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

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">F</font> be   <a href="armstrng.html#NM2">Dependency-set</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">K</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:91"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Olive">A</font>,<font color="Olive">B</font></span><a href="armstrng.html#K6" target="_self">]</a></span> where <font color="Olive">A</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : ( <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A</font> or <font color="Olive">B</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A</font> ) </span>}</span> 
 ;<br/>

<b>set </b><font color="Maroon">BB</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <font color="Olive">B</font> where <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> </span>}</span> ;<br/>
<a NAME="E2:91"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <font color="Olive">B</font> where <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:91_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <font color="Olive">B</font> where <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> </span>}</span> 
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:91_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">B</font> where <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> </span>}</span>  )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_1_1"><b>suppose </b></a><a NAME="E1:91_1_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:91_1_1_1"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T80">ZFMISC_1:80</a></i>;<br/><b>hence </b><a NAME="E3:91_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_1_1_2"><b>suppose </b></a><a NAME="E1:91_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">B</font> where <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> </span>}</span> 
 ;<br/><div class="add"><a NAME="E2:91_1_1_2"/><b>then </b>
 ex <font color="Olive">B</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Olive">B</font> &amp; not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> )
 ;<br/><b>hence </b><a NAME="E3:91_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">BB'</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <font color="Olive">B</font> where <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> </span>}</span>  as  non <a href="xboole_0.html#V1">empty</a> <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">X</font> ;<br/>
<a NAME="E4:91"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">BB'</font> is <a href="armstrng.html#V1" target="_self">(B1)</a>
 
<b>by </b><i/>;<br/>
<a NAME="E5:91"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">BB'</font> is <a href="finsub_1.html#V2">(B2)</a>
 
<b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">G</font> = <span class="p1">{<span class="default"> <span class="p2"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span> where <font color="Olive">a</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Olive">b</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB'</font> &amp; <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> holds <br/><font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> </span>}</span> ;<br/>
<a NAME="E6:91"/><i><font color="Green">E40</font></i>: 
<span class="p1">{<span class="default"> <span class="p2"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span> where <font color="Olive">a</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Olive">b</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB'</font> &amp; <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> holds <br/><font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> </span>}</span>  <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="armstrng.html#K10" target="_self">deps_encl_by</a> <font color="Maroon">BB'</font>
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:91_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 ;<br/><b>then consider </b><font color="Maroon">a</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Maroon">b</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E3:91_2_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span>
 <b>and </b><br/><a NAME="E4:91_2_1"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font> or <font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font> )
 <b>by </b><i><a class="ref" href="armstrng.html#T2" target="_self">Th2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><b>that </b><br/><a NAME="E1:91_2_1_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB'</font>
 <b>and </b><br/><a NAME="E2:91_2_1_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 ;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:91_2_1_1_1"/>
( <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font> or <font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_2_1_1_1_1"><b>suppose </b></a><a NAME="E1:91_2_1_1_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>thus </b><a NAME="E2:91_2_1_1_1_1"/>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2_1_1_1_1_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_2_1_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:91_2_1_1_1_1_1_1"/>
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">B</font> where <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> </span>}</span>  )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_2_1_1_1_1_1_1_1"><b>suppose </b></a><a NAME="E1:91_2_1_1_1_1_1_1_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:91_2_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:91_2_1_1_1_1_1_1_1"/>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_2_1_1_1_1_1_1_2"><b>suppose </b></a><a NAME="E1:91_2_1_1_1_1_1_1_2"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">B</font> where <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> </span>}</span> 
 ;<br/><div class="add"><a NAME="E2:91_2_1_1_1_1_1_1_2"/><b>then </b>
 ex <font color="Olive">B</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> st <br/>( <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">B</font> &amp; not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> )
 ;<br/><b>hence </b><a NAME="E3:91_2_1_1_1_1_1_1_2"/>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="armstrng.html#D1" target="_self">Def1</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="91_2_1_1_1_2"><b>suppose </b></a><a NAME="E1:91_2_1_1_1_2"/>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:91_2_1_1_1_2"/>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E6:91_2_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span> where <font color="Olive">a</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Olive">b</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB'</font> &amp; <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> holds <br/><font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> </span>}</span> 
 <b>by </b><i/>;<br/></div>
<b>end;</b></div><b>assume </b><a NAME="E2:91_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span> where <font color="Olive">a</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Olive">b</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB'</font> &amp; <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> holds <br/><font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">a</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Maroon">b</font> being   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font><b> such that </b><br/><a NAME="E4:91_2"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span>
 <b>and </b><br/><a NAME="E5:91_2"/><i><font color="Green">E75</font></i>: 
for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB'</font> &amp; <font color="Maroon">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> holds <br/><font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font>
 ;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_2_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:91_2_2"/>
not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font>
 ;<br/><a NAME="E2:91_2_2"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">B</font> where <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> </span>}</span> 
 ;<br/><a NAME="E3:91_2_2"/><b>then </b>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB'</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><b>hence </b><a NAME="E4:91_2_2"/>
<font color="Maroon">b</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">a</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:91_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">F</font>
 <b>by </b><i><a class="ref" href="armstrng.html#T2" target="_self">Th2</a>, </i>;<br/></div><b>end;</b></div>
<a NAME="E8:91"/><b>then </b>
<font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2"><a href="armstrng.html#K6" target="_self">[</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="armstrng.html#K6" target="_self">]</a></span> where <font color="Olive">a</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>, <font color="Olive">b</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : for <font color="Olive">c</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">c</font> <a href="hidden.html#R2">in</a> <font color="Maroon">BB'</font> &amp; <font color="Olive">a</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> holds <br/><font color="Olive">b</font> <a href="tarski.html#R1">c=</a> <font color="Olive">c</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>
<b>hence </b><a NAME="E9:91"/>
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">X</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <font color="Olive">B</font> where <font color="Olive">B</font> is   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font> : not <font color="Maroon">K</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> </span>}</span>  <a href="hidden.html#R1">=</a>  <a href="armstrng.html#K9" target="_self">saturated-subsets</a> <font color="Maroon">F</font>
 <b>by </b><i>, , , </i>;<br/>


</div>
