<?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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <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> implies for <font color="Olive" title="b1">s</font> being  <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/> for <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</font> being   <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>   st <font color="Olive" title="b2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> &amp; <font color="Olive" title="b3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> &amp; <font color="Olive" title="b4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">z</font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</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="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b3">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Olive" title="b4">a3</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a1</font> <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="Olive" title="b3">a2</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <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="Olive" title="b3">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b4">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b2">a1</font></span>)</span> ) )</span><br/>

<b>assume </b><a NAME="E1:101"/><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> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <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/> for <font color="Olive" title="b2">a1</font>, <font color="Olive" title="b3">a2</font>, <font color="Olive" title="b4">a3</font> being   <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>   st <font color="Olive" title="b2">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> &amp; <font color="Olive" title="b3">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> &amp; <font color="Olive" title="b4">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">z</font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</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="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b3">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Olive" title="b4">a3</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Olive" title="b1">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b2">a1</font> <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="Olive" title="b3">a2</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <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="Olive" title="b3">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b4">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b2">a1</font></span>)</span> )</span><br/>

<b>set </b><font color="Maroon" title="c8">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="c9">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="c10">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="c11">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="c12">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="c13">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">a1</font>, <font color="Olive" title="b2">a2</font>, <font color="Olive" title="b3">a3</font> being   <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>   st <font color="Olive" title="b1">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> &amp; <font color="Olive" title="b2">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> &amp; <font color="Olive" title="b3">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">z</font> holds <br/>( <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c13">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</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="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Olive" title="b2">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Olive" title="b3">a3</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c13">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">a1</font> <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="Olive" title="b2">a2</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <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="Olive" title="b2">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b3">a3</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Olive" title="b1">a1</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c14">a1</font>, <font color="Maroon" title="c15">a2</font>, <font color="Maroon" title="c16">a3</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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c14">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> &amp; <font color="Maroon" title="c15">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c16">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">z</font> implies ( <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c13">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</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="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c15">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c16">a3</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c13">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</font> <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="c15">a2</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <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="c15">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c16">a3</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="c16">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c14">a1</font></span>)</span> ) )</span><br/>



<b>assume </b><a NAME="E2:101"/><i><font color="Green" title="E60">A2</font></i>: 
( <font color="Maroon" title="c14">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> &amp; <font color="Maroon" title="c15">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c16">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">z</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c13">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</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="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c15">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c16">a3</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c13">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</font> <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="c15">a2</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <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="c15">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c16">a3</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="c16">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c14">a1</font></span>)</span> )</span><br/>

<a NAME="E3:101"/><i><font color="Green" title="E61">A3</font></i>: 
( <font color="Maroon" title="c5">x</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> &amp; <font color="Maroon" title="c6">y</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> &amp; <font color="Maroon" title="c7">z</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> )
 
<b>by </b><i><a class="ref" href="facirc_1.html#T60" title="FACIRC_1:th.60">FACIRC_1:60</a></i>;<br/>
<a NAME="E4:101"/><i><font color="Green" title="E62">A4</font></i>: 
( <font color="Maroon" title="c5">x</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> &amp; <font color="Maroon" title="c6">y</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> &amp; <font color="Maroon" title="c7">z</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="ref" href="gfacirc1.html#T55" target="_self" title="GFACIRC1:th.55">Th55</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c17">s1</font> = <font color="Maroon" title="c13">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="c18">s2</font> = <font color="Maroon" title="c13">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="c19">t</font> = <font color="Maroon" title="c13">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#K5" title="CIRCCOMB:func.5">+*</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="E8:101"/>
 <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="#E1:101"><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="E9:101"/><b>then </b><i><font color="Green" title="E63">A5</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="#E1:101"><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="E10:101"/><i><font color="Green" title="E64">A6</font></i>: 
(  <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="E11:101"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c17">s1</font> <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>
 
<b>by </b><i><a class="ref" href="circuit1.html#T4" title="CIRCUIT1:th.4">CIRCUIT1:4</a></i>;<br/>
<a NAME="E12:101"/><b>then </b>
( <font color="Maroon" title="c14">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> &amp; <font color="Maroon" title="c15">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c16">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">s1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">z</font> )
 
