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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font>, <font color="Maroon">c<sub>12</sub></font>, <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font>, <font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font>, <font color="Maroon">c<sub>18</sub></font>, <font color="Maroon">c<sub>19</sub></font>, <font color="Maroon">c<sub>20</sub></font>, <font color="Maroon">c<sub>21</sub></font>, <font color="Maroon">c<sub>22</sub></font>, <font color="Maroon">c<sub>23</sub></font>, <font color="Maroon">c<sub>24</sub></font>, <font color="Maroon">c<sub>25</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:8"/><i><font color="Green">E3</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>13</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>and </b><br/><a NAME="E2:8"/><i><font color="Green">E4</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E3:8"/><i><font color="Green">E5</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E4:8"/><i><font color="Green">E6</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E5:8"/><i><font color="Green">E7</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E6:8"/><i><font color="Green">E8</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E7:8"/><i><font color="Green">E9</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E8:8"/><i><font color="Green">E10</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10">XOR3</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E9:8"/><i><font color="Green">E11</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font>,<a href="xboole_0.html#K1">{}</a>  )
 <b>and </b><br/><a NAME="E10:8"/><i><font color="Green">E12</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K10">XOR3</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>23</sub></font> )
 <b>and </b><br/><a NAME="E11:8"/><i><font color="Green">E13</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>24</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <font color="Maroon">c<sub>16</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>23</sub></font> )
 <b>and </b><br/><a NAME="E12:8"/><i><font color="Green">E14</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>22</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>24</sub></font> )
 <b>and </b><br/><a NAME="E13:8"/><i><font color="Green">E15</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>25</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>24</sub></font> )
 <b>and </b><br/><a NAME="E14:8"/><i><font color="Green">E16</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>7</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>13</sub></font> )
 <b>and </b><br/><a NAME="E15:8"/><i><font color="Green">E17</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>14</sub></font> )
 <b>and </b><br/><a NAME="E16:8"/><i><font color="Green">E18</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> )
 <b>and </b><br/><a NAME="E17:8"/><i><font color="Green">E19</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>10</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> )
 <b>and </b><br/><a NAME="E18:8"/><i><font color="Green">E20</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>22</sub></font> )
 <b>and </b><br/><a NAME="E19:8"/><i><font color="Green">E21</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>25</sub></font> )
 ;<br/>

<b>set </b><font color="Maroon">c<sub>26</sub></font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>27</sub></font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>28</sub></font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>29</sub></font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>30</sub></font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>31</sub></font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>32</sub></font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>33</sub></font> =  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>
<a NAME="E20:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E3:8"><i><font color="Green">E5</font></i></a>, <a class="txt" href="gate_5.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E21:8"/><b>then </b><i><font color="Green">E22</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E22:8"/><i><font color="Green">E23</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E4:8"><i><font color="Green">E6</font></i></a>, <a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E23:8"/><i><font color="Green">E24</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E5:8"><i><font color="Green">E7</font></i></a>, <a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E24:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E6:8"><i><font color="Green">E8</font></i></a>, <a class="txt" href="gate_5.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E25:8"/><b>then </b><i><font color="Green">E25</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E26:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E7:8"><i><font color="Green">E9</font></i></a>, <a class="txt" href="gate_5.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E27:8"/><b>then </b><i><font color="Green">E26</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E28:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E8:8"><i><font color="Green">E10</font></i></a>, <a class="txt" href="gate_5.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E29:8"/><b>then </b><i><font color="Green">E27</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E30:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>15</sub></font>,<font color="Maroon">c<sub>17</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E9:8"><i><font color="Green">E11</font></i></a>, <a class="txt" href="gate_5.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E31:8"/><b>then </b><i><font color="Green">E28</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>15</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E32:8"/><i><font color="Green">E29</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E10:8"><i><font color="Green">E12</font></i></a>, <a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E33:8"/><i><font color="Green">E30</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>23</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>16</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>24</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E11:8"><i><font color="Green">E13</font></i></a>, <a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E34:8"/><i><font color="Green">E31</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>24</sub></font> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>24</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>22</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E12:8"><i><font color="Green">E14</font></i></a>, <a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E35:8"/><i><font color="Green">E32</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>19</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>24</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>24</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>25</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E13:8"><i><font color="Green">E15</font></i></a>, <a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<b>thus </b><a NAME="E36:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>7</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K5" target="_self">MULT310</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E1:8"><i><font color="Green">E3</font></i></a>, <a class="txt" href="gate_5.html#E14:8"><i><font color="Green">E16</font></i></a></i>;<br/>

<b>thus </b><a NAME="E37:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>8</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K6" target="_self">MULT311</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E2:8"><i><font color="Green">E4</font></i></a>, <a class="txt" href="gate_5.html#E15:8"><i><font color="Green">E17</font></i></a></i>;<br/>

<b>set </b><font color="Maroon">c<sub>34</sub></font> =  <a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
 <a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="gate_1.html#K35">ADD2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> 

