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<b>let </b><font color="Maroon" title="c1">x0</font>, <font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">x2</font>, <font color="Maroon" title="c4">y0</font>, <font color="Maroon" title="c5">y1</font>, <font color="Maroon" title="c6">y2</font>, <font color="Maroon" title="c7">z0</font>, <font color="Maroon" title="c8">z1</font>, <font color="Maroon" title="c9">z2</font>, <font color="Maroon" title="c10">z3</font>, <font color="Maroon" title="c11">z4</font>, <font color="Maroon" title="c12">z5</font>, <font color="Maroon" title="c13">q00</font>, <font color="Maroon" title="c14">q01</font>, <font color="Maroon" title="c15">q02</font>, <font color="Maroon" title="c16">c01</font>, <font color="Maroon" title="c17">c02</font>, <font color="Maroon" title="c18">q11</font>, <font color="Maroon" title="c19">q12</font>, <font color="Maroon" title="c20">c11</font>, <font color="Maroon" title="c21">c12</font>, <font color="Maroon" title="c22">q21</font>, <font color="Maroon" title="c23">q22</font>, <font color="Maroon" title="c24">c21</font>, <font color="Maroon" title="c25">c22</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:7"/><i><font color="Green" title="E3">A1</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">q00</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 <b>and </b><br/><a NAME="E2:7"/><i><font color="Green" title="E4">A2</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">q01</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>and </b><br/><a NAME="E3:7"/><i><font color="Green" title="E5">A3</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">c01</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>and </b><br/><a NAME="E4:7"/><i><font color="Green" title="E6">A4</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">q02</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>and </b><br/><a NAME="E5:7"/><i><font color="Green" title="E7">A5</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">c02</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>and </b><br/><a NAME="E6:7"/><i><font color="Green" title="E8">A6</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q11</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c15">q02</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">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<font color="Maroon" title="c16">c01</font> )
 <b>and </b><br/><a NAME="E7:7"/><i><font color="Green" title="E9">A7</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">c11</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c15">q02</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">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<font color="Maroon" title="c16">c01</font> )
 <b>and </b><br/><a NAME="E8:7"/><i><font color="Green" title="E10">A8</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q12</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<font color="Maroon" title="c17">c02</font> )
 <b>and </b><br/><a NAME="E9:7"/><i><font color="Green" title="E11">A9</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">c12</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<font color="Maroon" title="c17">c02</font> )
 <b>and </b><br/><a NAME="E10:7"/><i><font color="Green" title="E12">A10</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">q21</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c19">q12</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c20">c11</font> )
 <b>and </b><br/><a NAME="E11:7"/><i><font color="Green" title="E13">A11</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">c21</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <font color="Maroon" title="c19">q12</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c20">c11</font> )
 <b>and </b><br/><a NAME="E12:7"/><i><font color="Green" title="E14">A12</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c23">q22</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<font color="Maroon" title="c24">c21</font>,<font color="Maroon" title="c21">c12</font> )
 <b>and </b><br/><a NAME="E13:7"/><i><font color="Green" title="E15">A13</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c25">c22</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<font color="Maroon" title="c24">c21</font>,<font color="Maroon" title="c21">c12</font> )
 <b>and </b><br/><a NAME="E14:7"/><i><font color="Green" title="E16">A14</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">z0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">q00</font> )
 <b>and </b><br/><a NAME="E15:7"/><i><font color="Green" title="E17">A15</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">z1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">q01</font> )
 <b>and </b><br/><a NAME="E16:7"/><i><font color="Green" title="E18">A16</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">z2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q11</font> )
 <b>and </b><br/><a NAME="E17:7"/><i><font color="Green" title="E19">A17</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">z3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">q21</font> )
 <b>and </b><br/><a NAME="E18:7"/><i><font color="Green" title="E20">A18</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">z4</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c23">q22</font> )
