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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>

<b>thus </b><a href="twoscomp.html#K17" target="_self">and3</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="twoscomp.html#D16" target="_self">Def16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="binarith.html#T12">BINARITH:12</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T12">BINARITH:12</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>

<br/>.= 
<a href="twoscomp.html#K32" target="_self">nor3c</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D31" target="_self">Def31</a></i>
;<br/>

<b>thus </b><a href="twoscomp.html#K18" target="_self">and3a</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="twoscomp.html#D17" target="_self">Def17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="binarith.html#T12">BINARITH:12</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T12">BINARITH:12</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T20">BINARITH:20</a></i>
<br/>.= 
<a href="twoscomp.html#K31" target="_self">nor3b</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D30" target="_self">Def30</a></i>
;<br/>

<b>thus </b><a href="twoscomp.html#K19" target="_self">and3b</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="twoscomp.html#D18" target="_self">Def18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="binarith.html#T12">BINARITH:12</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T12">BINARITH:12</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="binarith.html#K3">'or'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span>

<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T20">BINARITH:20</a></i>
<br/>.= 
<a href="twoscomp.html#K30" target="_self">nor3a</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D29" target="_self">Def29</a></i>
;<br/>

<b>thus </b><a href="twoscomp.html#K20" target="_self">and3c</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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="twoscomp.html#D19" target="_self">Def19</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T12">BINARITH:12</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p5">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p0">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T12">BINARITH:12</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K3">'or'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p4">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K3">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K11">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span>

<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K3">'or'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>

<br/>.= 
<a href="twoscomp.html#K29" target="_self">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">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="facirc_1.html#K7">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D28" target="_self">Def28</a></i>
;<br/>


</div>