<br/>.= 
 <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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></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="E39:8"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E40:8"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E41:8"/><b>then </b><i><font color="Green">E33</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> or  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></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">c<sub>35</sub></font> =  <a href="gate_5.html#K10" target="_self">MULT321</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
<a NAME="E42:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K10" target="_self">MULT321</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E43:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>9</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K10" target="_self">MULT321</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E16:8"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_5.html#E21:8"><i><font color="Green">E22</font></i></a>, <a class="txt" href="gate_5.html#E22:8"><i><font color="Green">E23</font></i></a>, <a class="txt" href="gate_5.html#E29:8"><i><font color="Green">E27</font></i></a>, <a class="txt" href="gate_5.html#E41:8"><i><font color="Green">E33</font></i></a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E44:8"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></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="E45:8"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E46:8"/><b>then </b><i><font color="Green">E34</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>36</sub></font> =  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
 <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="gate_1.html#K37">ADD3</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> 

<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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></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="E48:8"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E49:8"/><b>then </b><i><font color="Green">E35</font></i>: 
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E46:8"><i><font color="Green">E34</font></i></a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>37</sub></font> =  <a href="gate_5.html#K11" target="_self">MULT322</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
 <a href="gate_5.html#K11" target="_self">MULT322</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="gate_1.html#K35">ADD2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> 

<br/>.= 
 <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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></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="E51:8"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E52:8"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E53:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>10</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K11" target="_self">MULT322</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E17:8"><i><font color="Green">E19</font></i></a>, <a class="txt" href="gate_5.html#E21:8"><i><font color="Green">E22</font></i></a>, <a class="txt" href="gate_5.html#E22:8"><i><font color="Green">E23</font></i></a>, <a class="txt" href="gate_5.html#E23:8"><i><font color="Green">E24</font></i></a>, <a class="txt" href="gate_5.html#E25:8"><i><font color="Green">E25</font></i></a>, <a class="txt" href="gate_5.html#E31:8"><i><font color="Green">E28</font></i></a>, <a class="txt" href="gate_5.html#E32:8"><i><font color="Green">E29</font></i></a>, <a class="txt" href="gate_5.html#E41:8"><i><font color="Green">E33</font></i></a>, <a class="txt" href="gate_5.html#E49:8"><i><font color="Green">E35</font></i></a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>

<b>set </b><font color="Maroon">c<sub>38</sub></font> =  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
 <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="gate_1.html#K38">CARR3</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> 

<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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></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="E55:8"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<a NAME="E56:8"/><b>then </b><i><font color="Green">E36</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) ) )
 
<b>by </b><i><a class="txt" href="gate_5.html#E46:8"><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">c<sub>39</sub></font> =  <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
 <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="gate_1.html#K37">ADD3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> 

<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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></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="E58:8"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T18">GATE_1:18</a></i>;<br/>
<a NAME="E59:8"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E60:8"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E61:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>11</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K12" target="_self">MULT323</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E18:8"><i><font color="Green">E20</font></i></a>, <a class="txt" href="gate_5.html#E21:8"><i><font color="Green">E22</font></i></a>, <a class="txt" href="gate_5.html#E22:8"><i><font color="Green">E23</font></i></a>, <a class="txt" href="gate_5.html#E23:8"><i><font color="Green">E24</font></i></a>, <a class="txt" href="gate_5.html#E25:8"><i><font color="Green">E25</font></i></a>, <a class="txt" href="gate_5.html#E27:8"><i><font color="Green">E26</font></i></a>, <a class="txt" href="gate_5.html#E31:8"><i><font color="Green">E28</font></i></a>, <a class="txt" href="gate_5.html#E33:8"><i><font color="Green">E30</font></i></a>, <a class="txt" href="gate_5.html#E34:8"><i><font color="Green">E31</font></i></a>, <a class="txt" href="gate_5.html#E41:8"><i><font color="Green">E33</font></i></a>, <a class="txt" href="gate_5.html#E49:8"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_5.html#E56:8"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>

<b>set </b><font color="Maroon">c<sub>40</sub></font> =  <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/>
 <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> = 
 <a href="gate_1.html#K38">CARR3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> 

<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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></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="E63:8"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a> </span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E64:8"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or (  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  ) or (  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>,<a href="xboole_0.html#K1">{}</a>  &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19">GATE_1:19</a></i>;<br/>
<a NAME="E65:8"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp; ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> ) or (  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>6</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" target="_self">MULT312</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> ) or (  <a href="gate_1.html#NR1" target="_self">$</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">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K8" target="_self">MULT313</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K9" target="_self">MULT314</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green">Lemma2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E66:8"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>12</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_5.html#K13" target="_self">MULT324</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E19:8"><i><font color="Green">E21</font></i></a>, <a class="txt" href="gate_5.html#E21:8"><i><font color="Green">E22</font></i></a>, <a class="txt" href="gate_5.html#E22:8"><i><font color="Green">E23</font></i></a>, <a class="txt" href="gate_5.html#E23:8"><i><font color="Green">E24</font></i></a>, <a class="txt" href="gate_5.html#E25:8"><i><font color="Green">E25</font></i></a>, <a class="txt" href="gate_5.html#E27:8"><i><font color="Green">E26</font></i></a>, <a class="txt" href="gate_5.html#E31:8"><i><font color="Green">E28</font></i></a>, <a class="txt" href="gate_5.html#E33:8"><i><font color="Green">E30</font></i></a>, <a class="txt" href="gate_5.html#E35:8"><i><font color="Green">E32</font></i></a>, <a class="txt" href="gate_5.html#E41:8"><i><font color="Green">E33</font></i></a>, <a class="txt" href="gate_5.html#E49:8"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_5.html#E56:8"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>


</div>
