<?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="E1:1"/><i><font color="Green">E29</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="E2:1"/><i><font color="Green">E30</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="E3:1"/><i><font color="Green">E31</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="E4:1"/><i><font color="Green">E32</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="E5:1"/><i><font color="Green">E33</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="E6:1"/><i><font color="Green">E34</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="E7:1"/><i><font color="Green">E35</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="E8:1"/><i><font color="Green">E36</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="E9:1"/><i><font color="Green">E37</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="E10:1"/><i><font color="Green">E38</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="E11:1"/><i><font color="Green">E39</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="E12:1"/><i><font color="Green">E40</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="E13:1"/><i><font color="Green">E41</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="E14:1"/><i><font color="Green">E42</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="E15:1"/><i><font color="Green">E43</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="E16:1"/><i><font color="Green">E44</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="E17:1"/><i><font color="Green">E45</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">q1</font> )
 <b>and </b><br/><a NAME="E18:1"/><i><font color="Green">E46</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#K4">XOR2</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font> )
 <b>and </b><br/><a NAME="E19:1"/><i><font color="Green">E47</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#K3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">q3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">q1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E20:1"/>
(  <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="E21:1"/><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">nq3</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i>, , <a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<a NAME="E22:1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns1</font> iff ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E23:1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns1</font> iff ( (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font> ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E24:1"/><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="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E25:1"/>
(  <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="E26:1"/>
(  <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="E27:1"/><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#K2">AND2</a> <font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" target="_self">$</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="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E28:1"/><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> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font> ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</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="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E29:1"/><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> <font color="Maroon">q3</font> or  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> &amp; not  <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="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E30:1"/><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>  <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="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E31:1"/>
(  <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">s1</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E32:1"/>
(  <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">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i>, , , <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E33:1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns3</font> iff ( not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E34:1"/><b>then </b>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">ns3</font> iff ( (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E35:1"/><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">$</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E36:1"/>
(  <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">s2</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E37:1"/>
(  <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="E38:1"/><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>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> or  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font></span>)</span> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</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="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E39:1"/><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">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font> ) ) &amp;  <a href="gate_1.html#NR1" target="_self">$</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="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E40:1"/><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> <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="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E41:1"/><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>  <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> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E42:1"/>
(  <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">s3</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E43:1"/>
(  <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="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E44:1"/><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> <font color="Maroon">nq3</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i>, , <a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<a NAME="E45:1"/><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#K2">AND2</a> <font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> or  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font></span>)</span> ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E46:1"/><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> <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="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<b>hence </b><a NAME="E47:1"/>
(  <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">s4</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E48:1"/>
(  <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="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E49:1"/><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>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> or  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font></span>)</span> ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</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="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E50:1"/><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">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> ) or (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font> ) ) &amp; not  <a href="gate_1.html#NR1" target="_self">$</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="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E51:1"/><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; not  <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="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E52:1"/><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">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E53:1"/>
(  <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">s5</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E54:1"/>
(  <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">nq3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q1</font>,<font color="Maroon">q2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i>, , , <a class="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>
<a NAME="E55:1"/><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#K2">AND2</a> <font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> or  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font></span>)</span> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> ) )
 
<b>by </b><i>, <a class="ref" href="gate_1.html#T7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E56:1"/><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> <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="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<b>hence </b><a NAME="E57:1"/>
(  <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">s6</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>

<a NAME="E58:1"/>
(  <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="E59:1"/><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#K2">AND2</a> <font color="Maroon">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font></span>)</span> &amp;  <a href="gate_1.html#NR1" target="_self">$</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="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<a NAME="E60:1"/><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> <font color="Maroon">q3</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K1">NOT1</a> <font color="Maroon">q1</font> ) &amp; (  not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">q1</font> or  not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">q2</font>,<font color="Maroon">q3</font> ) &amp;  <a href="gate_1.html#NR1" target="_self">$</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="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>
<a NAME="E61:1"/><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> <font color="Maroon">q3</font> or  <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">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="ref" href="gate_1.html#T4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E62:1"/>
(  <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">s7</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T16">GATE_1:16</a></i>;<br/>


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