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

<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">d</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">f</font> be  <a href="funct_1.html#V2">one-to-one</a> <a href="partfun1.html#NM1">PartFunc</a> of <font color="Maroon">C</font>,<font color="Maroon">D</font>;<br/>







<b>assume </b><a NAME="E1:17"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 ;<br/>

<a NAME="E2:17"/><b>then </b><i><font color="Green">E30</font></i>: 
( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun2.html#K2" target="_self">"</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font></span>)</span> &amp; <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun2.html#K2" target="_self">"</a> </span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">d</font> )
 
<b>by </b><i><a class="ref" href="funct_1.html#T57">FUNCT_1:57</a></i>;<br/>
<a NAME="E3:17"/>
<font color="Maroon">d</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun2.html#K2" target="_self">"</a> </span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#T59">FUNCT_1:59</a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
( <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun2.html#K2" target="_self">"</a> </span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">d</font></span>)</span> &amp; <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="partfun2.html#K2" target="_self">"</a> </span>)</span></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">d</font> )
 <b>by </b><i>, , , <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>;<br/>


</div>
