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<b>let </b><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>;<br/><b>let </b><font color="Maroon" title="c2">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c1">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c2">X</font>;<br/><b>let </b><font color="Maroon" title="c4">p</font> be    <a href="circcomb.html#M1" title="CIRCCOMB:mode.1">FinSeqLen</a> of <font color="Maroon" title="c1">n</font>;<br/>







<b>thus </b><a NAME="E1:90"/><i><font color="Green" title="E55">A1</font></i>: 
 <a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font> is <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="90_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">g</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D10" target="_self" title="CIRCCOMB:def.10">CIRCCOMB:def 10</a><br/>

<b>assume </b><a NAME="E1:90_1"/>
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span>
 ;<br/>

<a NAME="E2:90_1"/><b>then </b><i><font color="Green" title="E56">A2</font></i>: 
<font color="Maroon" title="c5">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 
<b>by </b><i><a class="ref" href="circcomb.html#T48" target="_self" title="CIRCCOMB:th.48">Th48</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c5">g</font> = 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<font color="Maroon" title="c3">f</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a> </span>)</span>,<span class="p2">(<span class="default">the <a href="msualg_1.html#U5" title="MSUALG_1:sel.5">Charact</a> of <span class="p3">(<span class="default"><a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">g</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
<b>by </b><i><a class="txt" href="circcomb.html#E2:90_1"><i><font color="Green" title="E56">A2</font></i></a>, <a class="ref" href="circcomb.html#D14" target="_self" title="CIRCCOMB:def.14">Def14</a></i>
;<br/><br/>


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

<b>take </b>
 <a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D11" target="_self" title="CIRCCOMB:def.11">CIRCCOMB:def 11</a><br/>

<b>thus </b><a NAME="E2:90"/>
 <a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c3">f</font> is <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a>
 <b>by </b><i><a class="txt" href="circcomb.html#E1:90"><i><font color="Green" title="E55">A1</font></i></a></i>;<br/>


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