<?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>assume </b><a NAME="E1:16"/><i><font color="Green">E33</font></i>: 
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="relat_1.html#K1">dom</a> <font color="Maroon">f</font> holds <br/> not <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> is <a href="facirc_1.html#V1" target="_self">pair</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="facirc_1.html#D3" target="_self">FACIRC_1:def 3</a><br/>

<b>let </b><font color="Maroon">y</font> be  <a href="facirc_1.html#V1" target="_self">pair</a>  <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="facirc_1.html#D2" target="_self">FACIRC_1:def 2</a><br/>

<b>assume </b><a NAME="E2:16"/>
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:16"/><i><font color="Green">E35</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> &amp; <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>thus </b><a NAME="E5:16"/>
contradiction
 <b>by </b><i>, </i>;<br/>


</div>