 <b>and </b><br/><a NAME="E19:7"/><i><font color="Green" title="E21">A19</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">z5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c25">c22</font> )
 ;<br/>

<b>set </b><font color="Maroon" title="c26">x1y0</font> =  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font>;<br/>
<b>set </b><font color="Maroon" title="c27">x2y0</font> =  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font>;<br/>
<b>set </b><font color="Maroon" title="c28">x0y1</font> =  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font>;<br/>
<b>set </b><font color="Maroon" title="c29">x1y1</font> =  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>;<br/>
<b>set </b><font color="Maroon" title="c30">x2y1</font> =  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font>;<br/>
<b>set </b><font color="Maroon" title="c31">x0y2</font> =  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font>;<br/>
<b>set </b><font color="Maroon" title="c32">x1y2</font> =  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font>;<br/>
<b>set </b><font color="Maroon" title="c33">x2y2</font> =  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>;<br/>
<a NAME="E20:7"/><i><font color="Green" title="E22">A20</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">c01</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E3:7"><i><font color="Green" title="E5">A3</font></i></a>, <a class="txt" href="gate_5.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<a NAME="E21:7"/><b>then </b><i><font color="Green" title="E23">A21</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">c01</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</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">x0</font>,<font color="Maroon" title="c5">y1</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E22:7"/><i><font color="Green" title="E24">A22</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">q02</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E4:7"><i><font color="Green" title="E6">A4</font></i></a>, <a class="txt" href="gate_5.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E23:7"/><b>then </b><i><font color="Green" title="E25">A23</font></i>: 
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">q02</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<a NAME="E24:7"/><i><font color="Green" title="E26">A24</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">c02</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E5:7"><i><font color="Green" title="E7">A5</font></i></a>, <a class="txt" href="gate_5.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<a NAME="E25:7"/><b>then </b><i><font color="Green" title="E27">A25</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">c02</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</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">x1</font>,<font color="Maroon" title="c5">y1</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E26:7"/><i><font color="Green" title="E28">A26</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">q02</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">q02</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font> ) ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">c01</font> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">q02</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">q02</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">c01</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q11</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E6:7"><i><font color="Green" title="E8">A6</font></i></a>, <a class="ref" href="gate_1.html#T18" title="GATE_1:th.18">GATE_1:18</a></i>;<br/>
<a NAME="E27:7"/><i><font color="Green" title="E29">A27</font></i>: 
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">q02</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">c01</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">c01</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">q02</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">c11</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E7:7"><i><font color="Green" title="E9">A7</font></i></a>, <a class="ref" href="gate_1.html#T19" title="GATE_1:th.19">GATE_1:19</a></i>;<br/>
<a NAME="E28:7"/><i><font color="Green" title="E30">A28</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">c02</font> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">c02</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q12</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E8:7"><i><font color="Green" title="E10">A8</font></i></a>, <a class="ref" href="gate_1.html#T18" title="GATE_1:th.18">GATE_1:18</a></i>;<br/>
<a NAME="E29:7"/><i><font color="Green" title="E31">A29</font></i>: 
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">c02</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">c02</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">c12</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E9:7"><i><font color="Green" title="E11">A9</font></i></a>, <a class="ref" href="gate_1.html#T19" title="GATE_1:th.19">GATE_1:19</a></i>;<br/>
