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<div class="add">

<b>let </b><font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</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" target="_self">FinSeqLen</a> of <font color="Maroon">n</font>;<br/>







<b>thus </b><a NAME="E1:91"/><i><font color="Green">E24</font></i>: 
 <a href="circcomb.html#K9" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font> is <a href="circcomb.html#V4" target="_self">gate`2=den</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="91_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">g</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D10" target="_self">CIRCCOMB:def 10</a><br/>

<b>assume </b><a NAME="E1:91_1"/>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span>
 ;<br/>

<a NAME="E2:91_1"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">g</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/>;<br/>
<b>hence </b><font color="Maroon">g</font> = 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="mcart_1.html#K1">`1</a> </span>)</span>,<span class="p2">(<span class="default">the <a href="msualg_1.html#U5">Charact</a> of <span class="p3">(<span class="default"><a href="circcomb.html#K9" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">g</font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i>, </i>
;<br/><br/>


</div><b>end;</b></div>

<b>take </b>
 <a href="circcomb.html#K9" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D11" target="_self">CIRCCOMB:def 11</a><br/>

<b>thus </b><a NAME="E2:91"/>
 <a href="circcomb.html#K9" target="_self">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font> is <a href="circcomb.html#V4" target="_self">gate`2=den</a>
 <b>by </b><i/>;<br/>


</div>
