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

<b>set </b><font color="Maroon">h</font> = <font color="Maroon">h2</font> <a href="pboole.html#K12">**</a> <font color="Maroon">h1</font>;<br/>
<a NAME="E1:2_1_1"/>
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">h1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">h2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font> )
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<b>then </b><i><font color="Green">E32</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">h2</font> <a href="pboole.html#K12">**</a> <font color="Maroon">h1</font></span>)</span> = 
<font color="Maroon">I</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">I</font>
<b>by </b><i><a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
<font color="Maroon">I</font>

;<br/>
<b>then reconsider </b><font color="Maroon">h</font> = <font color="Maroon">h2</font> <a href="pboole.html#K12">**</a> <font color="Maroon">h1</font> as    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I</font> <b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:2_1_1"/>
<font color="Maroon">h</font> is    <a href="pboole.html#M3">ManySortedFunction</a> of <font color="Maroon">A</font>,<font color="Maroon">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D18">PBOOLE:def 18</a><br/>

<b>assume </b><a NAME="E1:2_1_1_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">f</font> = <font color="Maroon">h1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>, <font color="Maroon">g</font> = <font color="Maroon">h2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> as   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <b>by </b><i><a class="ref" href="pboole.html#D18">PBOOLE:def 18</a></i>;<br/>
<a NAME="E3:2_1_1_2"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font>
 
<b>by </b><i>, , <a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>;<br/>
<b>hence </b><a NAME="E4:2_1_1_2"/>
<font color="Maroon">h</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is    <a href="relset_1.html#M2">Relation</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>,<font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E5:2_1_1"/>
<font color="Maroon">h2</font> <a href="pboole.html#K12">**</a> <font color="Maroon">h1</font> is    <a href="pboole.html#M3">ManySortedFunction</a> of <font color="Maroon">A</font>,<font color="Maroon">A</font>
 ;<br/>


</div>
