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

<b>set </b><font color="Maroon" title="c5">JA</font> = <font color="Maroon" title="c3">J</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c1">A</font>;<br/>
<b>set </b><font color="Maroon" title="c6">JB</font> = <font color="Maroon" title="c3">J</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c2">B</font>;<br/>
<a NAME="E1:62_1_1"/>
for <font color="Olive" title="b1">j</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font> holds <br/><span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">j</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c7">j</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:62_1_1_1"/>
<font color="Maroon" title="c7">j</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">J</font>
 ;<br/>

<a NAME="E2:62_1_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">A</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">B</font> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></i>;<br/>
<b>hence </b><a NAME="E3:62_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="waybel_5.html#K7" title="WAYBEL_5:func.7">=&gt;</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font> is   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c2">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">j</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:62_1_1"/>
<font color="Maroon" title="c3">J</font> <a href="waybel_5.html#NK11" title="WAYBEL_5:NK.11">=&gt;</a> <font color="Maroon" title="c4">f</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c3">J</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c3">J</font> <a href="pre_circ.html#K2" title="PRE_CIRC:func.2">--&gt;</a> <font color="Maroon" title="c2">B</font>
 <b>by </b><i><a class="ref" href="pboole.html#D18" title="PBOOLE:def.18">PBOOLE:def 18</a></i>;<br/>


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