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

<b>set </b><font color="Maroon" title="c1">f0</font> =  <a href="gfacirc1.html#K4" title="GFACIRC1:func.4">xor2c</a> ;<br/>
<b>set </b><font color="Maroon" title="c2">f1</font> =  <a href="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</a> ;<br/>
<b>set </b><font color="Maroon" title="c3">f2</font> =  <a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> ;<br/>
<b>set </b><font color="Maroon" title="c4">f3</font> =  <a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> ;<br/>
<b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font>, <font color="Maroon" title="c7">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E1:102"/><i><font color="Green" title="E59">A1</font></i>: 
( <font color="Maroon" title="c7">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="c5">x</font>,<font color="Maroon" title="c6">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="gfacirc1.html#K4" title="GFACIRC1:func.4">xor2c</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c5">x</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="c6">y</font>,<font color="Maroon" title="c7">z</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K3" title="TWOSCOMP:func.3">and2a</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c6">y</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="c7">z</font>,<font color="Maroon" title="c5">x</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="twoscomp.html#K2" title="TWOSCOMP:func.2">and2</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> &amp; <font color="Maroon" title="c7">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="c5">x</font>,<font color="Maroon" title="c6">y</font></span><a href="facirc_1.html#K6" title="FACIRC_1:func.6">*&gt;</a></span>,<a href="gfacirc1.html#K3" title="GFACIRC1:func.3">and2c</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )
 ;<br/>

<b>set </b><font color="Maroon" title="c8">S</font> =  <a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font>;<br/>
<b>set </b><font color="Maroon" title="c9">S1</font> =  <a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font>;<br/>
<b>set </b><font color="Maroon" title="c10">S2</font> =  <a href="gfacirc1.html#K19" title="GFACIRC1:func.19">GFA1CarryStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font>;<br/>
<b>set </b><font color="Maroon" title="c11">A</font> =  <a href="gfacirc1.html#K26" title="GFACIRC1:func.26">BitGFA1Circ</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font>;<br/>
<b>set </b><font color="Maroon" title="c12">A1</font> =  <a href="gfacirc1.html#K23" title="GFACIRC1:func.23">GFA1AdderCirc</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font>;<br/>
<b>set </b><font color="Maroon" title="c13">A2</font> =  <a href="gfacirc1.html#K20" title="GFACIRC1:func.20">GFA1CarryCirc</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font>;<br/>
<b>let </b><font color="Maroon" title="c14">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#K26" title="GFACIRC1:func.26">BitGFA1Circ</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span>;<br/>

<b>reconsider </b><font color="Maroon" title="c15">s1</font> = <font color="Maroon" title="c14">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> as   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K23" title="GFACIRC1:func.23">GFA1AdderCirc</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T26" title="FACIRC_1:th.26">FACIRC_1:26</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c16">s2</font> = <font color="Maroon" title="c14">s</font> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K19" title="GFACIRC1:func.19">GFA1CarryStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> as   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K20" title="GFACIRC1:func.20">GFA1CarryCirc</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> <b>by </b><i><a class="ref" href="facirc_1.html#T26" title="FACIRC_1:th.26">FACIRC_1:26</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">t</font> = <font color="Maroon" title="c14">s</font> as   <a href="circuit1.html#NM3" title="CIRCUIT1:NM.3">State</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="gfacirc1.html#K23" title="GFACIRC1:func.23">GFA1AdderCirc</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <span class="p2">(<span class="default"><a href="gfacirc1.html#K20" title="GFACIRC1:func.20">GFA1CarryCirc</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span></span>)</span> ;<br/>
<a NAME="E5:102"/>
 <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="enumset1.html#K1" title="ENUMSET1:func.1">{</a><span class="default"><font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span><a href="enumset1.html#K1" title="ENUMSET1:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="gfacirc1.html#E1:102"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="facirc_1.html#T57" title="FACIRC_1:th.57">FACIRC_1:57</a></i>;<br/>
<a NAME="E6:102"/><b>then </b><i><font color="Green" title="E60">A2</font></i>: 
 <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K19" title="GFACIRC1:func.19">GFA1CarryStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span>
 
<b>by </b><i><a class="txt" href="gfacirc1.html#E1:102"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="gfacirc1.html#T53" target="_self" title="GFACIRC1:th.53">Th53</a></i>;<br/>
<a NAME="E7:102"/>
(  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> &amp;  <a href="msafree2.html#K4" title="MSAFREE2:func.4">InnerVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K19" title="GFACIRC1:func.19">GFA1CarryStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="msafree2.html#K2" title="MSAFREE2:func.2">InputVertices</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K19" title="GFACIRC1:func.19">GFA1CarryStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T79" title="XBOOLE_1:th.79">XBOOLE_1:79</a></i>;<br/>
<a NAME="E8:102"/><b>then </b><i><font color="Green" title="E61">A3</font></i>: 
(  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c15">s1</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c17">t</font>,2</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> &amp;  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c15">s1</font>,3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c17">t</font>,3</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> &amp;  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c16">s2</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c17">t</font>,2</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K19" title="GFACIRC1:func.19">GFA1CarryStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> &amp;  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c16">s2</font>,3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c17">t</font>,3</span>)</span> <a href="relat_1.html#K7" title="RELAT_1:func.7">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K19" title="GFACIRC1:func.19">GFA1CarryStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gfacirc1.html#E6:102"><i><font color="Green" title="E60">A2</font></i></a>, <a class="ref" href="facirc_1.html#T30" title="FACIRC_1:th.30">FACIRC_1:30</a>, <a class="ref" href="facirc_1.html#T31" title="FACIRC_1:th.31">FACIRC_1:31</a></i>;<br/>
<a NAME="E9:102"/>
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c15">s1</font>,2 is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>
 
