<?xml version="1.0"?>
<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>  = <font color="Maroon">F<sub>4</sub></font>();<br/>
<b>set </b><font color="Maroon">c<sub>1</sub></font> = <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>;<br/>
<a NAME="E1:42_1"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:42_1_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>()
 ;<br/>

<a NAME="E2:42_1_1"/>
( <font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> &amp; <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<b>hence </b><a NAME="E3:42_1_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>3</sub></font>) <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:42_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">F<sub>1</sub></font>() <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">F<sub>2</sub></font>() <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></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="E3:42_1"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> holds <br/>( ( for <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> ) iff <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>;<br/>

<i><font color="Green">E31</font></i>: <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() = 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>()
<b>by </b><i><a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="txt" href="stirl2_1.html#E2:42"><i><font color="Green">E26</font></i></a>, <a class="ref" href="zfmisc_1.html#T67">ZFMISC_1:67</a></i>
;<br/>
<b>thus </b><a NAME="E2:42_1_2"/>
( ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> ) implies <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_2_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:42_1_2_2"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E2:42_1_2_2"/>
<font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E3:42_1_2_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>()
 <b>by </b><i><a class="txt" href="stirl2_1.html#E1:42_1_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="stirl2_1.html#E1:42_1_2_2"><i><font color="Green">E32</font></i></a></i>;<br/>


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

<b>thus </b><a NAME="E3:42_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() implies for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="stirl2_1.html#E1:42_1_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E4:42_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> st ( for <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>2</sub></font>) <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> ) holds <br/>( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] iff <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()] )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>;<br/>

<b>assume </b><a NAME="E1:42_1_3"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 ;<br/>

<a NAME="E2:42_1_3"/>
<font color="Maroon">F<sub>4</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>()
 
<b>by </b><i><a class="txt" href="stirl2_1.html#E3:42_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="stirl2_1.html#E1:42_1_3"><i><font color="Green">E32</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:42_1_3"/>
( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] iff <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()] )
 <b>by </b><i><a class="txt" href="stirl2_1.html#E3:42"><i><font color="Green">E27</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>2</sub></font>) ) ) </span>}</span> ;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() ) </span>}</span> ;<br/>
<a NAME="E5:42_1"/><i><font color="Green">E32</font></i>: 
 <a href="card_1.html#K1">Card</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()] </span>}</span>  <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>2</sub></font>) ) ) </span>}</span> 
 
<b>from </b><i><a class="ref" href="stirl2_1.html#S3" target="_self">STIRL2_1:sch 3</a>(<a class="txt" href="stirl2_1.html#E1:42_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="stirl2_1.html#E2:42_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="stirl2_1.html#E1:42"><i><font color="Green">E25</font></i></a>, <a class="txt" href="stirl2_1.html#E4:42_1"><i><font color="Green">E31</font></i></a>);<br/></i>
<a NAME="E6:42_1"/><i><font color="Green">E33</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>2</sub></font>) ) ) </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() ) </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_4"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></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="E1:42_1_4"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>2</sub></font>) ) ) </span>}</span> 
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span><b> such that </b><br/><a NAME="E3:42_1_4"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) ) )
 <b>by </b><i><a class="txt" href="stirl2_1.html#E1:42_1_4"><i><font color="Green">E34</font></i></a></i>;<br/>
<a NAME="E4:42_1_4"/>
<font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>()
 
<b>by </b><i><a class="txt" href="stirl2_1.html#E3:42_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="stirl2_1.html#E3:42_1_4"><i><font color="Green">E35</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:42_1_4"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() ) </span>}</span> 
 <b>by </b><i><a class="txt" href="stirl2_1.html#E3:42_1_4"><i><font color="Green">E35</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:42_1"/>
<span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() ) </span>}</span>  <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>2</sub></font>) ) ) </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_1_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>5</sub></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="E1:42_1_5"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() ) </span>}</span> 
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span><b> such that </b><br/><a NAME="E3:42_1_5"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() )
 <b>by </b><i><a class="txt" href="stirl2_1.html#E1:42_1_5"><i><font color="Green">E34</font></i></a></i>;<br/>
<a NAME="E4:42_1_5"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="stirl2_1.html#E3:42_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="stirl2_1.html#E3:42_1_5"><i><font color="Green">E35</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:42_1_5"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="subset_1.html#K6">\</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/><font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>2</sub></font>) ) ) </span>}</span> 
 <b>by </b><i><a class="txt" href="stirl2_1.html#E3:42_1_5"><i><font color="Green">E35</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E8:42_1"/>
 <a href="card_1.html#K1">Card</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>() : <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()] </span>}</span>  <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span> : ( <font color="Maroon">P<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">F<sub>1</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>3</sub></font>()</span><a href="tarski.html#K1">}</a></span>,<font color="Maroon">F<sub>2</sub></font>() <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">F<sub>4</sub></font>()</span><a href="tarski.html#K1">}</a></span>] &amp;  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="partfun1.html#K2">|</a> <font color="Maroon">F<sub>1</sub></font>()</span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Olive">b<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>() ) </span>}</span> 
 <b>by </b><i><a class="txt" href="stirl2_1.html#E5:42_1"><i><font color="Green">E32</font></i></a>, <a class="txt" href="stirl2_1.html#E6:42_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


</div>
