<?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>, <font color="Maroon">g1</font> be   <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">g2</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:4"/><i><font color="Green">E25</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> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</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>
 <b>and </b><br/><a NAME="E2:4"/><i><font color="Green">E26</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> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g1</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g2</font></span>)</span> holds <br/><font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="partfun1.html#D6">PARTFUN1:def 6</a><br/>

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="partfun1.html#D6">PARTFUN1:def 6</a><br/>

<b>assume </b><a NAME="E3:4"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g2</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E4:4"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font></span>)</span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:4"/><b>then </b><i><font color="Green">E27</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">g1</font> &amp; <font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g2</font> &amp; <font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T21">FUNCT_1:21</a></i>;<br/>
<a NAME="E6:4"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g1</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E7:4"/><b>then </b><i><font color="Green">E28</font></i>: 
<font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:4"/><b>then </b>
( <font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">g1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g2</font></span>)</span> <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> <span class="p1">(<span class="default"><font color="Maroon">g2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>hence </b><a NAME="E9:4"/>
<span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g1</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">g2</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 <b>by </b><i>, </i>;<br/>


</div>
