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

<b>set </b><font color="Maroon">f0</font> =  <a href="gfacirc1.html#K4" target="_self">xor2c</a> ;<br/>
<b>set </b><font color="Maroon">f1</font> =  <a href="twoscomp.html#K3">and2a</a> ;<br/>
<b>set </b><font color="Maroon">f2</font> =  <a href="gfacirc1.html#K3" target="_self">and2c</a> ;<br/>
<b>set </b><font color="Maroon">f3</font> =  <a href="twoscomp.html#K4">and2b</a> ;<br/>
<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:136"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="gfacirc1.html#K4" target="_self">xor2c</a> </span><a href="tarski.html#K4">]</a></span>
 <b>and </b><br/><a NAME="E2:136"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="gfacirc1.html#K3" target="_self">and2c</a> </span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">z</font>,<font color="Maroon">x</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K4">and2b</a> </span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">z</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K6">&lt;*</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="facirc_1.html#K6">*&gt;</a></span>,<a href="twoscomp.html#K3">and2a</a> </span><a href="tarski.html#K4">]</a></span> )
 ;<br/>

<b>set </b><font color="Maroon">S</font> =  <a href="gfacirc1.html#K37" target="_self">BitGFA2Str</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>;<br/>
<b>set </b><font color="Maroon">S1</font> =  <a href="gfacirc1.html#K34" target="_self">GFA2AdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>;<br/>
<b>set </b><font color="Maroon">S2</font> =  <a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>;<br/>
<a NAME="E3:136"/><i><font color="Green">E33</font></i>: 
 <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K34" target="_self">GFA2AdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i>, <a class="ref" href="facirc_1.html#T57">FACIRC_1:57</a></i>;<br/>
<a NAME="E4:136"/><i><font color="Green">E35</font></i>: 
 <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:136"/>
 <a href="gfacirc1.html#K34" target="_self">GFA2AdderStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font> <a href="circcomb.html#R1">tolerates</a>  <a href="gfacirc1.html#K31" target="_self">GFA2CarryStr</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#T55">CIRCCOMB:55</a></i>;<br/>
<b>hence </b><a NAME="E6:136"/>
 <a href="msafree2.html#K2">InputVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K37" target="_self">BitGFA2Str</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">z</font></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i>, , <a class="ref" href="facirc_2.html#T22">FACIRC_2:22</a></i>;<br/>


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