<?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> be    <a href="subset_1.html#M1">Element</a> of  <a href="circcomb.html#K10">BOOLEAN</a> ;<br/>

<b>thus </b> <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K4">'xor'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
 <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="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K12">'&amp;'</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>
<b>by </b><i><a class="ref" href="binarith.html#D2">BINARITH:def 2</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="margrel1.html#K12">'&amp;'</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> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K12">'&amp;'</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>
<b>by </b><i><a class="ref" href="binarith.html#T10">BINARITH:10</a></i>
<br/>.= 
<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> <font color="Maroon">c<sub>1</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>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> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K12">'&amp;'</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>
<b>by </b><i><a class="ref" href="binarith.html#T9">BINARITH:9</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <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>2</sub></font></span>)</span></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <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="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>2</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T9">BINARITH:9</a></i>
<br/>.= 
<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> <font color="Maroon">c<sub>2</sub></font></span>)</span></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>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</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> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T22">BINARITH:22</a></i>
<br/>.= 
<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> <font color="Maroon">c<sub>2</sub></font></span>)</span></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>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<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="binarith.html#K3">'or'</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>2</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T22">BINARITH:22</a></i>
<br/>.= 
<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> <font color="Maroon">c<sub>2</sub></font></span>)</span></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>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<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="binarith.html#K3">'or'</a> <a href="margrel1.html#K7">FALSE</a> </span>)</span>
<b>by </b><i><a class="ref" href="margrel1.html#T46">MARGREL1:46</a></i>
<br/>.= 
<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> <font color="Maroon">c<sub>2</sub></font></span>)</span></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>1</sub></font></span>)</span></span>)</span> <a href="binarith.html#K3">'or'</a> <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>
<b>by </b><i><a class="ref" href="binarith.html#T7">BINARITH:7</a></i>
<br/>.= 
<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="binarith.html#K3">'or'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="margrel1.html#K12">'&amp;'</a> <span class="p3">(<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="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="margrel1.html#K12">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T22">BINARITH:22</a></i>
<br/>.= 
<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="binarith.html#K3">'or'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K7">FALSE</a>  <a href="binarith.html#K3">'or'</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>2</sub></font></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="margrel1.html#T46">MARGREL1:46</a></i>
<br/>.= 
<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> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="margrel1.html#K12">'&amp;'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="binarith.html#K3">'or'</a> <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>
<b>by </b><i><a class="ref" href="binarith.html#T7">BINARITH:7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K4">'xor'</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="binarith.html#D2">BINARITH:def 2</a></i>
;<br/>

<b>hence </b> <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K4">'xor'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<a href="twoscomp.html#K15">xor2a</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D14">TWOSCOMP:def 14</a></i>
<br/>.= 
<a href="gfacirc1.html#K4" target="_self">xor2c</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="gfacirc1.html#T4" target="_self">Th4</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K4">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self">Def4</a></i>
;<br/><br/>

<b>thus </b><span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binarith.html#K4">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> = 
<a href="twoscomp.html#K16">xor2b</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D15">TWOSCOMP:def 15</a></i>
<br/>.= 
<a href="twoscomp.html#K14">xor2</a>  <a href="funct_1.html#K1">.</a> <span class="p1"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#T10">TWOSCOMP:10</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="binarith.html#K4">'xor'</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="twoscomp.html#D13">TWOSCOMP:def 13</a></i>
;<br/>


</div>
