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

<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">Q</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>





<b>set </b><font color="Maroon">k1</font> =  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font>;<br/>
<b>set </b><font color="Maroon">k2</font> =  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font>;<br/>
<b>set </b><font color="Maroon">k3</font> =  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">k4</font> =  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">k5</font> =  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon">k6</font> =  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:16"/>
<font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:16"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 
;<br/>
<a NAME="E3:16"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:16_1_1"/>
( <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> or <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> or <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> or <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span> or <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span> or <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span> or <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span> )
 </span><b>by </b><i>, <a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_1"><b>suppose </b></a><a NAME="E1:16_1_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 ;<br/><div class="add"><a NAME="E2:16_1_1_1"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><a NAME="E3:16_1_1_1"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><b>hence </b><a NAME="E4:16_1_1_1"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_2"><b>suppose </b></a><a NAME="E1:16_1_1_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font>
 ;<br/><div class="add"><a NAME="E2:16_1_1_2"/><b>then </b><i><font color="Green">E42</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><a NAME="E3:16_1_1_2"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="tops_1.html#T45">TOPS_1:45</a></i>;<br/><a NAME="E4:16_1_1_2"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><b>hence </b><a NAME="E5:16_1_1_2"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_3"><b>suppose </b></a><a NAME="E1:16_1_1_3"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font>
 ;<br/><div class="add"><a NAME="E2:16_1_1_3"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font>
 <b>by </b><i><a class="ref" href="tops_1.html#T26">TOPS_1:26</a></i>;<br/><a NAME="E3:16_1_1_3"/><b>then </b><i><font color="Green">E44</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><a NAME="E4:16_1_1_3"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><b>hence </b><a NAME="E5:16_1_1_3"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_4"><b>suppose </b></a><a NAME="E1:16_1_1_4"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:16_1_1_4"/><b>then </b><i><font color="Green">E61</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><a NAME="E3:16_1_1_4"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="tops_1.html#T45">TOPS_1:45</a></i>;<br/><a NAME="E4:16_1_1_4"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><b>hence </b><a NAME="E5:16_1_1_4"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_5"><b>suppose </b></a><a NAME="E1:16_1_1_5"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:16_1_1_5"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="tops_1.html#T26">TOPS_1:26</a></i>;<br/><a NAME="E3:16_1_1_5"/><b>then </b><i><font color="Green">E63</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><a NAME="E4:16_1_1_5"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><b>hence </b><a NAME="E5:16_1_1_5"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_6"><b>suppose </b></a><a NAME="E1:16_1_1_6"/><i><font color="Green">E64</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:16_1_1_6"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tops_1.html#T26">TOPS_1:26</a></i>;<br/><a NAME="E3:16_1_1_6"/><b>then </b><i><font color="Green">E65</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><a NAME="E4:16_1_1_6"/>
 <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="tdlat_1.html#T5">TDLAT_1:5</a></i>;<br/><a NAME="E5:16_1_1_6"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><b>hence </b><a NAME="E6:16_1_1_6"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="16_1_1_7"><b>suppose </b></a><a NAME="E1:16_1_1_7"/><i><font color="Green">E66</font></i>: 
<font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>
 ;<br/><div class="add"><a NAME="E2:16_1_1_7"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="tops_1.html#T58">TOPS_1:58</a></i>;<br/><a NAME="E3:16_1_1_7"/><b>then </b><i><font color="Green">E67</font></i>: 
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><a NAME="E4:16_1_1_7"/>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R1">=</a>  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="tops_1.html#T45">TOPS_1:45</a></i>;<br/><a NAME="E5:16_1_1_7"/><b>then </b>
 <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K5">{</a><span class="default"><font color="Maroon">A</font>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p4">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="tops_1.html#K1">Int</a> <span class="p3">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <span class="p4">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span></span><a href="enumset1.html#K5">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D5">ENUMSET1:def 5</a></i>;<br/><b>hence </b><a NAME="E6:16_1_1_7"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E4:16"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">Q</font> <a href="hidden.html#R2">in</a>  <a href="kurato_1.html#K5" target="_self">Kurat7Set</a> <font color="Maroon">A</font> )
 ;<br/>


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