<b>by </b><i><a class="txt" href="#E2:101"><i><font color="Green" title="E60">A2</font></i></a>, <a class="txt" href="#E3:101"><i><font color="Green" title="E61">A3</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<a NAME="E13:101"/><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="c19">t</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</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">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c17">s1</font>,2</span>)</span> <a href="twoscomp.html#K1" title="TWOSCOMP:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</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; <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c17">s1</font>,2</span>)</span> <a href="twoscomp.html#K1" title="TWOSCOMP:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</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="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c15">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c16">a3</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="#E1:101"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="#E9:101"><i><font color="Green" title="E63">A5</font></i></a>, <a class="txt" href="#E10:101"><i><font color="Green" title="E64">A6</font></i></a>, <a class="ref" href="gfacirc1.html#T74" target="_self" title="GFACIRC1:th.74">Th74</a>, <a class="ref" href="facirc_1.html#T32" title="FACIRC_1:th.32">FACIRC_1:32</a></i>;<br/>
<b>hence </b><a NAME="E14:101"/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c13">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K24" title="GFACIRC1:func.24">GFA1AdderOutput</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="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</font> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <span class="p3">(<span class="default"><a href="margrel1.html#K9" title="MARGREL1:func.9">'not'</a> <font color="Maroon" title="c15">a2</font></span>)</span></span>)</span> <a href="binarith.html#K2" title="BINARITH:func.2">'xor'</a> <font color="Maroon" title="c16">a3</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c13">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</font> <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="c15">a2</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <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="c15">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c16">a3</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="c16">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c14">a1</font></span>)</span></span><br/>

<a NAME="E15:101"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c18">s2</font> <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="E16:101"/><b>then </b>
( <font color="Maroon" title="c14">a1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">x</font> &amp; <font color="Maroon" title="c15">a2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">y</font> &amp; <font color="Maroon" title="c16">a3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c18">s2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">z</font> )
 
<b>by </b><i><a class="txt" href="#E2:101"><i><font color="Green" title="E60">A2</font></i></a>, <a class="txt" href="#E4:101"><i><font color="Green" title="E62">A4</font></i></a>, <a class="ref" href="funct_1.html#T70" title="FUNCT_1:th.70">FUNCT_1:70</a></i>;<br/>
<a NAME="E17:101"/><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="c19">t</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c18">s2</font>,2</span>)</span> <a href="twoscomp.html#K1" title="TWOSCOMP:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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; <span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c18">s2</font>,2</span>)</span> <a href="twoscomp.html#K1" title="TWOSCOMP:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</font> <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="c15">a2</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <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="c15">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c16">a3</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="c16">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c14">a1</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="#E1:101"><i><font color="Green" title="E59">A1</font></i></a>, <a class="txt" href="#E9:101"><i><font color="Green" title="E63">A5</font></i></a>, <a class="txt" href="#E10:101"><i><font color="Green" title="E64">A6</font></i></a>, <a class="ref" href="gfacirc1.html#T61" target="_self" title="GFACIRC1:th.61">Th61</a>, <a class="ref" href="facirc_1.html#T33" title="FACIRC_1:th.33">FACIRC_1:33</a></i>;<br/>
<b>hence </b><a NAME="E18:101"/>
<span class="p1">(<span class="default"><a href="facirc_1.html#K9" title="FACIRC_1:func.9">Following</a> <font color="Maroon" title="c13">s</font>,2</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="gfacirc1.html#K21" title="GFACIRC1:func.21">GFA1CarryOutput</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">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c14">a1</font> <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="c15">a2</font></span>)</span></span>)</span> <a href="binarith.html#K1" title="BINARITH:func.1">'or'</a> <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="c15">a2</font></span>)</span> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c16">a3</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="c16">a3</font> <a href="margrel1.html#K10" title="MARGREL1:func.10">'&amp;'</a> <font color="Maroon" title="c14">a1</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
