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

<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">B</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f1</font> be   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="zfmisc_1.html#K3">:]</a></span>,<font color="Maroon">D</font>, <font color="Maroon">f2</font> be   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K3">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font>,<font color="Maroon">C</font></span><a href="zfmisc_1.html#K3">:]</a></span>,<font color="Maroon">D</font>;<br/>









<b>assume </b><a NAME="E1:5"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font><br/> for <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">B</font><br/> for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font> holds  <font color="Maroon">f1</font> <a href="multop_1.html#K2" target="_self">.</a> <font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="multop_1.html#K2" target="_self">.</a> <font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">c</font>
 ;<br/>

<a NAME="E2:5"/>
for <font color="Olive">a</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font><br/> for <font color="Olive">b</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">B</font><br/> for <font color="Olive">c</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font> holds  <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">c</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">c</font></span><a href="domain_1.html#K4">]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">C</font>;<br/>





<a NAME="E1:5_1"/>
( <font color="Maroon">f1</font> <a href="multop_1.html#K2" target="_self">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K4">]</a></span> &amp; <font color="Maroon">f2</font> <a href="multop_1.html#K2" target="_self">.</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K4">]</a></span> )
 
;<br/>
<b>hence </b><a NAME="E2:5_1"/>
<font color="Maroon">f1</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="domain_1.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="domain_1.html#K4">]</a></span>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:5"/>
<font color="Maroon">f1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">f2</font>
 <b>by </b><i/>;<br/>


</div>
