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

<b>let </b><font color="Maroon">x0</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y0</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">y2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z0</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z3</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z4</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">z5</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q00</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q01</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q02</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">c01</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">c02</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q11</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q12</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">c11</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">c12</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q21</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q22</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">c21</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">c22</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:7"/><i><font color="Green">E21</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q00</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 <b>and </b><br/><a NAME="E2:7"/><i><font color="Green">E22</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q01</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E3:7"/><i><font color="Green">E23</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c01</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E4:7"/><i><font color="Green">E24</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q02</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E5:7"/><i><font color="Green">E25</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c02</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E6:7"/><i><font color="Green">E26</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q11</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10">XOR3</a> <font color="Maroon">q02</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<font color="Maroon">c01</font> )
 <b>and </b><br/><a NAME="E7:7"/><i><font color="Green">E27</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c11</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <font color="Maroon">q02</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<font color="Maroon">c01</font> )
 <b>and </b><br/><a NAME="E8:7"/><i><font color="Green">E28</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q12</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<font color="Maroon">c02</font> )
 <b>and </b><br/><a NAME="E9:7"/><i><font color="Green">E29</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c12</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<font color="Maroon">c02</font> )
 <b>and </b><br/><a NAME="E10:7"/><i><font color="Green">E33</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q21</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10">XOR3</a> <font color="Maroon">q12</font>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c11</font> )
 <b>and </b><br/><a NAME="E11:7"/><i><font color="Green">E34</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c21</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <font color="Maroon">q12</font>,<a href="xboole_0.html#K1">{}</a> ,<font color="Maroon">c11</font> )
 <b>and </b><br/><a NAME="E12:7"/><i><font color="Green">E49</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q22</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font></span>)</span>,<font color="Maroon">c21</font>,<font color="Maroon">c12</font> )
 <b>and </b><br/><a NAME="E13:7"/><i><font color="Green">E50</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c22</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font></span>)</span>,<font color="Maroon">c21</font>,<font color="Maroon">c12</font> )
 <b>and </b><br/><a NAME="E14:7"/><i><font color="Green">E51</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q00</font> )
 <b>and </b><br/><a NAME="E15:7"/><i><font color="Green">E52</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z1</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q01</font> )
 <b>and </b><br/><a NAME="E16:7"/><i><font color="Green">E53</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z2</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q11</font> )
 <b>and </b><br/><a NAME="E17:7"/><i><font color="Green">E54</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z3</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q21</font> )
 <b>and </b><br/><a NAME="E18:7"/><i><font color="Green">E55</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z4</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q22</font> )
 <b>and </b><br/><a NAME="E19:7"/><i><font color="Green">E56</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z5</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c22</font> )
 ;<br/>

<b>set </b><font color="Maroon">x1y0</font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font>;<br/>
<b>set </b><font color="Maroon">x2y0</font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font>;<br/>
<b>set </b><font color="Maroon">x0y1</font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font>;<br/>
<b>set </b><font color="Maroon">x1y1</font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font>;<br/>
<b>set </b><font color="Maroon">x2y1</font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font>;<br/>
<b>set </b><font color="Maroon">x0y2</font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font>;<br/>
<b>set </b><font color="Maroon">x1y2</font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font>;<br/>
<b>set </b><font color="Maroon">x2y2</font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>;<br/>
<a NAME="E20:7"/><i><font color="Green">E62</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c01</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E21:7"/><b>then </b><i><font color="Green">E63</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c01</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E22:7"/><i><font color="Green">E64</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q02</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E23:7"/><b>then </b><i><font color="Green">E65</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q02</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E24:7"/><i><font color="Green">E66</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c02</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green">Lemma7</font></i></a>, </i>;<br/>
<a NAME="E25:7"/><b>then </b><i><font color="Green">E67</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c02</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E26:7"/><i><font color="Green">E68</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q02</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q02</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c01</font> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q02</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q02</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c01</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q11</font> )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E27:7"/><i><font color="Green">E69</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q02</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c01</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c01</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q02</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c11</font> )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E28:7"/><i><font color="Green">E70</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c02</font> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c02</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q12</font> )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E29:7"/><i><font color="Green">E71</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c02</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c02</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c12</font> )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E30:7"/><i><font color="Green">E72</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q21</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q12</font>,<font color="Maroon">c11</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E31:7"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c21</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q12</font>,<font color="Maroon">c11</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E32:7"/><b>then </b><i><font color="Green">E73</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c21</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q12</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c11</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E33:7"/><i><font color="Green">E74</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c21</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c21</font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c12</font> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c21</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c21</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c12</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q22</font> )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E34:7"/><i><font color="Green">E75</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c21</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c21</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c12</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c12</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c22</font> )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<b>thus </b><a NAME="E35:7"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K5" target="_self">MULT310</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 <b>by </b><i>, </i>;<br/>

<b>thus </b><a NAME="E36:7"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z1</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K6" target="_self">MULT311</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E1"><i><font color="Green">Lemma4</font></i></a>, </i>;<br/>