<a NAME="E30:7"/><i><font color="Green" title="E32">A30</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">q21</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">q12</font>,<font color="Maroon" title="c20">c11</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E10:7"><i><font color="Green" title="E12">A10</font></i></a>, <a class="txt" href="gate_5.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E31:7"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">c21</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c19">q12</font>,<font color="Maroon" title="c20">c11</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E11:7"><i><font color="Green" title="E13">A11</font></i></a>, <a class="txt" href="gate_5.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<a NAME="E32:7"/><b>then </b><i><font color="Green" title="E33">A31</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">c21</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q12</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">c11</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E33:7"/><i><font color="Green" title="E34">A32</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">c21</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">c21</font> ) ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">c12</font> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">c21</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">c21</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">c12</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c23">q22</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E12:7"><i><font color="Green" title="E14">A12</font></i></a>, <a class="ref" href="gate_1.html#T18" title="GATE_1:th.18">GATE_1:18</a></i>;<br/>
<a NAME="E34:7"/><i><font color="Green" title="E35">A33</font></i>: 
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">c21</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">c21</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">c12</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">c12</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c25">c22</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E13:7"><i><font color="Green" title="E15">A13</font></i></a>, <a class="ref" href="gate_1.html#T19" title="GATE_1:th.19">GATE_1:19</a></i>;<br/>
<b>thus </b><a NAME="E35:7"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">z0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K5" title="GATE_5:func.5">MULT310</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E1:7"><i><font color="Green" title="E3">A1</font></i></a>, <a class="txt" href="gate_5.html#E14:7"><i><font color="Green" title="E16">A14</font></i></a></i>;<br/>

<b>thus </b><a NAME="E36:7"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">z1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K6" title="GATE_5:func.6">MULT311</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E2:7"><i><font color="Green" title="E4">A2</font></i></a>, <a class="txt" href="gate_5.html#E15:7"><i><font color="Green" title="E17">A15</font></i></a></i>;<br/>

<b>set </b><font color="Maroon" title="c34">m312</font> =  <a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font>;<br/>
<a NAME="E37:7"/>
 <a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="gate_1.html#D37" title="GATE_1:def.37">GATE_1:def 37</a></i>;<br/>
<a NAME="E38:7"/><b>then </b><i><font color="Green" title="E36">A34</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T18" title="GATE_1:th.18">GATE_1:18</a></i>;<br/>
<a NAME="E39:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<a NAME="E40:7"/><b>then </b><i><font color="Green" title="E37">A35</font></i>: 
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font> ) ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<b>set </b><font color="Maroon" title="c35">m321</font> =  <a href="gate_5.html#K10" title="GATE_5:func.10">MULT321</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font>;<br/>
<a NAME="E41:7"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K10" title="GATE_5:func.10">MULT321</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E42:7"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">z2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K10" title="GATE_5:func.10">MULT321</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E3:7"><i><font color="Green" title="E5">A3</font></i></a>, <a class="txt" href="gate_5.html#E16:7"><i><font color="Green" title="E18">A16</font></i></a>, <a class="txt" href="gate_5.html#E22:7"><i><font color="Green" title="E24">A22</font></i></a>, <a class="txt" href="gate_5.html#E26:7"><i><font color="Green" title="E28">A26</font></i></a>, <a class="txt" href="gate_5.html#E38:7"><i><font color="Green" title="E36">A34</font></i></a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<a NAME="E43:7"/>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19" title="GATE_1:th.19">GATE_1:19</a></i>;<br/>
<a NAME="E44:7"/><b>then </b><i><font color="Green" title="E38">A36</font></i>: 
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<a NAME="E45:7"/><b>then </b><i><font color="Green" title="E39">A37</font></i>: 
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<b>set </b><font color="Maroon" title="c36">m313</font> =  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font>;<br/>
 <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> = 
 <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K36" title="GATE_1:func.36">CARR2</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D39" title="GATE_1:def.39">GATE_1:def 39</a></i>
