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

<b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<a NAME="E1:17"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> implies ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<a NAME="E2:17_1"/><i><font color="Green">E17</font></i>: 
( ( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> ) implies ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_1_1"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> )
 ;<br/>

<a NAME="E2:17_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:17_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:17_1"/>
( ( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> ) implies ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_1_2"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> )
 ;<br/>

<a NAME="E2:17_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span>
 
<b>by </b><i><a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<b>hence </b><a NAME="E3:17_1_2"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:17_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="txt" href="realset2.html#E1:17_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="realset2.html#E2:17_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="realset2.html#E19"><i><font color="Green">Lemma13</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:17"/>
( ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span> implies <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_2"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">c<sub>13</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E1:17_2"/><i><font color="Green">E16</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span>
 ;<br/>

<a NAME="E2:17_2"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Maroon">c<sub>13</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> )
 
<b>by </b><i><a class="txt" href="realset2.html#E1:17_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E3:17_2"/><b>then </b>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E4:17_2"/>
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="txt" href="realset2.html#E18"><i><font color="Green">Lemma12</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:17"/>
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> iff ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>12</sub></font>,<font color="Olive">b<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span> )
 <b>by </b><i><a class="txt" href="realset2.html#E1:17"><i><font color="Green">E15</font></i></a></i>;<br/>


</div>