<b>set </b><font color="Maroon">m312</font> =  <a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font>;<br/>
<a NAME="E37:7"/>
 <a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> <a href="hidden.html#R1">=</a>  <a href="gate_1.html#K10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="gate_1.html#D37">GATE_1:def 37</a></i>;<br/>
<a NAME="E38:7"/><b>then </b><i><font color="Green">E77</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E39:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E40:7"/><b>then </b><i><font color="Green">E78</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> ) ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<b>set </b><font color="Maroon">m321</font> =  <a href="gate_5.html#K10" target="_self">MULT321</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font>;<br/>
<a NAME="E41:7"/>
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K10" target="_self">MULT321</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E42:7"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z2</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K10" target="_self">MULT321</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 <b>by </b><i>, , <a class="txt" href="gate_5.html#E4:7"><i><font color="Green">E24</font></i></a>, <a class="txt" href="gate_5.html#E8:7"><i><font color="Green">E28</font></i></a>, , <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E43:7"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E44:7"/><b>then </b><i><font color="Green">E80</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E45:7"/><b>then </b><i><font color="Green">E81</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<b>set </b><font color="Maroon">m313</font> =  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font>;<br/>
 <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> = 
 <a href="gate_1.html#K10">XOR3</a> <a href="xboole_0.html#K1">{}</a> ,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K36">CARR2</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D39">GATE_1:def 39</a></i>
<br/>.= 
 <a href="gate_1.html#K10">XOR3</a> <a href="xboole_0.html#K1">{}</a> ,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D38">GATE_1:def 38</a></i>
;<br/>
<a NAME="E47:7"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E48:7"/><b>then </b><i><font color="Green">E83</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> ) ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> ) ) ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>set </b><font color="Maroon">m322</font> =  <a href="gate_5.html#K11" target="_self">MULT322</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font>;<br/>
<a NAME="E49:7"/>
 <a href="gate_5.html#K11" target="_self">MULT322</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> <a href="hidden.html#R1">=</a>  <a href="gate_1.html#K10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="gate_1.html#D37">GATE_1:def 37</a></i>;<br/>
<a NAME="E50:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K11" target="_self">MULT322</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E51:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K11" target="_self">MULT322</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E52:7"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z3</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K11" target="_self">MULT322</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 <b>by </b><i>, <a class="txt" href="gate_5.html#E2:7"><i><font color="Green">E22</font></i></a>, <a class="txt" href="gate_5.html#E4:7"><i><font color="Green">E24</font></i></a>, <a class="txt" href="gate_5.html#E6:7"><i><font color="Green">E26</font></i></a>, <a class="txt" href="gate_5.html#E9:7"><i><font color="Green">E29</font></i></a>, , , , , <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<b>set </b><font color="Maroon">m314</font> =  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font>;<br/>
 <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> = 
 <a href="gate_1.html#K11">MAJ3</a> <a href="xboole_0.html#K1">{}</a> ,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K36">CARR2</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D40">GATE_1:def 40</a></i>
<br/>.= 
 <a href="gate_1.html#K11">MAJ3</a> <a href="xboole_0.html#K1">{}</a> ,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D38">GATE_1:def 38</a></i>
;<br/>
<a NAME="E54:7"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E55:7"/><b>then </b><i><font color="Green">E86</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y1</font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y0</font> ) ) ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<b>set </b><font color="Maroon">m323</font> =  <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font>;<br/>
 <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> = 
 <a href="gate_1.html#K10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K36">CARR2</a> <span class="p2">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D39">GATE_1:def 39</a></i>
<br/>.= 
 <a href="gate_1.html#K10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D38">GATE_1:def 38</a></i>
;<br/>
<a NAME="E57:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E58:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E59:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E60:7"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z4</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 <b>by </b><i>, <a class="txt" href="gate_5.html#E3:7"><i><font color="Green">E23</font></i></a>, <a class="txt" href="gate_5.html#E5:7"><i><font color="Green">E25</font></i></a>, <a class="txt" href="gate_5.html#E7:7"><i><font color="Green">E27</font></i></a>, <a class="txt" href="gate_5.html#E9:7"><i><font color="Green">E29</font></i></a>, , , <a class="txt" href="gate_5.html#E10:7"><i><font color="Green">E33</font></i></a>, <a class="txt" href="gate_5.html#E11:7"><i><font color="Green">E34</font></i></a>, , , , <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>

<b>set </b><font color="Maroon">m324</font> =  <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font>;<br/>
 <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> = 
 <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K36">CARR2</a> <span class="p2">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D40">GATE_1:def 40</a></i>
<br/>.= 
 <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D38">GATE_1:def 38</a></i>
;<br/>
<a NAME="E62:7"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E63:7"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E64:7"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">x1</font>,<font color="Maroon">y2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">x0</font>,<font color="Maroon">y2</font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">x2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E65:7"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">z5</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">x2</font>,<font color="Maroon">y2</font>,<font color="Maroon">x1</font>,<font color="Maroon">y1</font>,<font color="Maroon">x0</font>,<font color="Maroon">y0</font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E1:7"><i><font color="Green">E21</font></i></a>, <a class="txt" href="gate_5.html#E3:7"><i><font color="Green">E23</font></i></a>, <a class="txt" href="gate_5.html#E5:7"><i><font color="Green">E25</font></i></a>, <a class="txt" href="gate_5.html#E7:7"><i><font color="Green">E27</font></i></a>, <a class="txt" href="gate_5.html#E9:7"><i><font color="Green">E29</font></i></a>, , , <a class="txt" href="gate_5.html#E10:7"><i><font color="Green">E33</font></i></a>, , , , , <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>


</div>
