<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">f1</font> =  <a href="twoscomp.html#K4">and2b</a> ;<br/>
<b>set </b><font color="Maroon">f2</font> =  <a href="twoscomp.html#K4">and2b</a> ;<br/>
<b>set </b><font color="Maroon">f3</font> =  <a href="twoscomp.html#K4">and2b</a> ;<br/>
<b>set </b><font color="Maroon">f4</font> =  <a href="twoscomp.html#K29">nor3</a> ;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<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="gfacirc1.html#K44" target="_self">GFA3CarryCirc</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span>;<br/>



<b>set </b><font color="Maroon">xy</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">y</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>set </b><font color="Maroon">yz</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">y</font>,<font color="Maroon">z</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>set </b><font color="Maroon">zx</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">z</font>,<font color="Maroon">x</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span>;<br/>
<b>let </b><font color="Maroon">a1</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> , <font color="Maroon">a2</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> , <font color="Maroon">a3</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>

<b>assume </b><a NAME="E1:162"/><i><font color="Green">E27</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <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">y</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <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">y</font>,<font color="Maroon">z</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <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">z</font>,<font color="Maroon">x</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span> )
 ;<br/>

<b>set </b><font color="Maroon">S</font> =  <a href="gfacirc1.html#K43" target="_self">GFA3CarryStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>;<br/>
<a NAME="E2:162"/><i><font color="Green">E32</font></i>: 
 <a href="msafree2.html#K4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K43" target="_self">GFA3CarryStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K43" target="_self">GFA3CarryStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T37">FACIRC_1:37</a></i>;<br/>
<a NAME="E3:162"/><i><font color="Green">E33</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</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="gfacirc1.html#K43" target="_self">GFA3CarryStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4">CIRCUIT1:4</a></i>;<br/>
<b>reconsider </b><font color="Maroon">xy</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">y</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span>, <font color="Maroon">yz</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">y</font>,<font color="Maroon">z</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span>, <font color="Maroon">zx</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">z</font>,<font color="Maroon">x</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</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="gfacirc1.html#K43" target="_self">GFA3CarryStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span> <b>by </b><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="twoscomp.html#K1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K45" target="_self">GFA3CarryOutput</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span> = 
<a href="twoscomp.html#K29">nor3</a>  <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">xy</font>,<font color="Maroon">yz</font>,<font color="Maroon">zx</font></span><a href="facirc_1.html#K7">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#T14" target="_self">Th14</a>, <a class="ref" href="facirc_1.html#T35">FACIRC_1:35</a></i>
<br/>.= 
<a href="twoscomp.html#K29">nor3</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">a3</font></span><a href="facirc_1.html#K7">*&gt;</a></span>
<b>by </b><i>, , <a class="ref" href="finseq_2.html#T146">FINSEQ_2:146</a></i>
<br/>.= 
 <a href="margrel1.html#K9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">a1</font> <a href="binarith.html#K1">'or'</a> <font color="Maroon">a2</font></span>)</span> <a href="binarith.html#K1">'or'</a> <font color="Maroon">a3</font></span>)</span>
<b>by </b><i><a class="ref" href="twoscomp.html#D28">TWOSCOMP:def 28</a></i>
;<br/>


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