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<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 NAME="E1:11"/>
<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> <a href="hidden.html#R1">=</a> <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/>

<b>thus </b><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> = 
<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/>.= 
<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="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> <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#D2">BINARITH:def 2</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>

<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/>.= 
<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/>

<b>thus </b><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> = 
<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/>.= 
<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="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> <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#D2">BINARITH:def 2</a></i>
<br/>.= 
<a href="twoscomp.html#K8">or2</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"><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> <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 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></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D7">TWOSCOMP:def 7</a></i>
<br/>.= 
<a href="twoscomp.html#K8">or2</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"><a href="twoscomp.html#K4">and2b</a>  <a href="funct_1.html#K1">.</a> <span class="p3"><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></span>)</span>,<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></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D3">TWOSCOMP:def 3</a></i>
<br/>.= 
<a href="twoscomp.html#K8">or2</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"><a href="twoscomp.html#K4">and2b</a>  <a href="funct_1.html#K1">.</a> <span class="p3"><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></span>)</span>,<span class="p2">(<span class="default"><a href="twoscomp.html#K2">and2</a>  <a href="funct_1.html#K1">.</a> <span class="p3"><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></span>)</span></span><a href="facirc_1.html#K6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D1">TWOSCOMP:def 1</a></i>
;<br/>

<b>thus </b><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">0,0</span><a href="facirc_1.html#K6">*&gt;</a></span> = 
<a href="margrel1.html#K7">FALSE</a>  <a href="binarith.html#K4">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K7">FALSE</a> </span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self">Def4</a>, <a class="ref" href="margrel1.html#T36">MARGREL1:36</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="binarith.html#T17">BINARITH:17</a>, <a class="ref" href="margrel1.html#T36">MARGREL1:36</a></i>
;<br/>

<b>thus </b><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">0,1</span><a href="facirc_1.html#K6">*&gt;</a></span> = 
<a href="margrel1.html#K7">FALSE</a>  <a href="binarith.html#K4">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K8">TRUE</a> </span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self">Def4</a>, <a class="ref" href="margrel1.html#T36">MARGREL1:36</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K8">TRUE</a> 
<b>by </b><i><a class="ref" href="binarith.html#T14">BINARITH:14</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="margrel1.html#T36">MARGREL1:36</a>, <a class="ref" href="margrel1.html#T41">MARGREL1:41</a></i>
;<br/>

<b>thus </b><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">1,0</span><a href="facirc_1.html#K6">*&gt;</a></span> = 
<a href="margrel1.html#K8">TRUE</a>  <a href="binarith.html#K4">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K7">FALSE</a> </span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self">Def4</a>, <a class="ref" href="margrel1.html#T36">MARGREL1:36</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K7">FALSE</a> </span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T13">BINARITH:13</a></i>
<br/>.= 
0
<b>by </b><i><a class="ref" href="margrel1.html#T36">MARGREL1:36</a></i>
;<br/>

<b>thus </b><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">1,1</span><a href="facirc_1.html#K6">*&gt;</a></span> = 
<a href="margrel1.html#K8">TRUE</a>  <a href="binarith.html#K4">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K8">TRUE</a> </span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self">Def4</a>, <a class="ref" href="margrel1.html#T36">MARGREL1:36</a></i>
<br/>.= 
 <a href="margrel1.html#K11">'not'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K11">'not'</a> <a href="margrel1.html#K8">TRUE</a> </span>)</span>
<b>by </b><i><a class="ref" href="binarith.html#T13">BINARITH:13</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="margrel1.html#T36">MARGREL1:36</a></i>
;<br/>


</div>
