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<b>consider </b><font color="Maroon" title="c2">X</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , <font color="Maroon" title="c3">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c4">p</font> being    <a href="circcomb.html#M1" title="CIRCCOMB:mode.1">FinSeqLen</a> of <font color="Maroon" title="c3">n</font>, <font color="Maroon" title="c5">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c3">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><b> such that </b><br/><a NAME="E2:30_1_1"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circcomb.html#K7" title="CIRCCOMB:func.7">1GateCircStr</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">f</font>
 <b>by </b><i><a class="ref" href="circcmb3.html#D6" target="_self" title="CIRCCMB3:def.6">Def6</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">A</font> =  <a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c4">p</font>,<font color="Maroon" title="c5">f</font> as  <a href="msafree2.html#V4" title="MSAFREE2:attr.4">locally-finite</a>  <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font> <b>by </b><i><a class="txt" href="circcmb3.html#E2:30_1_1"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">A</font>
;<br/>

<b>thus </b><a NAME="E4:30_1_1"/>
( <font color="Maroon" title="c6">A</font> is <a href="circcmb3.html#V5" title="CIRCCMB3:attr.5">one-gate</a> &amp; <font color="Maroon" title="c6">A</font> is <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> )
 <b>by </b><i><a class="txt" href="circcmb3.html#E2:30_1_1"><i><font color="Green" title="E17">A1</font></i></a></i>;<br/>


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