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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>





<b>set </b><font color="Maroon" title="c4">xc</font> = <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon" title="c5">S3</font> =  <a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> ;<br/>
<b>set </b><font color="Maroon" title="c6">A3</font> =  <a href="facirc_1.html#K10" title="FACIRC_1:func.10">1GateCircuit</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> ;<br/>
<b>set </b><font color="Maroon" title="c7">S</font> =  <a href="fscirc_1.html#K3" title="FSCIRC_1:func.3">BorrowIStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>;<br/>
<b>set </b><font color="Maroon" title="c8">A</font> =  <a href="fscirc_1.html#K5" title="FSCIRC_1:func.5">BorrowICirc</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font>;<br/>
<b>set </b><font color="Maroon" title="c9">v3</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>let </b><font color="Maroon" title="c10">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="fscirc_1.html#K5" title="FSCIRC_1:func.5">BorrowICirc</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c11">a</font>, <font color="Maroon" title="c12">b</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K9" title="CIRCCOMB:func.9">BOOLEAN</a> ;<br/>



<b>assume </b><a NAME="E1:10"/><i><font color="Green" title="E3">A1</font></i>: 
( <font color="Maroon" title="c11">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">x</font> &amp; <font color="Maroon" title="c12">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">c</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c13">v3</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T47" title="FACIRC_1:th.47">FACIRC_1:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c14">v</font> = <font color="Maroon" title="c13">v3</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="fscirc_1.html#K3" title="FSCIRC_1:func.3">BorrowIStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T21" title="FACIRC_1:th.21">FACIRC_1:21</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c15">s3</font> = <font color="Maroon" title="c10">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span>)</span> as   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K10" title="FACIRC_1:func.10">1GateCircuit</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T26" title="FACIRC_1:th.26">FACIRC_1:26</a></i>;<br/>
<a NAME="E5:10"/><i><font color="Green" title="E4">A2</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c15">s3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4" title="CIRCUIT1:th.4">CIRCUIT1:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">xx</font> = <font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c17">cc</font> = <font color="Maroon" title="c3">c</font> as   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" title="CIRCCOMB:func.6">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T43" title="FACIRC_1:th.43">FACIRC_1:43</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c18">xx</font> = <font color="Maroon" title="c16">xx</font>, <font color="Maroon" title="c19">cc</font> = <font color="Maroon" title="c17">cc</font> as   <a href="msafree2.html#NM1" title="MSAFREE2:NM.1">Vertex</a> of <span class="p1">(<span class="default"><a href="fscirc_1.html#K3" title="FSCIRC_1:func.3">BorrowIStr</a> <font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font>,<font color="Maroon" title="c3">c</font></span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T20" title="FACIRC_1:th.20">FACIRC_1:20</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c10">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c3">c</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> = 
<span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <font color="Maroon" title="c15">s3</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">v</font>
<b>by </b><i><a class="ref" href="circcomb.html#T72" title="CIRCCOMB:th.72">CIRCCOMB:72</a></i>
<br/>.= 
<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c15">s3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">xx</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c15">s3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">cc</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="facirc_1.html#T50" title="FACIRC_1:th.50">FACIRC_1:50</a></i>
<br/>.= 
<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="facirc_1.html#K15" title="FACIRC_1:func.15">.</a> <font color="Maroon" title="c18">xx</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c15">s3</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c19">cc</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="fscirc_1.html#E5:10"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
<br/>.= 
<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="facirc_1.html#K15" title="FACIRC_1:func.15">.</a> <font color="Maroon" title="c18">xx</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c10">s</font> <a href="facirc_1.html#K15" title="FACIRC_1:func.15">.</a> <font color="Maroon" title="c19">cc</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="fscirc_1.html#E5:10"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c12">b</font>
<b>by </b><i><a class="txt" href="fscirc_1.html#E1:10"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="twoscomp.html#D2" title="TWOSCOMP:def.2">TWOSCOMP:def 2</a></i>
;<br/>


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