<?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">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">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">p</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">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">g12</font> )
 <b>and </b><br/><a NAME="E2:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E3:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E4:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E5:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E6:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E7:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E8:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E9:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E10:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E11:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E12:1"/><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">a11</font></span>)</span> )
 <b>and </b><br/><a NAME="E13:1"/><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">a11</font></span>)</span> )
 ;<br/>

<b>thus </b><a NAME="E14:1"/>
(  <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#K2">AND2</a> <font color="Maroon">g12</font>,<font color="Maroon">a11</font> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T6">GATE_1:6</a></i>;<br/>

<a NAME="E15:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E16:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E17:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E18:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E19:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E20:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E21:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E22:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E23:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E24:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E25:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E26:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E27:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E28:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E29:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E30:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E31:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E32:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E33:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E34:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E35:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E36:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>

<a NAME="E37:1"/>
( ( (  <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">a11</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">a11</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">a11</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="E38:1"/>
(  <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">a11</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="gate_1.html#T8">GATE_1:8</a></i>;<br/>


</div>
