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<b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c1">S</font>;<br/>

<b>assume </b><a NAME="E1:38_1_1"/><i><font color="Green" title="E20">A1</font></i>: 
<font color="Maroon" title="c2">A</font> is <a href="circcmb3.html#V5" title="CIRCCMB3:attr.5">one-gate</a>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">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="c4">n</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> , <font color="Maroon" title="c5">p</font> being    <a href="circcomb.html#M1" title="CIRCCOMB:mode.1">FinSeqLen</a> of <font color="Maroon" title="c4">n</font>, <font color="Maroon" title="c6">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c4">n</font> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c3">X</font><b> such that </b><br/><a NAME="E3:38_1_1"/><i><font color="Green" title="E21">A2</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="c5">p</font>,<font color="Maroon" title="c6">f</font> &amp; <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circcomb.html#K9" title="CIRCCOMB:func.9">1GateCircuit</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">f</font> )
 <b>by </b><i><a class="ref" href="circcmb3.html#D7" target="_self" title="CIRCCMB3:def.7">Def7</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">S1</font> = <font color="Maroon" title="c1">S</font> as  <a href="circcmb3.html#V4" title="CIRCCMB3:attr.4">one-gate</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a>  <b>by </b><i><a class="txt" href="circcmb3.html#E3:38_1_1"><i><font color="Green" title="E21">A2</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">A1</font> = <font color="Maroon" title="c2">A</font> as  <a href="circcmb3.html#V5" title="CIRCCMB3:attr.5">one-gate</a> <a href="circuit1.html#NM1" title="CIRCUIT1:NM.1">Circuit</a> of <font color="Maroon" title="c7">S1</font> <b>by </b><i><a class="txt" href="circcmb3.html#E1:38_1_1"><i><font color="Green" title="E20">A1</font></i></a></i>;<br/>
<b>take </b>
1
; <i><font color="Red">:: according to </font></i><a class="ref" href="circcmb3.html#D3" target="_self" title="CIRCCMB3:def.3">CIRCCMB3:def 3</a><br/>

<b>let </b><font color="Maroon" title="c9">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c2">A</font>;<br/>

<b>reconsider </b><font color="Maroon" title="c10">s1</font> = <font color="Maroon" title="c9">s</font> as   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <font color="Maroon" title="c8">A1</font> ;<br/>
<a NAME="E7:38_1_1"/>
 <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c10">s1</font> is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>
 
<b>by </b><i><a class="ref" href="circcmb3.html#T20" target="_self" title="CIRCCMB3:th.20">Th20</a></i>;<br/>
<b>hence </b><a NAME="E8:38_1_1"/>
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c9">s</font>,1 is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>
 <b>by </b><i><a class="ref" href="facirc_1.html#T14" title="FACIRC_1:th.14">FACIRC_1:14</a></i>;<br/>


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