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<b>set </b><font color="Maroon" title="c1">f</font> =  <a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> ;<br/>
<b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:45"/><i><font color="Green" title="E30">A1</font></i>: 
<font color="Maroon" title="c4">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 ;<br/>

<b>set </b><font color="Maroon" title="c5">xy</font> = <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>;<br/>
<b>set </b><font color="Maroon" title="c6">A</font> =  <a href="gfacirc1.html#K11" title="GFACIRC1:func.11">GFA0AdderCirc</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>;<br/>
<b>let </b><font color="Maroon" title="c7">s</font> be   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K11" title="GFACIRC1:func.11">GFA0AdderCirc</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font></span>)</span>;<br/><b>let </b><font color="Maroon" title="c8">a1</font>, <font color="Maroon" title="c9">a2</font>, <font color="Maroon" title="c10">a3</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="circcomb.html#K10" title="CIRCCOMB:func.10">BOOLEAN</a> ;<br/>



<b>assume </b><a NAME="E2:45"/><i><font color="Green" title="E31">A2</font></i>: 
( <font color="Maroon" title="c8">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> &amp; <font color="Maroon" title="c9">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c10">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">z</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c11">C</font> =  <a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,2</span>)</span> <a href="twoscomp.html#K1" title="TWOSCOMP:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K12" title="GFACIRC1:func.12">GFA0AdderOutput</a> <font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font></span>)</span> = 
<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</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#K14" title="TWOSCOMP:func.14">xor2</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="c8">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span></span>)</span>,<font color="Maroon" title="c10">a3</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
<b>by </b><i><a class="txt" href="gfacirc1.html#E1:45"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="gfacirc1.html#E2:45"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="facirc_1.html#T62" title="FACIRC_1:th.62">FACIRC_1:62</a></i>
<br/>.= 
<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</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"><font color="Maroon" title="c8">a1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c9">a2</font></span>)</span>,<font color="Maroon" title="c10">a3</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#D13" title="TWOSCOMP:def.13">TWOSCOMP:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">a1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c9">a2</font></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c10">a3</font>
<b>by </b><i><a class="ref" href="twoscomp.html#D13" title="TWOSCOMP:def.13">TWOSCOMP:def 13</a></i>
;<br/>

<a NAME="E4:45"/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</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="c8">a1</font>,<font color="Maroon" title="c9">a2</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>
 
<b>by </b><i><a class="txt" href="gfacirc1.html#E1:45"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="gfacirc1.html#E2:45"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="facirc_1.html#T62" title="FACIRC_1:th.62">FACIRC_1:62</a></i>;<br/>
<b>hence </b><a NAME="E5:45"/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6" title="FACIRC_1:func.6">&lt;*</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K14" title="TWOSCOMP:func.14">xor2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c9">a2</font>
 <b>by </b><i><a class="ref" href="twoscomp.html#D13" title="TWOSCOMP:def.13">TWOSCOMP:def 13</a></i>;<br/>

<b>thus </b><a NAME="E6:45"/>
( <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">a1</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">a2</font> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c7">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">a3</font> )
 <b>by </b><i><a class="txt" href="gfacirc1.html#E1:45"><i><font color="Green" title="E30">A1</font></i></a>, <a class="txt" href="gfacirc1.html#E2:45"><i><font color="Green" title="E31">A2</font></i></a>, <a class="ref" href="facirc_1.html#T62" title="FACIRC_1:th.62">FACIRC_1:62</a></i>;<br/>


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