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

<b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</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">f</font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font>,<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="finsub_1.html#K5">Fin</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/><b>let </b><font color="Maroon">B</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="finsub_1.html#K5">Fin</a> <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">X</font>;<br/>









<b>assume </b><a NAME="E1:22"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 ;<br/>

<b>then </b><span class="p1">(<span class="default"><a href="normform.html#K5" target="_self">FinPairUnion</a> <font color="Maroon">A</font></span>)</span> <a href="setwiseo.html#K7">$$</a> <font color="Maroon">B</font>,<font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><a href="normform.html#K5" target="_self">FinPairUnion</a> <font color="Maroon">A</font></span>)</span> <a href="setwiseo.html#K7">$$</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="setwiseo.html#K5">\/</a> <span class="p2"><a href="setwiseo.html#K2">{.</a><span class="default"><font color="Maroon">x</font></span><a href="setwiseo.html#K2">.}</a></span></span>)</span>,<font color="Maroon">f</font>
<b>by </b><i><a class="ref" href="zfmisc_1.html#T46">ZFMISC_1:46</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="normform.html#K5" target="_self">FinPairUnion</a> <font color="Maroon">A</font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="normform.html#K5" target="_self">FinPairUnion</a> <font color="Maroon">A</font></span>)</span> <a href="setwiseo.html#K7">$$</a> <font color="Maroon">B</font>,<font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="normform.html#T4" target="_self">Th4</a>, <a class="ref" href="setwiseo.html#T29">SETWISEO:29</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="normform.html#K5" target="_self">FinPairUnion</a> <font color="Maroon">A</font></span>)</span> <a href="setwiseo.html#K7">$$</a> <font color="Maroon">B</font>,<font color="Maroon">f</font></span>)</span> <a href="normform.html#K1" target="_self">\/</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i/>
;<br/>
<a NAME="E3:22"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="normform.html#R1" target="_self">c=</a> <span class="p1">(<span class="default"><a href="normform.html#K5" target="_self">FinPairUnion</a> <font color="Maroon">A</font></span>)</span> <a href="setwiseo.html#K7">$$</a> <font color="Maroon">B</font>,<font color="Maroon">f</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:22"/>
<font color="Maroon">f</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">x</font> <a href="normform.html#R1" target="_self">c=</a>  <a href="normform.html#K6" target="_self">FinPairUnion</a> <font color="Maroon">B</font>,<font color="Maroon">f</font>
 ;<br/>


</div>
