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

<b>let </b><font color="Maroon">s0</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s3</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s4</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s5</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s6</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s7</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s8</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s9</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s10</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s11</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s12</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s13</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s14</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">s15</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns0</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns3</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns4</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns5</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns6</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns7</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns8</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns9</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns10</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns11</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns12</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns13</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns14</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">ns15</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q3</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">q4</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">nq1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">nq2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">nq3</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">nq4</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">R</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:6"/><i><font color="Green">E14</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E2:6"/><i><font color="Green">E15</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s1</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font></span>)</span>,<font color="Maroon">q1</font> )
 <b>and </b><br/><a NAME="E3:6"/><i><font color="Green">E16</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s2</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font></span>)</span>,<font color="Maroon">q2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E4:6"/><i><font color="Green">E17</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s3</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font></span>)</span>,<font color="Maroon">q2</font>,<font color="Maroon">q1</font> )
 <b>and </b><br/><a NAME="E5:6"/><i><font color="Green">E18</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s4</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font></span>)</span>,<font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E6:6"/><i><font color="Green">E19</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s5</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font></span>)</span>,<font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font></span>)</span>,<font color="Maroon">q1</font> )
 <b>and </b><br/><a NAME="E7:6"/><i><font color="Green">E20</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s6</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font></span>)</span>,<font color="Maroon">q3</font>,<font color="Maroon">q2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E8:6"/><i><font color="Green">E21</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s7</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font></span>)</span>,<font color="Maroon">q3</font>,<font color="Maroon">q2</font>,<font color="Maroon">q1</font> )
 <b>and </b><br/><a NAME="E9:6"/><i><font color="Green">E22</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s8</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">q4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E10:6"/><i><font color="Green">E23</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s9</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">q4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font></span>)</span>,<font color="Maroon">q1</font> )
 <b>and </b><br/><a NAME="E11:6"/><i><font color="Green">E35</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s10</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">q4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font></span>)</span>,<font color="Maroon">q2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E12:6"/><i><font color="Green">E36</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s11</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">q4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font></span>)</span>,<font color="Maroon">q2</font>,<font color="Maroon">q1</font> )
 <b>and </b><br/><a NAME="E13:6"/><i><font color="Green">E37</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s12</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">q4</font>,<font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E14:6"/><i><font color="Green">E38</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s13</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">q4</font>,<font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font></span>)</span>,<font color="Maroon">q1</font> )
 <b>and </b><br/><a NAME="E15:6"/><i><font color="Green">E39</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s14</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">q4</font>,<font color="Maroon">q3</font>,<font color="Maroon">q2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E16:6"/><i><font color="Green">E40</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s15</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">q4</font>,<font color="Maroon">q3</font>,<font color="Maroon">q2</font>,<font color="Maroon">q1</font> )
 <b>and </b><br/><a NAME="E17:6"/><i><font color="Green">E41</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E18:6"/><i><font color="Green">E42</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns1</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font></span>)</span>,<font color="Maroon">nq1</font> )
 <b>and </b><br/><a NAME="E19:6"/><i><font color="Green">E43</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns2</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font></span>)</span>,<font color="Maroon">nq2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E20:6"/><i><font color="Green">E62</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns3</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font></span>)</span>,<font color="Maroon">nq2</font>,<font color="Maroon">nq1</font> )
 <b>and </b><br/><a NAME="E21:6"/><i><font color="Green">E63</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns4</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font></span>)</span>,<font color="Maroon">nq3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E22:6"/><i><font color="Green">E64</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns5</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font></span>)</span>,<font color="Maroon">nq3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font></span>)</span>,<font color="Maroon">nq1</font> )
 <b>and </b><br/><a NAME="E23:6"/><i><font color="Green">E65</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns6</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font></span>)</span>,<font color="Maroon">nq3</font>,<font color="Maroon">nq2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E24:6"/><i><font color="Green">E66</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns7</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font></span>)</span>,<font color="Maroon">nq3</font>,<font color="Maroon">nq2</font>,<font color="Maroon">nq1</font> )
 <b>and </b><br/><a NAME="E25:6"/><i><font color="Green">E67</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns8</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">nq4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E26:6"/><i><font color="Green">E68</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns9</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">nq4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font></span>)</span>,<font color="Maroon">nq1</font> )
 <b>and </b><br/><a NAME="E27:6"/><i><font color="Green">E69</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns10</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">nq4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font></span>)</span>,<font color="Maroon">nq2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E28:6"/><i><font color="Green">E70</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns11</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">nq4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font></span>)</span>,<font color="Maroon">nq2</font>,<font color="Maroon">nq1</font> )
 <b>and </b><br/><a NAME="E29:6"/><i><font color="Green">E71</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns12</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">nq4</font>,<font color="Maroon">nq3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E30:6"/><i><font color="Green">E72</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns13</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">nq4</font>,<font color="Maroon">nq3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font></span>)</span>,<font color="Maroon">nq1</font> )
 <b>and </b><br/><a NAME="E31:6"/><i><font color="Green">E73</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns14</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">nq4</font>,<font color="Maroon">nq3</font>,<font color="Maroon">nq2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E32:6"/><i><font color="Green">E74</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns15</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K14">AND4</a> <font color="Maroon">nq4</font>,<font color="Maroon">nq3</font>,<font color="Maroon">nq2</font>,<font color="Maroon">nq1</font> )
 <b>and </b><br/><a NAME="E33:6"/><i><font color="Green">E75</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq1</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font></span>)</span>,<font color="Maroon">R</font> )
 <b>and </b><br/><a NAME="E34:6"/><i><font color="Green">E76</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq2</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q1</font>,<font color="Maroon">R</font> )
 <b>and </b><br/><a NAME="E35:6"/><i><font color="Green">E77</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq3</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q2</font>,<font color="Maroon">R</font> )
 <b>and </b><br/><a NAME="E36:6"/><i><font color="Green">E78</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq4</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q3</font>,<font color="Maroon">R</font> )
 ;<br/>

