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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="ordinal2.html#NM1">Ordinal-Sequence</a>;<br/>



<b>assume </b><a NAME="E1:19"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="ordinal2.html#V2">increasing</a>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>; <i><font color="Red">:: according to </font></i><a class="ref" href="ordinal2.html#D16">ORDINAL2:def 16</a><br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/>



<b>assume </b><a NAME="E2:19"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 ;<br/>

<a NAME="E3:19"/><b>then </b><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#T19">ORDINAL1:19</a>, <a class="ref" href="ordinal3.html#D2">ORDINAL3:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font> as   <a href="ordinal1.html#NM2">Ordinal</a> ;<br/>
<a NAME="E5:19"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</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>6</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</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>7</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="zfrefle1.html#E1:19"><i><font color="Green">E13</font></i></a>, <a class="txt" href="zfrefle1.html#E2:19"><i><font color="Green">E14</font></i></a>, <a class="txt" href="zfrefle1.html#E3:19"><i><font color="Green">E15</font></i></a>, <a class="ref" href="ordinal2.html#D16">ORDINAL2:def 16</a>, <a class="ref" href="ordinal3.html#D2">ORDINAL3:def 2</a></i>;<br/>
<b>hence </b><a NAME="E6:19"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="ordinal3.html#K1">+^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="ordinal2.html#T49">ORDINAL2:49</a></i>;<br/>


</div>