<b>by </b><i><a class="txt" href="gfacirc1.html#E1:102"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="facirc_1.html#T63" title="FACIRC_1:th.63">FACIRC_1:63</a></i>;<br/>
<b>then </b><i><font color="Green" title="E62">A4</font></i>:  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c15">s1</font>,2 = 
 <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c15">s1</font>,2</span>)</span>
<b>by </b><i><a class="ref" href="circuit2.html#D6" title="CIRCUIT2:def.6">CIRCUIT2:def 6</a></i>
<br/>.= 
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c15">s1</font>,<span class="p1">(<span class="default">2 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="facirc_1.html#T12" title="FACIRC_1:th.12">FACIRC_1:12</a></i>
;<br/>
<a NAME="E11:102"/>
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c16">s2</font>,2 is <a href="circuit2.html#V1" title="CIRCUIT2:attr.1">stable</a>
 
<b>by </b><i><a class="txt" href="gfacirc1.html#E1:102"><i><font color="Green" title="E59">A1</font></i></a>, <a class="ref" href="gfacirc1.html#T62" target="_self" title="GFACIRC1:th.62">Th62</a></i>;<br/>
<b>then </b><i><font color="Green" title="E63">A5</font></i>:  <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c16">s2</font>,2 = 
 <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c16">s2</font>,2</span>)</span>
<b>by </b><i><a class="ref" href="circuit2.html#D6" title="CIRCUIT2:def.6">CIRCUIT2:def 6</a></i>
<br/>.= 
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c16">s2</font>,<span class="p1">(<span class="default">2 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="facirc_1.html#T12" title="FACIRC_1:th.12">FACIRC_1:12</a></i>
;<br/>
<a NAME="E13:102"/><i><font color="Green" title="E64">A6</font></i>: 
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c14">s</font>,<span class="p1">(<span class="default">2 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c14">s</font>,2</span>)</span>
 
<b>by </b><i><a class="ref" href="facirc_1.html#T12" title="FACIRC_1:th.12">FACIRC_1:12</a></i>;<br/>
<a NAME="E14:102"/><i><font color="Green" title="E65">A7</font></i>: 
(  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c14">s</font>,2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c14">s</font>,3</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c15">s1</font>,2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> &amp;  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c16">s2</font>,2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K19" title="GFACIRC1:func.19">GFA1CarryStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="circuit1.html#T4" title="CIRCUIT1:th.4">CIRCUIT1:4</a></i>;<br/>
<a NAME="E15:102"/><i><font color="Green" title="E66">A8</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K19" title="GFACIRC1:func.19">GFA1CarryStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="102_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c18">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:102_3"/>
<font color="Maroon" title="c18">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K25" title="GFACIRC1:func.25">BitGFA1Str</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span>
 ;<br/><a NAME="E2:102_3"/><b>then </b>
( <font color="Maroon" title="c18">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K22" title="GFACIRC1:func.22">GFA1AdderStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> or <font color="Maroon" title="c18">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="gfacirc1.html#K19" title="GFACIRC1:func.19">GFA1CarryStr</a> <font color="Maroon" title="c5">x</font>,<font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c7">z</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gfacirc1.html#E15:102"><i><font color="Green" title="E66">A8</font></i></a>, <a class="ref" href="xboole_0.html#D2" title="XBOOLE_0:def.2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E3:102_3"/><b>then </b>
( ( <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c14">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c15">s1</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">a</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="c14">s</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c15">s1</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">a</font> ) or ( <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c14">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c16">s2</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">a</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="c14">s</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c16">s2</font>,3</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">a</font> ) )
 <b>by </b><i><a class="txt" href="gfacirc1.html#E8:102"><i><font color="Green" title="E61">A3</font></i></a>, <a class="txt" href="gfacirc1.html#E10:102"><i><font color="Green" title="E62">A4</font></i></a>, <a class="txt" href="gfacirc1.html#E12:102"><i><font color="Green" title="E63">A5</font></i></a>, <a class="txt" href="gfacirc1.html#E14:102"><i><font color="Green" title="E65">A7</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/><b>hence </b><a NAME="E4:102_3"/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c14">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <span class="p2">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c14">s</font>,2</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c18">a</font>
 <b>by </b><i><a class="txt" href="gfacirc1.html#E10:102"><i><font color="Green" title="E62">A4</font></i></a>, <a class="txt" href="gfacirc1.html#E12:102"><i><font color="Green" title="E63">A5</font></i></a>, <a class="ref" href="facirc_1.html#T12" title="FACIRC_1:th.12">FACIRC_1:12</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E17:102"/>
 <a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c14">s</font>,2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="circuit2.html#K6" title="CIRCUIT2:func.6">Following</a> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c14">s</font>,2</span>)</span>
 <b>by </b><i><a class="txt" href="gfacirc1.html#E13:102"><i><font color="Green" title="E64">A6</font></i></a>, <a class="txt" href="gfacirc1.html#E14:102"><i><font color="Green" title="E65">A7</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="circuit2.html#D6" title="CIRCUIT2:def.6">CIRCUIT2:def 6</a><br/>


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