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<b>let </b><font color="Maroon">S</font> be  <a href="circcmb3.html#V4" target="_self">one-gate</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">A</font> be  <a href="circcmb3.html#V5" target="_self">one-gate</a> <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">n</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <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>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="circcomb.html#M1">FinSeqLen</a> of <font color="Maroon">n</font>;<br/>











<b>assume </b><a NAME="E1:35"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="circcomb.html#K9">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>
 ;<br/>

<b>consider </b><font color="Maroon">X1</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">n1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">p1</font> being    <a href="circcomb.html#M1">FinSeqLen</a> of <font color="Maroon">n1</font>, <font color="Maroon">f1</font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">n1</font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">X1</font>,<font color="Maroon">X1</font><b> such that </b><br/><a NAME="E3:35"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="circcomb.html#K7">1GateCircStr</a> <font color="Maroon">p1</font>,<font color="Maroon">f1</font> &amp; <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="circcomb.html#K9">1GateCircuit</a> <font color="Maroon">p1</font>,<font color="Maroon">f1</font> )
 <b>by </b><i/>;<br/>
<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> = 
the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span>
<b>by </b><i><a class="ref" href="circcomb.html#D6">CIRCCOMB:def 6</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U5">Charact</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K9">1GateCircuit</a> <font color="Maroon">p1</font>,<font color="Maroon">f1</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>
<br/>.= 
the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <font color="Maroon">p1</font>,<font color="Maroon">f1</font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>
<br/>.= 
<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">p1</font>,<font color="Maroon">f1</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="E5:35"/><b>then </b>
<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> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p1</font>,<font color="Maroon">f1</font></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T6">ZFMISC_1:6</a></i>;<br/>
<a NAME="E6:35"/><b>then </b>
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">f</font> <a href="funct_2.html#R1">=</a> <font color="Maroon">f1</font> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E7:35"/>
<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/>


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