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

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">Z</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:128_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>and </b><br/><a NAME="E2:128_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E3:128_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</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>
 <b>and </b><br/><a NAME="E4:128_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
 <b>and </b><br/><a NAME="E5:128_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>
 <b>and </b><br/><a NAME="E6:128_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span>
 <b>and </b><br/><a NAME="E7:128_1"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
 <b>and </b><br/><a NAME="E8:128_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">Z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
 ;<br/><a NAME="E9:128_1"/>
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">Z</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="128_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</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="E1:128_1_1"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 ;<br/>

<div><i><font color="Green">E58</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="128_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:128_1_1_1"/>
not <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 ;<br/><a NAME="E2:128_1_1_1"/><b>then </b><i><font color="Green">E59</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K4">\</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>
 <b>by </b><i><a class="txt" href="zfmisc_1.html#E8:128_1"><i><font color="Green">E56</font></i></a>, </i>;<br/><span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K4">\</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> = 
<span class="p1">(<span class="default"><span class="p2"><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="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span></span>)</span> <a href="xboole_0.html#K4">\</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>
<b>by </b><i><a class="ref" href="enumset1.html#T42">ENUMSET1:42</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K4">\</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>
<b>by </b><i><a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>
;<br/><a NAME="E4:128_1_1_1"/><b>then </b>
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K4">\</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="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E5:128_1_1_1"/><b>then </b>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T43" target="_self">Th43</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><b>hence </b><a NAME="E6:128_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="zfmisc_1.html#E1:128_1_1"><i><font color="Green">E57</font></i></a>, <a class="txt" href="zfmisc_1.html#E2:128_1_1_1"><i><font color="Green">E59</font></i></a>, <a class="txt" href="zfmisc_1.html#E3:128_1_1"><i><font color="Green">E60</font></i></a>, <a class="txt" href="zfmisc_1.html#E52"><i><font color="Green">Lemma62</font></i></a>, <a class="txt" href="zfmisc_1.html#E1"><i><font color="Green">Lemma24</font></i></a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E60</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="128_1_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:128_1_1_2"/>
not <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 ;<br/><a NAME="E2:128_1_1_2"/><b>then </b><i><font color="Green">E92</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="zfmisc_1.html#E8:128_1"><i><font color="Green">E56</font></i></a>, </i>;<br/><span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><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="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><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="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>
;<br/><a NAME="E4:128_1_1_2"/><b>then </b>
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E5:128_1_1_2"/><b>then </b>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T55" target="_self">Th55</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><b>hence </b><a NAME="E6:128_1_1_2"/>
contradiction
 <b>by </b><i><a class="txt" href="zfmisc_1.html#E1:128_1_1"><i><font color="Green">E57</font></i></a>, <a class="txt" href="zfmisc_1.html#E2:128_1_1"><i><font color="Green">E58</font></i></a>, <a class="txt" href="zfmisc_1.html#E3:128_1_1"><i><font color="Green">E60</font></i></a>, <a class="ref" href="zfmisc_1.html#T33" target="_self">Th33</a>, <a class="txt" href="zfmisc_1.html#E1"><i><font color="Green">Lemma24</font></i></a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="128_1_1_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:128_1_1_3"/>
not <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 ;<br/><a NAME="E2:128_1_1_3"/><b>then </b><i><font color="Green">E93</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="zfmisc_1.html#E8:128_1"><i><font color="Green">E56</font></i></a>, </i>;<br/><span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span> = 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>
;<br/><a NAME="E4:128_1_1_3"/><b>then </b>
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K4">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T36">XBOOLE_1:36</a></i>;<br/><a NAME="E5:128_1_1_3"/><b>then </b>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T55" target="_self">Th55</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/><b>hence </b><a NAME="E6:128_1_1_3"/>
contradiction
 <b>by </b><i><a class="txt" href="zfmisc_1.html#E1:128_1_1"><i><font color="Green">E57</font></i></a>, <a class="txt" href="zfmisc_1.html#E2:128_1_1"><i><font color="Green">E58</font></i></a>, , <a class="txt" href="zfmisc_1.html#E50"><i><font color="Green">Lemma61</font></i></a>, <a class="txt" href="zfmisc_1.html#E1"><i><font color="Green">Lemma24</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:128_1_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Z</font>
 <b>by </b><i><a class="txt" href="zfmisc_1.html#E55"><i><font color="Green">Lemma64</font></i></a>, <a class="ref" href="zfmisc_1.html#T38" target="_self">Th38</a>, <a class="ref" href="zfmisc_1.html#T43" target="_self">Th43</a>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E10:128_1"/>
<font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="zfmisc_1.html#E8:128_1"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:128"/><i><font color="Green">E94</font></i>: 
( <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</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">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> )
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:128_2"/>
( <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</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">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span> or <font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span> )
 </span><b>by </b><i/>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_2_1"><b>suppose </b></a><a NAME="E1:128_2_1"/>
<font color="Maroon">Z</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:128_2_1"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_2_2"><b>suppose </b></a><a NAME="E1:128_2_2"/>
<font color="Maroon">Z</font> <a href="hidden.html#R1">=</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="E2:128_2_2"/><b>then </b>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</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"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><b>hence </b><a NAME="E3:128_2_2"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#T42">ENUMSET1:42</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_2_3"><b>suppose </b></a><a NAME="E1:128_2_3"/>
<font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:128_2_3"/><b>then </b><i><font color="Green">E96</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i/>;<br/><a NAME="E3:128_2_3"/>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><a NAME="E4:128_2_3"/><b>then </b>
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/><b>hence </b><a NAME="E5:128_2_3"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_2_4"><b>suppose </b></a><a NAME="E1:128_2_4"/>
<font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><a NAME="E2:128_2_4"/><b>then </b>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><b>hence </b><a NAME="E3:128_2_4"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_2_5"><b>suppose </b></a><a NAME="E1:128_2_5"/>
<font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span>
 ;<br/><div class="add"><a NAME="E2:128_2_5"/><b>then </b>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><b>hence </b><a NAME="E3:128_2_5"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#T43">ENUMSET1:43</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_2_6"><b>suppose </b></a><a NAME="E1:128_2_6"/>
<font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
 ;<br/><div class="add"><a NAME="E2:128_2_6"/><b>then </b>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</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"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><b>hence </b><a NAME="E3:128_2_6"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#T42">ENUMSET1:42</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_2_7"><b>suppose </b></a><a NAME="E1:128_2_7"/>
<font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
 ;<br/><div class="add"><a NAME="E2:128_2_7"/><b>then </b><i><font color="Green">E97</font></i>: 
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/><span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span> = 
<span class="p1">(<span class="default"><span class="p2"><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="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
<br/>.= 
<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"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">y</font></span><a href="tarski.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T4">XBOOLE_1:4</a></i>
<br/>.= 
<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"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T41">ENUMSET1:41</a></i>
;<br/><b>hence </b><a NAME="E4:128_2_7"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="enumset1.html#T42">ENUMSET1:42</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="128_2_8"><b>suppose </b></a><a NAME="E1:128_2_8"/>
<font color="Maroon">Z</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 ;<br/><div class="add"><b>hence </b><a NAME="E2:128_2_8"/>
<font color="Maroon">Z</font> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

</div>
