal3.html#T15">ORDINAL3:15</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E10:9_2_1_4"/><b>then </b><i><font color="Green">E47</font></i>: 
( <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Maroon">C</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font></span>)</span> &amp; <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">psi</font> &amp; <font color="Maroon">fi</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font></span>)</span> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font></span>)</span> )
 <b>by </b><i>, , <a class="txt" href="ordinal4.html#E1:9"><i><font color="Green">E13</font></i></a>, </i>;<br/><b>reconsider </b><font color="Maroon">A3</font> = <font color="Maroon">psi</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">A2</font></span>)</span> as   <a href="ordinal1.html#NM2">Ordinal</a> ;<br/><a NAME="E12:9_2_1_4"/>
( <font color="Maroon">A3</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">C</font> &amp; <font color="Maroon">C</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A3</font> )
 <b>by </b><i>, <a class="ref" href="ordinal1.html#T34">ORDINAL1:34</a></i>;<br/><b>hence </b><a NAME="E13:9_2_1_4"/>
contradiction
 <b>by </b><i><a class="ref" href="ordinal1.html#T7">ORDINAL1:7</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E7:9"/>
<font color="Maroon">B</font> <a href="ordinal1.html#R1">c=</a> <font color="Maroon">C</font>
 ;<br/>


</div>
