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

<b>let </b><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>;<br/>

<b>reconsider </b><font color="Maroon" title="c2">u</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> <b>by </b><i><a class="ref" href="classes2.html#T62" title="CLASSES2:th.62">CLASSES2:62</a></i>;<br/>
<b>set </b><font color="Maroon" title="c3">x1</font> = <span class="p1"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span>;<br/>
<a NAME="E2:77"/>
 <a href="algstr_1.html#K1" title="ALGSTR_1:func.1">Extract</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">u</font>
 
<b>by </b><i><a class="ref" href="algstr_1.html#D3" title="ALGSTR_1:def.3">ALGSTR_1:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">x4</font> =  <a href="algstr_1.html#K1" title="ALGSTR_1:func.1">Extract</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">x3</font> =  <a href="vectsp_1.html#K7" title="VECTSP_1:func.7">comp</a> <a href="algstr_1.html#K2" title="ALGSTR_1:func.2">L_Trivial</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> <b>by </b><i><a class="ref" href="grcat_1.html#T6" target="_self" title="GRCAT_1:th.6">Th6</a>, <a class="ref" href="grcat_1.html#T13" target="_self" title="GRCAT_1:th.13">Th13</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">x2</font> =  <a href="midsp_1.html#K2" title="MIDSP_1:func.2">op2</a>  as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font> <b>by </b><i><a class="ref" href="grcat_1.html#T6" target="_self" title="GRCAT_1:th.6">Th6</a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">x</font> = <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span>;<br/>
<a NAME="E6:77"/><i><font color="Green" title="E43">A1</font></i>: 
<span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">UN</font>
 
<b>by </b><i><a class="ref" href="grcat_1.html#T3" target="_self" title="GRCAT_1:th.3">Th3</a></i>;<br/>
<b>take </b>
<span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span>
;<br/>

<b>thus </b><a NAME="E7:77"/>
( <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">UN</font> &amp;  <a href="grcat_1.html#R1" title="GRCAT_1:pred.1">GO</a> <span class="p1"><a href="domain_1.html#K5" title="DOMAIN_1:func.5">[</a><span class="default"><span class="p2"><a href="classes2.html#K1" title="CLASSES2:func.1">{</a><span class="default"><font color="Maroon" title="c2">u</font></span><a href="classes2.html#K1" title="CLASSES2:func.1">}</a></span>,<font color="Maroon" title="c6">x2</font>,<font color="Maroon" title="c5">x3</font>,<font color="Maroon" title="c4">x4</font></span><a href="domain_1.html#K5" title="DOMAIN_1:func.5">]</a></span>, <a href="algstr_1.html#K2" title="ALGSTR_1:func.2">L_Trivial</a>  )
 <b>by </b><i><a class="txt" href="grcat_1.html#E6:77"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="grcat_1.html#D28" target="_self" title="GRCAT_1:def.28">Def28</a>, <a class="ref" href="algstr_1.html#D4" title="ALGSTR_1:def.4">ALGSTR_1:def 4</a></i>;<br/>


</div>
