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

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">p</font>, <font color="Olive">r</font> being   <a href="hidden.html#M1">set</a>  st <font color="Maroon">a<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">p</font>,<font color="Olive">r</font></span><a href="tarski.html#K4">]</a></span>;<br/>
<b>set </b><font color="Maroon">Z</font> = <font color="Maroon">x</font> <a href="zf_fund1.html#K1" target="_self">(#)</a> <font color="Maroon">y</font>;<br/>
<a NAME="E1:2_1_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">x</font> <a href="zf_fund1.html#K1" target="_self">(#)</a> <font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">o</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="E1:2_1_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> <a href="zf_fund1.html#K1" target="_self">(#)</a> <font color="Maroon">y</font>
 ;<br/>

<b>then consider </b><font color="Maroon">q</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">r</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">s</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:2_1_1_1"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">s</font></span><a href="tarski.html#K4">]</a></span> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> )
 <b>by </b><i/>;<br/>
<a NAME="E4:2_1_1_1"/>
( <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> &amp; <font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/>
<a NAME="E5:2_1_1_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:2_1_1_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K2">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">q</font></span><a href="tarski.html#K1">}</a></span></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K2">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">r</font></span><a href="tarski.html#K1">}</a></span></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> )
 
;<br/>
<a NAME="E7:2_1_1_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K2">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">q</font></span><a href="tarski.html#K1">}</a></span></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K2">}</a></span>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">r</font></span><a href="tarski.html#K1">}</a></span></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/>
<a NAME="E8:2_1_1_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">q</font></span><a href="tarski.html#K1">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K2">}</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/>
<a NAME="E9:2_1_1_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">q</font></span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> &amp; <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">r</font>,<font color="Maroon">s</font></span><a href="tarski.html#K2">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> )
 
<b>by </b><i><a class="ref" href="ordinal1.html#D2">ORDINAL1:def 2</a></i>;<br/>
<a NAME="E10:2_1_1_1"/><b>then </b>
( <font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T37">ZFMISC_1:37</a>, <a class="ref" href="zfmisc_1.html#T38">ZFMISC_1:38</a></i>;<br/>
<b>hence </b><a NAME="E11:2_1_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="classes2.html#T64">CLASSES2:64</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_2"><b>now </b></a><div class="add"><b>consider </b><font color="Maroon">A</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:2_1_1_2"/><i><font color="Green">E61</font></i>: 
for <font color="Olive">o</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> iff ( <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">o</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i><b>consider </b><font color="Maroon">B</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:2_1_1_2"/><i><font color="Green">E62</font></i>: 
for <font color="Olive">o</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> iff ( <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">o</font>] ) )
 <b>from </b><i><a class="ref" href="xboole_0.html#S1">XBOOLE_0:sch 1</a>();<br/></i><a NAME="E5:2_1_1_2"/>
 ex <font color="Olive">g</font> being  <a href="funct_1.html#NM1">Function</a> st <br/>(  <a href="relat_1.html#K1">dom</a> <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; <font color="Maroon">x</font> <a href="zf_fund1.html#K1" target="_self">(#)</a> <font color="Maroon">y</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Olive">g</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_2_1"><b>proof </b></a><div class="add">

<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">a<sub>1</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span>;<br/>
<b>consider </b><font color="Maroon">g</font> being   <a href="funct_1.html#NM1">Function</a><b> such that </b><br/><a NAME="E2:2_1_1_2_1"/><i><font color="Green">E63</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; ( for <font color="Olive">o</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span> holds <br/><font color="Maroon">g</font> <a href="funct_1.html#K1">.</a> <font color="Olive">o</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">o</font>) ) )
 <b>from </b><i><a class="ref" href="funct_1.html#S3">FUNCT_1:sch 3</a>();<br/></i>
<b>take </b>
<font color="Maroon">g</font>
;<br/>

