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

<b>let </b><font color="Maroon">f1</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">f2</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:9_1_2"/><i><font color="Green">E46</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span>
 <b>and </b><br/><a NAME="E2:9_1_2"/><i><font color="Green">E50</font></i>: 
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <font color="Olive">X</font>
 <b>and </b><br/><a NAME="E3:9_1_2"/><i><font color="Green">E51</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span>
 <b>and </b><br/><a NAME="E4:9_1_2"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">X</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">X</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> holds <br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">X</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <font color="Olive">X</font>
 ;<br/>

<a NAME="E5:9_1_2"/>
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="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:9_1_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span>
 ;<br/>

<a NAME="E2:9_1_2_1"/><b>then </b>
( <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <font color="Maroon">x</font> &amp; <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="relat_1.html#K9">.:</a> <font color="Maroon">x</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E3:9_1_2_1"/>
<font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:9_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
