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

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">X</font> be  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>









<b>assume </b><a NAME="E1:18"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> &amp; not <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> )
 ;<br/>

<b>set </b><font color="Maroon">F1</font> = <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span> ;<br/>
<b>set </b><font color="Maroon">F2</font> = <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span> ;<br/>
<a NAME="E2:18"/><i><font color="Green">E50</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="card_fin.html#K1" target="_self">Choose</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1</span>)</span>,<font color="Maroon">x</font>,<font color="Maroon">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x1</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="E1:18_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span> 
 ;<br/>

<a NAME="E2:18_1"/>
 ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> st <br/>( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:18_1"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="card_fin.html#K1" target="_self">Choose</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1</span>)</span>,<font color="Maroon">x</font>,<font color="Maroon">y</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E3:18"/>
<span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="card_fin.html#K1" target="_self">Choose</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1</span>)</span>,<font color="Maroon">x</font>,<font color="Maroon">y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x1</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="E1:18_2"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span> 
 ;<br/>

<a NAME="E2:18_2"/>
 ex <font color="Olive">f</font> being  <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> st <br/>( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:18_2"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="card_fin.html#K1" target="_self">Choose</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1</span>)</span>,<font color="Maroon">x</font>,<font color="Maroon">y</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E4:18"/><b>then </b><i><font color="Green">E57</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span>  <a href="tarski.html#R1">c=</a>  <a href="card_fin.html#K1" target="_self">Choose</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1</span>)</span>,<font color="Maroon">x</font>,<font color="Maroon">y</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T8">XBOOLE_1:8</a></i>;<br/>
<a NAME="E5:18"/><i><font color="Green">E58</font></i>: 
 <a href="card_fin.html#K1" target="_self">Choose</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1</span>)</span>,<font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_3"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x1</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="E1:18_3"/><i><font color="Green">E59</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="card_fin.html#K1" target="_self">Choose</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1</span>)</span>,<font color="Maroon">x</font>,<font color="Maroon">y</font>
 ;<br/>

<b>consider </b><font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span><b> such that </b><br/><a NAME="E3:18_3"/><i><font color="Green">E60</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 )
 <b>by </b><i>, </i>;<br/>
<a NAME="E4:18_3"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<a NAME="E5:18_3"/><b>then </b>
( <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relset_1.html#K4">dom</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E6:18_3"/><b>then </b>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E7:18_3"/><b>then </b>
( <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> or <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/>
<a NAME="E8:18_3"/><b>then </b>
( <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  or <font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span>  )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E9:18_3"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:18"/>
<span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  <a href="xboole_0.html#R1">misses</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_4"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:18_4"/>
<span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span> 
 ;<br/>

<a NAME="E2:18_4"/><b>then </b>
<span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  <a href="xboole_0.html#K3">/\</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span>  <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>then consider </b><font color="Maroon">x1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:18_4"/><i><font color="Green">E61</font></i>: 
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  <a href="xboole_0.html#K3">/\</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span> 
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/>
<a NAME="E5:18_4"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span> 
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">f1</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span><b> such that </b><br/><a NAME="E7:18_4"/><i><font color="Green">E62</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f1</font> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 ;<br/>
<a NAME="E8:18_4"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span> 
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>then consider </b><font color="Maroon">f2</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span><b> such that </b><br/><a NAME="E10:18_4"/><i><font color="Green">E63</font></i>: 
( <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font> &amp;  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Maroon">f2</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 ;<br/>
<b>thus </b><a NAME="E11:18_4"/>
contradiction
 <b>by </b><i>, , </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E7:18"/>
( <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  <a href="xboole_0.html#K2">\/</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span>  <a href="hidden.html#R1">=</a>  <a href="card_fin.html#K1" target="_self">Choose</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1</span>)</span>,<font color="Maroon">x</font>,<font color="Maroon">y</font> &amp; <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> ) </span>}</span>  <a href="xboole_0.html#R1">misses</a> <span class="p1">{<span class="default"> <font color="Olive">f</font> where <font color="Olive">f</font> is   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">X</font> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">z</font></span><a href="tarski.html#K1">}</a></span>,<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K2">}</a></span> : (  <a href="card_1.html#K1">Card</a> <span class="p1">(<span class="default"><font color="Olive">f</font> <a href="relset_1.html#K11">"</a> <span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font> <a href="binop_2.html#K23">+</a> 1 &amp; <font color="Olive">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">z</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> ) </span>}</span>  )
 <b>by </b><i>, , <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


</div>