<b>thus </b><a NAME="E3:2_1_1_2_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E4:2_1_1_2_1"/>
<font color="Maroon">x</font> <a href="zf_fund1.html#K1" target="_self">(#)</a> <font color="Maroon">y</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_2_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">o</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="E1:2_1_1_2_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> <a href="zf_fund1.html#K1" target="_self">(#)</a> <font color="Maroon">y</font>
 ;<br/>

<b>then consider </b><font color="Maroon">p</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">q</font> being    <a href="hidden.html#M1">set</a> , <font color="Maroon">r</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:2_1_1_2_1_1"/><i><font color="Green">E64</font></i>: 
( <font color="Maroon">o</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font> )
 <b>by </b><i/>;<br/>
<b>set </b><font color="Maroon">s</font> = <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">p</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span>;<br/>
<a NAME="E4:2_1_1_2_1_1"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> )
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:2_1_1_2_1_1"/><b>then </b><i><font color="Green">E65</font></i>: 
<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">p</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>then </b><font color="Maroon">g</font> <a href="funct_1.html#K1">.</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">p</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> = 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K4">[</a><span class="default"><span class="p5"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span>,<span class="p5"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a> </span>)</span> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K4">[</a><span class="default"><span class="p5"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span>,<span class="p5"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i/>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4"><a href="tarski.html#K4">[</a><span class="default"><span class="p5"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span>,<span class="p5"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">q</font></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">r</font></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K2">`2</a> </span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<font color="Maroon">o</font>
<b>by </b><i>, <a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
;<br/>
<b>hence </b><a NAME="E7:2_1_1_2_1_1"/>
<font color="Maroon">o</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">g</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>


</div><b>end;</b></div>


</div><b>end;</b></div><a NAME="E6:2_1_1_2"/><b>then </b><i><font color="Green">E66</font></i>: 
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="zf_fund1.html#K1" target="_self">(#)</a> <font color="Maroon">y</font></span>)</span> <a href="card_1.html#NR1" target="_self">&lt;=`</a>  <a href="card_1.html#K1">Card</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 <b>by </b><i><a class="ref" href="card_1.html#T28">CARD_1:28</a></i>;<br/><a NAME="E7:2_1_1_2"/>
( <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1_1_2_2"><b>proof </b></a><div class="add">

<a NAME="E1:2_1_1_2_2"/>
for <font color="Olive">o</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:2_1_1_2_2"/>
<font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>

<a NAME="E3:2_1_1_2_2"/>
for <font color="Olive">o</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> holds <br/><font color="Olive">o</font> <a href="hidden.html#R2">in</a> <font color="Maroon">y</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:2_1_1_2_2"/>
<font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


</div><b>end;</b></div><a NAME="E8:2_1_1_2"/><b>then </b>
( <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> &amp; <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font> )
 <b>by </b><i><a class="ref" href="classes1.html#D1">CLASSES1:def 1</a></i>;<br/><a NAME="E9:2_1_1_2"/><b>then </b>
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 <b>by </b><i><a class="ref" href="classes2.html#T67">CLASSES2:67</a></i>;<br/><a NAME="E10:2_1_1_2"/><b>then </b>
 <a href="card_1.html#K1">Card</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><font color="Maroon">A</font>,<font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">V</font>
 <b>by </b><i><a class="ref" href="classes2.html#T1">CLASSES2:1</a></i>;<br/><b>hence </b><a NAME="E11:2_1_1_2"/>
 <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="zf_fund1.html#K1" target="_self">(#)</a> <font color="Maroon">y</font></span>)</span> <a href="card_1.html#NR2" target="_self">&lt;`</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="ordinal1.html#T22">ORDINAL1:22</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:2_1_1"/>
<font color="Maroon">x</font> <a href="zf_fund1.html#K1" target="_self">(#)</a> <font color="Maroon">y</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">V</font>
 <b>by </b><i>, <a class="ref" href="classes1.html#T2">CLASSES1:2</a></i>;<br/>


</div>