<a NAME="E37:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns1</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E5:6"><i><font color="Green">E18</font></i></a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E38:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns1</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E39:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns1</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E40:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns1</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s0</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E41:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns3</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E7:6"><i><font color="Green">E20</font></i></a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E42:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns3</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E43:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns3</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E44:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns3</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s1</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E45:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns7</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E46:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns7</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E47:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns7</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E48:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns7</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s3</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E49:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns15</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i>, , , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<b>hence </b><a NAME="E50:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns15</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s7</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E51:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns14</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E52:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns14</font> iff ( (  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E53:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns14</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E54:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns14</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s15</font>,<font color="Maroon">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E3:6"><i><font color="Green">E16</font></i></a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E55:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns12</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E56:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns12</font> iff ( (  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E57:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns12</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E58:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns12</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s14</font>,<font color="Maroon">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E2:6"><i><font color="Green">E15</font></i></a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E59:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns8</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E60:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns8</font> iff ( (  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E61:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns8</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E62:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns8</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s12</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E63:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns0</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E4:6"><i><font color="Green">E17</font></i></a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E64:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns0</font> iff ( (  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E65:6"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<a NAME="E66:6"/><b>then </b>
( (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s8</font>,<font color="Maroon">R</font> or  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">R</font> ) iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns0</font> )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<b>hence </b><a NAME="E67:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">s8</font>,<font color="Maroon">R</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">R</font></span>)</span> )
 <b>by </b><i><a class="ref" href="gate_1.html#T7">GATE_1:7</a></i>;<br/>

<a NAME="E68:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns5</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E9:6"><i><font color="Green">E22</font></i></a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E69:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns5</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E70:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns5</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E71:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns5</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s2</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E72:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns11</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E73:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns11</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E74:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns11</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E75:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns11</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s5</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E76:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns6</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E10:6"><i><font color="Green">E23</font></i></a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E77:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns6</font> iff ( (  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E78:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns6</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E79:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns6</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s11</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E80:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns13</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E81:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns13</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E82:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns13</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E83:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns13</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s6</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E84:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns10</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E85:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns10</font> iff ( (  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E86:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns10</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E87:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns10</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s13</font>,<font color="Maroon">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E1:6"><i><font color="Green">E14</font></i></a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E88:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns4</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E8:6"><i><font color="Green">E21</font></i></a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E89:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns4</font> iff ( (  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E90:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns4</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E91:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns4</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s10</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E92:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns9</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E93:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns9</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E94:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns9</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E95:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns9</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s4</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>

<a NAME="E96:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns2</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">nq2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E6:6"><i><font color="Green">E19</font></i></a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>
<a NAME="E97:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns2</font> iff ( (  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q4</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i>, , <a class="txt" href="gate_3.html#E11:6"><i><font color="Green">E35</font></i></a>, <a class="txt" href="gate_3.html#E12:6"><i><font color="Green">E36</font></i></a>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E98:6"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns2</font> iff (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E99:6"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns2</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">s9</font>,<font color="Maroon">R</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22">GATE_1:22</a></i>;<br/>


</div>
