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<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="E2:30_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/>
<b>reconsider </b><font color="Maroon">A</font> =  <a href="circcomb.html#K9">1GateCircuit</a> <font color="Maroon">p</font>,<font color="Maroon">f</font> as  <a href="msafree2.html#V4">locally-finite</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<b>thus </b><a NAME="E4:30_1_1"/>
( <font color="Maroon">A</font> is <a href="circcmb3.html#V5" target="_self">one-gate</a> &amp; <font color="Maroon">A</font> is <a href="msualg_1.html#V5">non-empty</a> )
 <b>by </b><i/>;<br/>


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