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<b>consider </b><font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font> being   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">c<sub>4</sub></font> being    <a href="circcomb.html#M1">FinSeqLen</a> of <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>5</sub></font> being   <a href="funct_2.html#NM1">Function</a> of <font color="Maroon">c<sub>3</sub></font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E2:30_1_1"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="circcomb.html#K7">1GateCircStr</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="circcmb3.html#D6" target="_self">Def6</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="circcomb.html#K9">1GateCircuit</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> as  <a href="msafree2.html#V4">locally-finite</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="circcmb3.html#E2:30_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>6</sub></font>
;<br/>

<b>thus </b><a NAME="E4:30_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> is <a href="circcmb3.html#V5" target="_self">one-gate</a> &amp; <font color="Maroon">c<sub>6</sub></font> is <a href="msualg_1.html#V5">non-empty</a> )
 <b>by </b><i><a class="txt" href="circcmb3.html#E2:30_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>


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