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

<b>let </b><font color="Maroon">F</font> be  <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">F</font>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">J</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:21"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="hallmar1.html#K2" target="_self">Cut</a> <font color="Maroon">A</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span> &amp; <font color="Maroon">J</font> <a href="tarski.html#R1">c=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="hallmar1.html#K2" target="_self">Cut</a> <font color="Maroon">A</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span> )
 <b>and </b><br/><a NAME="E2:21"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">J</font>
 ;<br/>

 <a href="hallmar1.html#K1" target="_self">union</a> <span class="p1">(<span class="default"><a href="hallmar1.html#K2" target="_self">Cut</a> <font color="Maroon">A</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span>,<font color="Maroon">J</font> = 
<span class="p1">(<span class="default"><a href="hallmar1.html#K1" target="_self">union</a> <span class="p2">(<span class="default"><a href="hallmar1.html#K2" target="_self">Cut</a> <font color="Maroon">A</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hallmar1.html#K2" target="_self">Cut</a> <font color="Maroon">A</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="hallmar1.html#T1" target="_self">Th1</a>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><a href="hallmar1.html#K1" target="_self">union</a> <font color="Maroon">A</font>,<span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="hallmar1.html#K2" target="_self">Cut</a> <font color="Maroon">A</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="hallmar1.html#K1" target="_self">union</a> <font color="Maroon">A</font>,<span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="subset_1.html#K6">\</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>
<b>by </b><i><a class="ref" href="hallmar1.html#T1" target="_self">Th1</a>, </i>
;<br/>
<b>hence </b><a NAME="E4:21"/>
 <a href="hallmar1.html#K1" target="_self">union</a> <span class="p1">(<span class="default"><a href="hallmar1.html#K2" target="_self">Cut</a> <font color="Maroon">A</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font></span>)</span>,<font color="Maroon">J</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="hallmar1.html#K1" target="_self">union</a> <font color="Maroon">A</font>,<span class="p2">(<span class="default"><font color="Maroon">J</font> <a href="subset_1.html#K6">\</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">i</font></span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="subset_1.html#K6">\</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>
 ;<br/>


</div>
