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

<b>let </b><font color="Maroon">g0</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g3</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g4</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g5</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g6</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g7</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g8</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g9</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g10</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g11</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g12</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g13</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g14</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g15</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">g16</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a0</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a3</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a4</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a5</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a6</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a7</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a8</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a9</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a10</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a11</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a12</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a13</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a14</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">a15</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b0</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b2</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b3</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b4</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b5</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b6</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b7</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b8</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b9</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b10</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b11</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b12</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b13</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b14</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">b15</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">p</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:2"/><i><font color="Green">E40</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">g0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">g16</font> )
 <b>and </b><br/><a NAME="E2:2"/><i><font color="Green">E41</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g0</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E3:2"/><i><font color="Green">E42</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b1</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a0</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g1</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E4:2"/><i><font color="Green">E43</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b2</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g2</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E5:2"/><i><font color="Green">E44</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b3</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g3</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E6:2"/><i><font color="Green">E45</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b4</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g4</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E7:2"/><i><font color="Green">E46</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b5</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g5</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E8:2"/><i><font color="Green">E47</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b6</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a5</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g6</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E9:2"/><i><font color="Green">E48</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b7</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a6</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g7</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E10:2"/><i><font color="Green">E49</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b8</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a7</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g8</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E11:2"/><i><font color="Green">E50</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b9</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a8</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g9</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E12:2"/><i><font color="Green">E51</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b10</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a9</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g10</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E13:2"/><i><font color="Green">E52</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b11</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a10</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g11</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E14:2"/><i><font color="Green">E65</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b12</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a11</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g12</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E15:2"/><i><font color="Green">E66</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b13</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a12</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g13</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E16:2"/><i><font color="Green">E67</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b14</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a13</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g14</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E17:2"/><i><font color="Green">E68</font></i>: 
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b15</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">a14</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g15</font>,<font color="Maroon">a15</font></span>)</span> )
 ;<br/>

<b>thus </b><a NAME="E18:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a15</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g16</font>,<font color="Maroon">a15</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>

<a NAME="E19:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b15</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g15</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b15</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g15</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b15</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g15</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E20:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a14</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b15</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g15</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E21:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b14</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g14</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b14</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g14</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b14</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g14</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E22:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a13</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b14</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g14</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E23:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b13</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g13</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b13</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g13</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b13</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g13</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E24:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a12</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b13</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g13</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E25:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b12</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g12</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b12</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g12</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b12</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g12</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E26:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a11</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b12</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g12</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E27:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b11</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g11</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b11</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g11</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b11</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g11</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E28:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a10</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b11</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g11</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E29:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b10</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g10</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b10</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g10</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b10</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g10</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E30:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a9</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b10</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g10</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E31:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b9</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g9</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b9</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g9</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b9</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g9</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E32:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a8</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b9</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g9</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E33:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b8</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g8</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b8</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g8</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b8</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g8</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E34:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a7</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b8</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g8</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E35:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b7</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g7</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b7</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g7</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b7</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g7</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E36:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a6</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b7</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g7</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E37:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b6</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g6</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b6</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g6</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b6</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g6</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E38:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a5</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b6</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g6</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E39:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b5</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g5</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b5</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g5</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b5</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g5</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E40:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a4</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b5</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g5</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E41:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b4</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g4</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b4</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g4</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g4</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E42:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a3</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g4</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E43:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b3</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g3</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b3</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g3</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g3</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E44:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a2</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g3</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E45:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b2</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g2</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b2</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g2</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g2</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E46:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a1</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g2</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E47:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b1</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g1</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b1</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g1</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g1</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E48:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">a0</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g1</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E49:2"/>
( ( (  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b0</font> &amp; not  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g0</font>,<font color="Maroon">a15</font> ) or ( not  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">b0</font> &amp;  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K2">AND2</a> <font color="Maroon">g0</font>,<font color="Maroon">a15</font> ) ) iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b0</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g0</font>,<font color="Maroon">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E50:2"/>
(  <a href="gate_1.html#NR1" target="_self">$</a> <font color="Maroon">p</font> iff  <a href="gate_1.html#NR1" target="_self">$</a>  <a href="gate_1.html#K4">XOR2</a> <font color="Maroon">b0</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2">AND2</a> <font color="Maroon">g0</font>,<font color="Maroon">a15</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>


</div>
