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

<b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>thus </b><a NAME="E1:3"/>
( <font color="Maroon">f</font> is   <a href="comseq_1.html#NM1">Complex_Sequence</a> implies (  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; ( for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a>  ) ) )
 <b>by </b><i/>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:3"/><i><font color="Green">E32</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a> 
 <b>and </b><br/><a NAME="E3:3"/><i><font color="Green">E33</font></i>: 
for <font color="Olive">n</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds  <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">n</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> 
 ;<br/>

<a NAME="E4:3"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  holds <br/><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> is    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K2">COMPLEX</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:3"/>
<font color="Maroon">f</font> is   <a href="comseq_1.html#NM1">Complex_Sequence</a>
 <b>by </b><i>, </i>;<br/>


</div>
