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<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>set </b><font color="Maroon">xy</font> = <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">yc</font> = <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">xc</font> = <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>;<br/>
<b>set </b><font color="Maroon">S1</font> =  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> ;<br/>
<b>set </b><font color="Maroon">A1</font> =  <a href="facirc_1.html#K10">1GateCircuit</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<a href="twoscomp.html#K3">and2a</a> ;<br/>
<b>set </b><font color="Maroon">S2</font> =  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K2">and2</a> ;<br/>
<b>set </b><font color="Maroon">A2</font> =  <a href="facirc_1.html#K10">1GateCircuit</a> <font color="Maroon">y</font>,<font color="Maroon">c</font>,<a href="twoscomp.html#K2">and2</a> ;<br/>
<b>set </b><font color="Maroon">S3</font> =  <a href="circcomb.html#K7">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> ;<br/>
<b>set </b><font color="Maroon">A3</font> =  <a href="facirc_1.html#K10">1GateCircuit</a> <font color="Maroon">x</font>,<font color="Maroon">c</font>,<a href="twoscomp.html#K3">and2a</a> ;<br/>
<b>set </b><font color="Maroon">S</font> =  <a href="fscirc_1.html#K3" target="_self">BorrowIStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>;<br/>
<b>set </b><font color="Maroon">A</font> =  <a href="fscirc_1.html#K5" target="_self">BorrowICirc</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font>;<br/>
<b>set </b><font color="Maroon">v3</font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="fscirc_1.html#K5" target="_self">BorrowICirc</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span>;<br/><b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> , <font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>



<b>assume </b><a NAME="E1:10"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c</font> )
 ;<br/>

<b>reconsider </b><font color="Maroon">v3</font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span><a href="tarski.html#K4">]</a></span> as    <a href="subset_1.html#M2">Element</a> of  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T47">FACIRC_1:47</a></i>;<br/>
<b>reconsider </b><font color="Maroon">v</font> = <font color="Maroon">v3</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="fscirc_1.html#K3" target="_self">BorrowIStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T21">FACIRC_1:21</a></i>;<br/>
<b>reconsider </b><font color="Maroon">s3</font> = <font color="Maroon">s</font> <a href="relat_1.html#K7">|</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span>)</span> as   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="facirc_1.html#K10">1GateCircuit</a> <font color="Maroon">x</font>,<font color="Maroon">c</font>,<a href="twoscomp.html#K3">and2a</a> </span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T26">FACIRC_1:26</a></i>;<br/>
<a NAME="E5:10"/><i><font color="Green">E31</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s3</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4">CIRCUIT1:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">xx</font> = <font color="Maroon">x</font>, <font color="Maroon">cc</font> = <font color="Maroon">c</font> as   <a href="msafree2.html#NM1">Vertex</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T43">FACIRC_1:43</a></i>;<br/>
<b>reconsider </b><font color="Maroon">xx</font> = <font color="Maroon">xx</font>, <font color="Maroon">cc</font> = <font color="Maroon">cc</font> as   <a href="msafree2.html#NM1">Vertex</a> of <span class="p1">(<span class="default"><a href="fscirc_1.html#K3" target="_self">BorrowIStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">c</font></span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T20">FACIRC_1:20</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">c</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span><a href="tarski.html#K4">]</a></span> = 
<span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s3</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">v</font>
<b>by </b><i><a class="ref" href="circcomb.html#T72">CIRCCOMB:72</a></i>
<br/>.= 
<a href="twoscomp.html#K3">and2a</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">s3</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">xx</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s3</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">cc</font></span>)</span></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="facirc_1.html#T50">FACIRC_1:50</a></i>
<br/>.= 
<a href="twoscomp.html#K3">and2a</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="facirc_1.html#K15">.</a> <font color="Maroon">xx</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s3</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">cc</font></span>)</span></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<a href="twoscomp.html#K3">and2a</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="facirc_1.html#K15">.</a> <font color="Maroon">xx</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">s</font> <a href="facirc_1.html#K15">.</a> <font color="Maroon">cc</font></span>)</span></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K9">'not'</a> <font color="Maroon">a</font></span>)</span> <a href="margrel1.html#K10">'&amp;'</a> <font color="Maroon">b</font>
<b>by </b><i>, <a class="ref" href="twoscomp.html#D2">TWOSCOMP:def 2</a></i>
;<br/>


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