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<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> ;<br/>







<b>set </b><font color="Maroon">f</font> =  <a href="hallmar1.html#K2" target="_self">Cut</a> <font color="Maroon">A</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font>;<br/>
<b>assume </b><a NAME="E1:32"/><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> <font color="Maroon">A</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> )
 ;<br/>

<a NAME="E2:32"/><i><font color="Green">E24</font></i>: 
 <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> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:32"/><i><font color="Green">E25</font></i>: 
for <font color="Olive">j</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">j</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">A</font> &amp; <font color="Olive">j</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">i</font> holds <br/><font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font> <a href="hidden.html#R1">=</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> <a href="funct_1.html#K1">.</a> <font color="Olive">j</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:32"/>
<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> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<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="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, , </i>;<br/>
<b>hence </b><a NAME="E5:32"/>
 <a href="hallmar1.html#K2" target="_self">Cut</a> <font color="Maroon">A</font>,<font color="Maroon">i</font>,<font color="Maroon">x</font> is    <a href="hallmar1.html#M1" target="_self">Reduction</a> of <font color="Maroon">A</font>,<font color="Maroon">i</font>
 <b>by </b><i>, , </i>;<br/>


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