<?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">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">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">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> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:3"/><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#K8">AND3</a> <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="E2:3"/><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#K8">AND3</a> <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="E3:3"/><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#K8">AND3</a> <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="E4:3"/><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#K8">AND3</a> <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="E5:3"/><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#K8">AND3</a> <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="E6:3"/><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#K8">AND3</a> <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="E7:3"/><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#K8">AND3</a> <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="E8:3"/><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#K8">AND3</a> <font color="Maroon">q3</font>,<font color="Maroon">q2</font>,<font color="Maroon">q1</font> )
 <b>and </b><br/><a NAME="E9:3"/><i><font color="Green">E22</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#K8">AND3</a> <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="E10:3"/><i><font color="Green">E23</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#K8">AND3</a> <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="E11:3"/><i><font color="Green">E35</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#K8">AND3</a> <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="E12:3"/><i><font color="Green">E36</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#K8">AND3</a> <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="E13:3"/><i><font color="Green">E37</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#K8">AND3</a> <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="E14:3"/><i><font color="Green">E38</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#K8">AND3</a> <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="E15:3"/><i><font color="Green">E39</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#K8">AND3</a> <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="E16:3"/><i><font color="Green">E40</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#K8">AND3</a> <font color="Maroon">nq3</font>,<font color="Maroon">nq2</font>,<font color="Maroon">nq1</font> )
 <b>and </b><br/><a NAME="E17:3"/><i><font color="Green">E41</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#K1">NOT1</a> <font color="Maroon">q3</font> )
 <b>and </b><br/><a NAME="E18:3"/><i><font color="Green">E42</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> <font color="Maroon">q1</font> )
 <b>and </b><br/><a NAME="E19:3"/><i><font color="Green">E43</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> <font color="Maroon">q2</font> )
 ;<br/>

<a NAME="E20:3"/>
(  <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">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#T16">GATE_1:16</a></i>;<br/>
<a NAME="E21:3"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns1</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E4:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E5:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E6:3"><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">$</a> <font color="Maroon">ns1</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s0</font> )
 <b>by </b><i>, <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">$</a> <font color="Maroon">ns3</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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#T16">GATE_1:16</a></i>;<br/>
<a NAME="E24:3"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns3</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E4:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E5:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E6:3"><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">$</a> <font color="Maroon">ns3</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s1</font> )
 <b>by </b><i>, <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">$</a> <font color="Maroon">ns7</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s3</font> )
 <b>by </b><i>, <a class="txt" href="gate_3.html#E3:3"><i><font color="Green">E16</font></i></a>, <a class="txt" href="gate_3.html#E4:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E5:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E6:3"><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">$</a> <font color="Maroon">ns6</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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#E2:3"><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">$</a> <font color="Maroon">ns6</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E4:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E5:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E6:3"><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">$</a> <font color="Maroon">ns6</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s7</font> )
 <b>by </b><i>, <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">$</a> <font color="Maroon">ns4</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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#T16">GATE_1:16</a></i>;<br/>
<a NAME="E31:3"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns4</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E4:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E5:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E6:3"><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">$</a> <font color="Maroon">ns4</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s6</font> )
 <b>by </b><i>, <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">$</a> <font color="Maroon">ns0</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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#T16">GATE_1:16</a></i>;<br/>
<a NAME="E34:3"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns0</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E4:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E5:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E6:3"><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">$</a> <font color="Maroon">ns0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s4</font> )
 <b>by </b><i>, <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">$</a> <font color="Maroon">ns2</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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#T16">GATE_1:16</a></i>;<br/>
<a NAME="E37:3"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns2</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E4:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E5:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E6:3"><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">$</a> <font color="Maroon">ns2</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s5</font> )
 <b>by </b><i>, <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">$</a> <font color="Maroon">ns5</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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#E1:3"><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">$</a> <font color="Maroon">ns5</font> iff (  <a href="gate_1.html#NR1" target="_self">$</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> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E4:3"><i><font color="Green">E17</font></i></a>, <a class="txt" href="gate_3.html#E5:3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="gate_3.html#E6:3"><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">$</a> <font color="Maroon">ns5</font> iff  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">s2</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>


</div>
