<?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> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:3"/><i><font color="Green">E1</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>1</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E2:3"/><i><font color="Green">E2</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>2</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<font color="Maroon">c<sub>17</sub></font> )
 <b>and </b><br/><a NAME="E3:3"/><i><font color="Green">E3</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>3</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>,<font color="Maroon">c<sub>18</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E4:3"/><i><font color="Green">E4</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>4</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>19</sub></font></span>)</span>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>17</sub></font> )
 <b>and </b><br/><a NAME="E5:3"/><i><font color="Green">E5</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>5</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K8">AND3</a> <font color="Maroon">c<sub>19</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E6:3"/><i><font color="Green">E6</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>6</sub></font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K8">AND3</a> <font color="Maroon">c<sub>19</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>18</sub></font></span>)</span>,<font color="Maroon">c<sub>17</sub></font> )
 <b>and </b><br/><a NAME="E7:3"/><i><font color="Green">E7</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>  <a href="gate_1.html#K8">AND3</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>17</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E8:3"/><i><font color="Green">E8</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>  <a href="gate_1.html#K8">AND3</a> <font color="Maroon">c<sub>19</sub></font>,<font color="Maroon">c<sub>18</sub></font>,<font color="Maroon">c<sub>17</sub></font> )
 <b>and </b><br/><a NAME="E9:3"/><i><font color="Green">E9</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>  <a href="gate_1.html#K8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>21</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E10:3"/><i><font color="Green">E10</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>  <a href="gate_1.html#K8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>21</sub></font></span>)</span>,<font color="Maroon">c<sub>20</sub></font> )
 <b>and </b><br/><a NAME="E11:3"/><i><font color="Green">E11</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>  <a href="gate_1.html#K8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>,<font color="Maroon">c<sub>21</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E12:3"/><i><font color="Green">E12</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>  <a href="gate_1.html#K8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>22</sub></font></span>)</span>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>20</sub></font> )
 <b>and </b><br/><a NAME="E13:3"/><i><font color="Green">E13</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#K8">AND3</a> <font color="Maroon">c<sub>22</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>21</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E14:3"/><i><font color="Green">E14</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#K8">AND3</a> <font color="Maroon">c<sub>22</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>21</sub></font></span>)</span>,<font color="Maroon">c<sub>20</sub></font> )
 <b>and </b><br/><a NAME="E15:3"/><i><font color="Green">E15</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#K8">AND3</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>20</sub></font></span>)</span> )
 <b>and </b><br/><a NAME="E16:3"/><i><font color="Green">E16</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#K8">AND3</a> <font color="Maroon">c<sub>22</sub></font>,<font color="Maroon">c<sub>21</sub></font>,<font color="Maroon">c<sub>20</sub></font> )
 <b>and </b><br/><a NAME="E17:3"/><i><font color="Green">E17</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#K1">NOT1</a> <font color="Maroon">c<sub>19</sub></font> )
 <b>and </b><br/><a NAME="E18:3"/><i><font color="Green">E18</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> <font color="Maroon">c<sub>17</sub></font> )
 <b>and </b><br/><a NAME="E19:3"/><i><font color="Green">E19</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> <font color="Maroon">c<sub>18</sub></font> )
 ;<br/>

<a NAME="E20:3"/>
(  <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_1.html#K1">NOT1</a> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E10:3"><i><font color="Green">E10</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E21:3"/><b>then </b>
(  <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_1.html#K1">NOT1</a> <font color="Maroon">c<sub>19</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>17</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E17:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E22:3"/>
(  <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>1</sub></font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E1:3"><i><font color="Green">E1</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E23:3"/>
(  <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_1.html#K1">NOT1</a> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E12:3"><i><font color="Green">E12</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E24:3"/><b>then </b>
(  <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_1.html#K1">NOT1</a> <font color="Maroon">c<sub>19</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E17:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E25:3"/>
(  <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>2</sub></font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E2:3"><i><font color="Green">E2</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<b>thus </b><a NAME="E26:3"/>
(  <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>4</sub></font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E4:3"><i><font color="Green">E4</font></i></a>, <a class="txt" href="gate_3.html#E16:3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="gate_3.html#E17:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E27:3"/>
(  <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> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>20</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E15:3"><i><font color="Green">E15</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E28:3"/><b>then </b>
(  <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> <font color="Maroon">c<sub>19</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>17</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E17:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E29:3"/>
(  <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> <font color="Maroon">c<sub>8</sub></font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E8:3"><i><font color="Green">E8</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E30:3"/>
(  <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> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>20</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E13:3"><i><font color="Green">E13</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E31:3"/><b>then </b>
(  <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> <font color="Maroon">c<sub>19</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>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>17</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E17:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E32:3"/>
(  <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> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E7:3"><i><font color="Green">E7</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E33:3"/>
(  <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_1.html#K1">NOT1</a> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>20</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E9:3"><i><font color="Green">E9</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E34:3"/><b>then </b>
(  <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>19</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>17</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E17:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E35:3"/>
(  <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>5</sub></font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E5:3"><i><font color="Green">E5</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E36:3"/>
(  <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_1.html#K1">NOT1</a> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>20</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E11:3"><i><font color="Green">E11</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E37:3"/><b>then </b>
(  <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>19</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>18</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>17</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E17:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E38:3"/>
(  <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>6</sub></font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E6:3"><i><font color="Green">E6</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E39:3"/>
(  <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> <font color="Maroon">c<sub>22</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>21</sub></font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">c<sub>20</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E14:3"><i><font color="Green">E14</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E40:3"/><b>then </b>
(  <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#K1">NOT1</a> <font color="Maroon">c<sub>19</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>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">c<sub>17</sub></font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E17:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><i><font color="Green">E19</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E41:3"/>
(  <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> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E3:3"><i><font color="Green">E3</font></i></a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>


</div>
