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

<b>consider </b><font color="Maroon">X</font> being  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">n</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">p</font> being    <a href="circcomb.html#M1">FinSeqLen</a> of <font color="Maroon">n</font>, <font color="Maroon">f</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">X</font>,<font color="Maroon">X</font><b> such that </b><br/><a NAME="E2:32_1_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="circcomb.html#K7">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>
 <b>by </b><i/>;<br/>
<a NAME="E3:32_1_1"/><i><font color="Green">E36</font></i>: 
the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="circcomb.html#D6">CIRCCOMB:def 6</a></i>;<br/>
<a NAME="E4:32_1_1"/>
 <a href="circcmb3.html#K5" target="_self">Output</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T31">ZFMISC_1:31</a></i>;<br/>
<b>hence </b><a NAME="E5:32_1_1"/>
 <a href="circcmb3.html#K5" target="_self">Output</a> <font color="Maroon">S</font> is <a href="facirc_1.html#V1">pair</a>
 ;<br/>


</div>
