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<div class="add">

<b>let </b><font color="Maroon" title="c1">g0</font>, <font color="Maroon" title="c2">g1</font>, <font color="Maroon" title="c3">g2</font>, <font color="Maroon" title="c4">g3</font>, <font color="Maroon" title="c5">g4</font>, <font color="Maroon" title="c6">g5</font>, <font color="Maroon" title="c7">g6</font>, <font color="Maroon" title="c8">g7</font>, <font color="Maroon" title="c9">g8</font>, <font color="Maroon" title="c10">g9</font>, <font color="Maroon" title="c11">g10</font>, <font color="Maroon" title="c12">g11</font>, <font color="Maroon" title="c13">g12</font>, <font color="Maroon" title="c14">g13</font>, <font color="Maroon" title="c15">g14</font>, <font color="Maroon" title="c16">g15</font>, <font color="Maroon" title="c17">g16</font>, <font color="Maroon" title="c18">a0</font>, <font color="Maroon" title="c19">a1</font>, <font color="Maroon" title="c20">a2</font>, <font color="Maroon" title="c21">a3</font>, <font color="Maroon" title="c22">a4</font>, <font color="Maroon" title="c23">a5</font>, <font color="Maroon" title="c24">a6</font>, <font color="Maroon" title="c25">a7</font>, <font color="Maroon" title="c26">a8</font>, <font color="Maroon" title="c27">a9</font>, <font color="Maroon" title="c28">a10</font>, <font color="Maroon" title="c29">a11</font>, <font color="Maroon" title="c30">a12</font>, <font color="Maroon" title="c31">a13</font>, <font color="Maroon" title="c32">a14</font>, <font color="Maroon" title="c33">a15</font>, <font color="Maroon" title="c34">b0</font>, <font color="Maroon" title="c35">b1</font>, <font color="Maroon" title="c36">b2</font>, <font color="Maroon" title="c37">b3</font>, <font color="Maroon" title="c38">b4</font>, <font color="Maroon" title="c39">b5</font>, <font color="Maroon" title="c40">b6</font>, <font color="Maroon" title="c41">b7</font>, <font color="Maroon" title="c42">b8</font>, <font color="Maroon" title="c43">b9</font>, <font color="Maroon" title="c44">b10</font>, <font color="Maroon" title="c45">b11</font>, <font color="Maroon" title="c46">b12</font>, <font color="Maroon" title="c47">b13</font>, <font color="Maroon" title="c48">b14</font>, <font color="Maroon" title="c49">b15</font>, <font color="Maroon" title="c50">p</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:2"/><i><font color="Green" title="E1">A1</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">g0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">g16</font> )
 <b>and </b><br/><a NAME="E2:2"/><i><font color="Green" title="E2">A2</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">b0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c50">p</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E3:2"/><i><font color="Green" title="E3">A3</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">b1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a0</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E4:2"/><i><font color="Green" title="E4">A4</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">b2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E5:2"/><i><font color="Green" title="E5">A5</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">b3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E6:2"/><i><font color="Green" title="E6">A6</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">b4</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E7:2"/><i><font color="Green" title="E7">A7</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">b5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E8:2"/><i><font color="Green" title="E8">A8</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">b6</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a5</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E9:2"/><i><font color="Green" title="E9">A9</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">b7</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">a6</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E10:2"/><i><font color="Green" title="E10">A10</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c42">b8</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c25">a7</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E11:2"/><i><font color="Green" title="E11">A11</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c43">b9</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c26">a8</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E12:2"/><i><font color="Green" title="E12">A12</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c44">b10</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c27">a9</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E13:2"/><i><font color="Green" title="E13">A13</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c45">b11</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c28">a10</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E14:2"/><i><font color="Green" title="E14">A14</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c46">b12</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c29">a11</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c13">g12</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E15:2"/><i><font color="Green" title="E15">A15</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c47">b13</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c30">a12</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c14">g13</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E16:2"/><i><font color="Green" title="E16">A16</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c48">b14</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c31">a13</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c15">g14</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>and </b><br/><a NAME="E17:2"/><i><font color="Green" title="E17">A17</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c49">b15</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c32">a14</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c16">g15</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 ;<br/>

<b>thus </b><a NAME="E18:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">a15</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">g16</font>,<font color="Maroon" title="c33">a15</font> )
 <b>by </b><i><a class="txt" href="gate_4.html#E1:2"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>

<a NAME="E19:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c49">b15</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c16">g15</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c49">b15</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c16">g15</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c49">b15</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c16">g15</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E20:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c32">a14</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c49">b15</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c16">g15</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E17:2"><i><font color="Green" title="E17">A17</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E21:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c48">b14</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c15">g14</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c48">b14</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c15">g14</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c48">b14</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c15">g14</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E22:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c31">a13</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c48">b14</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c15">g14</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E16:2"><i><font color="Green" title="E16">A16</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E23:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c47">b13</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c14">g13</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c47">b13</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c14">g13</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c47">b13</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c14">g13</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E24:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c30">a12</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c47">b13</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c14">g13</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E15:2"><i><font color="Green" title="E15">A15</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E25:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c46">b12</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c13">g12</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c46">b12</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c13">g12</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c46">b12</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c13">g12</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E26:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c29">a11</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c46">b12</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c13">g12</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E14:2"><i><font color="Green" title="E14">A14</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E27:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c45">b11</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c45">b11</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c45">b11</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E28:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c28">a10</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c45">b11</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E13:2"><i><font color="Green" title="E13">A13</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E29:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c44">b10</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c44">b10</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c44">b10</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E30:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c27">a9</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c44">b10</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E12:2"><i><font color="Green" title="E12">A12</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E31:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c43">b9</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c43">b9</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c43">b9</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E32:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c26">a8</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c43">b9</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E11:2"><i><font color="Green" title="E11">A11</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E33:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c42">b8</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c42">b8</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c42">b8</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E34:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c25">a7</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c42">b8</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E10:2"><i><font color="Green" title="E10">A10</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E35:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">b7</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">b7</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c41">b7</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E36:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">a6</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c41">b7</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E9:2"><i><font color="Green" title="E9">A9</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E37:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">b6</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">b6</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c40">b6</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E38:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c23">a5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c40">b6</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E8:2"><i><font color="Green" title="E8">A8</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E39:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">b5</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">b5</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c39">b5</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E40:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">a4</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c39">b5</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E7:2"><i><font color="Green" title="E7">A7</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E41:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">b4</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">b4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">b4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E42:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">a3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">b4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E6:2"><i><font color="Green" title="E6">A6</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E43:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">b3</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">b3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c37">b3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E44:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">a2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c37">b3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E5:2"><i><font color="Green" title="E5">A5</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E45:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">b2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">b2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c36">b2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E46:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">a1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c36">b2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E4:2"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E47:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">b1</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">b1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c35">b1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E48:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">a0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c35">b1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E3:2"><i><font color="Green" title="E3">A3</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E49:2"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">b0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c33">a15</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">b0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c33">a15</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c34">b0</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E50:2"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c50">p</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c34">b0</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c33">a15</font></span>)</span> )
 <b>by </b><i><a class="txt" href="gate_4.html#E2:2"><i><font color="Green" title="E2">A2</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>


</div>
