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

<b>let </b><font color="Maroon">i1</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">i2</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>given </b><font color="Maroon">x</font> being   <a href="finseq_1.html#NM1">FinSequence</a><b> such that </b><a NAME="E1:40_1_2_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font>
 ;<br/><b>assume </b><a NAME="E2:40_1_2_1"/>
for <font color="Olive">x</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">i1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">x</font>
 ;<br/><a NAME="E3:40_1_2_1"/><b>then </b>
<font color="Maroon">i1</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">x</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E4:40_1_2_1"/>
( ( for <font color="Olive">x</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">i2</font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Olive">x</font> ) implies <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> )
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:40_1_2"/>
( ( for <font color="Olive">x</font> being  <a href="finseq_1.html#NM1">FinSequence</a>  holds not <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> ) &amp; <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> 0 &amp; <font color="Maroon">i2</font> <a href="hidden.html#R1">=</a> 0 implies <font color="Maroon">i1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i2</font> )
 ;<br/>


</div>
