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<b>let </b><font color="Maroon" title="c1">x</font>, <font color="Maroon" title="c2">y</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> ;<br/>

<b>thus </b><a NAME="E1:11"/>
<a href="gfacirc1.html#K4" title="GFACIRC1:func.4">xor2c</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">x</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self" title="GFACIRC1:def.4">Def4</a></i>;<br/>

<b>thus </b><a href="gfacirc1.html#K4" title="GFACIRC1:func.4">xor2c</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span> = 
<font color="Maroon" title="c1">x</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">y</font></span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self" title="GFACIRC1:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c2">y</font>

<br/>.= 
<a href="twoscomp.html#K15" title="TWOSCOMP:func.15">xor2a</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D14" title="TWOSCOMP:def.14">TWOSCOMP:def 14</a></i>
;<br/>

<b>thus </b><a href="gfacirc1.html#K4" title="GFACIRC1:func.4">xor2c</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span> = 
<font color="Maroon" title="c1">x</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">y</font></span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self" title="GFACIRC1:def.4">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p2">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<a href="twoscomp.html#K8" title="TWOSCOMP:func.8">or2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c2">y</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D7" title="TWOSCOMP:def.7">TWOSCOMP:def 7</a></i>
<br/>.= 
<a href="twoscomp.html#K8" title="TWOSCOMP:func.8">or2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">x</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c2">y</font></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D3" title="TWOSCOMP:def.3">TWOSCOMP:def 3</a></i>
<br/>.= 
<a href="twoscomp.html#K8" title="TWOSCOMP:func.8">or2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="twoscomp.html#K4" title="TWOSCOMP:func.4">and2b</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c1">x</font>,<font color="Maroon" title="c2">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span></span>)</span></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="ref" href="twoscomp.html#D1" title="TWOSCOMP:def.1">TWOSCOMP:def 1</a></i>
;<br/>

<b>thus </b><a href="gfacirc1.html#K4" title="GFACIRC1:func.4">xor2c</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span> = 
<a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> </span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self" title="GFACIRC1:def.4">Def4</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="xboolean.html#T102" title="XBOOLEAN:th.102">XBOOLEAN:102</a></i>
;<br/>

<b>thus </b><a href="gfacirc1.html#K4" title="GFACIRC1:func.4">xor2c</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,1</span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span> = 
<a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a>  <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self" title="GFACIRC1:def.4">Def4</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/>

<b>thus </b><a href="gfacirc1.html#K4" title="GFACIRC1:func.4">xor2c</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default">1,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span> = 
<a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <a href="margrel1.html#K7" title="MARGREL1:func.7">FALSE</a> </span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self" title="GFACIRC1:def.4">Def4</a></i>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 

;<br/>

<b>thus </b><a href="gfacirc1.html#K4" title="GFACIRC1:func.4">xor2c</a>  <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default">1,1</span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span> = 
<a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a>  <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p1">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <a href="margrel1.html#K8" title="MARGREL1:func.8">TRUE</a> </span>)</span>
<b>by </b><i><a class="ref" href="gfacirc1.html#D4" target="_self" title="GFACIRC1:def.4">Def4</a></i>
<br/>.= 
1
<b>by </b><i><a class="ref" href="binarith.html#T13" title="BINARITH:th.13">BINARITH:13</a></i>
;<br/>


</div>