<br/>.= 
 <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D38" title="GATE_1:def.38">GATE_1:def 38</a></i>
;<br/>
<a NAME="E47:7"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E1"><i><font color="Green" title="E1">Lm1</font></i></a></i>;<br/>
<a NAME="E48:7"/><b>then </b><i><font color="Green" title="E40">A38</font></i>: 
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font> &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> ) ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font> &amp; ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> ) ) ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E44:7"><i><font color="Green" title="E38">A36</font></i></a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>set </b><font color="Maroon" title="c37">m322</font> =  <a href="gate_5.html#K11" title="GATE_5:func.11">MULT322</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font>;<br/>
<a NAME="E49:7"/>
 <a href="gate_5.html#K11" title="GATE_5:func.11">MULT322</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="gate_1.html#D37" title="GATE_1:def.37">GATE_1:def 37</a></i>;<br/>
<a NAME="E50:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K11" title="GATE_5:func.11">MULT322</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T18" title="GATE_1:th.18">GATE_1:18</a></i>;<br/>
<a NAME="E51:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K11" title="GATE_5:func.11">MULT322</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E52:7"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">z3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K11" title="GATE_5:func.11">MULT322</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E17:7"><i><font color="Green" title="E19">A17</font></i></a>, <a class="txt" href="gate_5.html#E20:7"><i><font color="Green" title="E22">A20</font></i></a>, <a class="txt" href="gate_5.html#E22:7"><i><font color="Green" title="E24">A22</font></i></a>, <a class="txt" href="gate_5.html#E24:7"><i><font color="Green" title="E26">A24</font></i></a>, <a class="txt" href="gate_5.html#E27:7"><i><font color="Green" title="E29">A27</font></i></a>, <a class="txt" href="gate_5.html#E28:7"><i><font color="Green" title="E30">A28</font></i></a>, <a class="txt" href="gate_5.html#E30:7"><i><font color="Green" title="E32">A30</font></i></a>, <a class="txt" href="gate_5.html#E40:7"><i><font color="Green" title="E37">A35</font></i></a>, <a class="txt" href="gate_5.html#E48:7"><i><font color="Green" title="E40">A38</font></i></a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>

<b>set </b><font color="Maroon" title="c38">m314</font> =  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font>;<br/>
 <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> = 
 <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K36" title="GATE_1:func.36">CARR2</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D40" title="GATE_1:def.40">GATE_1:def 40</a></i>
<br/>.= 
 <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D38" title="GATE_1:def.38">GATE_1:def 38</a></i>
;<br/>
<a NAME="E54:7"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span>)</span> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<a NAME="E55:7"/><b>then </b><i><font color="Green" title="E41">A39</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c5">y1</font> &amp; ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c5">y1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c4">y0</font> ) ) ) )
 
<b>by </b><i><a class="txt" href="gate_5.html#E45:7"><i><font color="Green" title="E39">A37</font></i></a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<b>set </b><font color="Maroon" title="c39">m323</font> =  <a href="gate_5.html#K12" title="GATE_5:func.12">MULT323</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font>;<br/>
 <a href="gate_5.html#K12" title="GATE_5:func.12">MULT323</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> = 
 <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K36" title="GATE_1:func.36">CARR2</a> <span class="p2">(<span class="default"><a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D39" title="GATE_1:def.39">GATE_1:def 39</a></i>
<br/>.= 
 <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D38" title="GATE_1:def.38">GATE_1:def 38</a></i>
;<br/>
<a NAME="E57:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K12" title="GATE_5:func.12">MULT323</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T18" title="GATE_1:th.18">GATE_1:18</a></i>;<br/>
<a NAME="E58:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) &amp; ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K12" title="GATE_5:func.12">MULT323</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19" title="GATE_1:th.19">GATE_1:19</a></i>;<br/>
<a NAME="E59:7"/><b>then </b>
( ( ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) or ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> ) &amp; not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) or ( not <!--HUMANRECFAILED-->(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) &amp; ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K12" title="GATE_5:func.12">MULT323</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E60:7"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">z4</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K12" title="GATE_5:func.12">MULT323</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E18:7"><i><font color="Green" title="E20">A18</font></i></a>, <a class="txt" href="gate_5.html#E21:7"><i><font color="Green" title="E23">A21</font></i></a>, <a class="txt" href="gate_5.html#E23:7"><i><font color="Green" title="E25">A23</font></i></a>, <a class="txt" href="gate_5.html#E25:7"><i><font color="Green" title="E27">A25</font></i></a>, <a class="txt" href="gate_5.html#E27:7"><i><font color="Green" title="E29">A27</font></i></a>, <a class="txt" href="gate_5.html#E28:7"><i><font color="Green" title="E30">A28</font></i></a>, <a class="txt" href="gate_5.html#E29:7"><i><font color="Green" title="E31">A29</font></i></a>, <a class="txt" href="gate_5.html#E32:7"><i><font color="Green" title="E33">A31</font></i></a>, <a class="txt" href="gate_5.html#E33:7"><i><font color="Green" title="E34">A32</font></i></a>, <a class="txt" href="gate_5.html#E40:7"><i><font color="Green" title="E37">A35</font></i></a>, <a class="txt" href="gate_5.html#E48:7"><i><font color="Green" title="E40">A38</font></i></a>, <a class="txt" href="gate_5.html#E55:7"><i><font color="Green" title="E41">A39</font></i></a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>

<b>set </b><font color="Maroon" title="c40">m324</font> =  <a href="gate_5.html#K13" title="GATE_5:func.13">MULT324</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font>;<br/>
 <a href="gate_5.html#K13" title="GATE_5:func.13">MULT324</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> = 
 <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K36" title="GATE_1:func.36">CARR2</a> <span class="p2">(<span class="default"><a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D40" title="GATE_1:def.40">GATE_1:def 40</a></i>
<br/>.= 
 <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p3">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p3">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="gate_1.html#D38" title="GATE_1:def.38">GATE_1:def 38</a></i>
;<br/>
<a NAME="E62:7"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p2">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span>)</span> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K13" title="GATE_5:func.13">MULT324</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19" title="GATE_1:th.19">GATE_1:19</a></i>;<br/>
<a NAME="E63:7"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> &amp; ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K11" title="GATE_1:func.11">MAJ3</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K13" title="GATE_5:func.13">MULT324</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T19" title="GATE_1:th.19">GATE_1:19</a></i>;<br/>
<a NAME="E64:7"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font> &amp; ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) ) or ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c6">y2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <span class="p1">(<span class="default"><a href="gate_5.html#K7" title="GATE_5:func.7">MULT312</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c6">y2</font></span>)</span> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K8" title="GATE_5:func.8">MULT313</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K9" title="GATE_5:func.9">MULT314</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> ) ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K13" title="GATE_5:func.13">MULT324</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 
<b>by </b><i><a class="txt" href="gate_5.html#E2"><i><font color="Green" title="E2">Lm2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E65:7"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">z5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_5.html#K13" title="GATE_5:func.13">MULT324</a> <font color="Maroon" title="c3">x2</font>,<font color="Maroon" title="c6">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c5">y1</font>,<font color="Maroon" title="c1">x0</font>,<font color="Maroon" title="c4">y0</font> )
 <b>by </b><i><a class="txt" href="gate_5.html#E19:7"><i><font color="Green" title="E21">A19</font></i></a>, <a class="txt" href="gate_5.html#E21:7"><i><font color="Green" title="E23">A21</font></i></a>, <a class="txt" href="gate_5.html#E23:7"><i><font color="Green" title="E25">A23</font></i></a>, <a class="txt" href="gate_5.html#E25:7"><i><font color="Green" title="E27">A25</font></i></a>, <a class="txt" href="gate_5.html#E27:7"><i><font color="Green" title="E29">A27</font></i></a>, <a class="txt" href="gate_5.html#E28:7"><i><font color="Green" title="E30">A28</font></i></a>, <a class="txt" href="gate_5.html#E29:7"><i><font color="Green" title="E31">A29</font></i></a>, <a class="txt" href="gate_5.html#E32:7"><i><font color="Green" title="E33">A31</font></i></a>, <a class="txt" href="gate_5.html#E34:7"><i><font color="Green" title="E35">A33</font></i></a>, <a class="txt" href="gate_5.html#E40:7"><i><font color="Green" title="E37">A35</font></i></a>, <a class="txt" href="gate_5.html#E48:7"><i><font color="Green" title="E40">A38</font></i></a>, <a class="txt" href="gate_5.html#E55:7"><i><font color="Green" title="E41">A39</font></i></a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>


</div>
