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<b>let </b><font color="Maroon" title="c1">s0</font>, <font color="Maroon" title="c2">s1</font>, <font color="Maroon" title="c3">s2</font>, <font color="Maroon" title="c4">s3</font>, <font color="Maroon" title="c5">s4</font>, <font color="Maroon" title="c6">s5</font>, <font color="Maroon" title="c7">s6</font>, <font color="Maroon" title="c8">s7</font>, <font color="Maroon" title="c9">s8</font>, <font color="Maroon" title="c10">s9</font>, <font color="Maroon" title="c11">s10</font>, <font color="Maroon" title="c12">s11</font>, <font color="Maroon" title="c13">s12</font>, <font color="Maroon" title="c14">s13</font>, <font color="Maroon" title="c15">s14</font>, <font color="Maroon" title="c16">s15</font>, <font color="Maroon" title="c17">ns0</font>, <font color="Maroon" title="c18">ns1</font>, <font color="Maroon" title="c19">ns2</font>, <font color="Maroon" title="c20">ns3</font>, <font color="Maroon" title="c21">ns4</font>, <font color="Maroon" title="c22">ns5</font>, <font color="Maroon" title="c23">ns6</font>, <font color="Maroon" title="c24">ns7</font>, <font color="Maroon" title="c25">ns8</font>, <font color="Maroon" title="c26">ns9</font>, <font color="Maroon" title="c27">ns10</font>, <font color="Maroon" title="c28">ns11</font>, <font color="Maroon" title="c29">ns12</font>, <font color="Maroon" title="c30">ns13</font>, <font color="Maroon" title="c31">ns14</font>, <font color="Maroon" title="c32">ns15</font>, <font color="Maroon" title="c33">q1</font>, <font color="Maroon" title="c34">q2</font>, <font color="Maroon" title="c35">q3</font>, <font color="Maroon" title="c36">q4</font>, <font color="Maroon" title="c37">nq1</font>, <font color="Maroon" title="c38">nq2</font>, <font color="Maroon" title="c39">nq3</font>, <font color="Maroon" title="c40">nq4</font>, <font color="Maroon" title="c41">R</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:6"/><i><font color="Green" title="E1">A1</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">s0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E2:6"/><i><font color="Green" title="E2">A2</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">s1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font></span>)</span>,<font color="Maroon" title="c33">q1</font> )
 <b>and </b><br/><a NAME="E3:6"/><i><font color="Green" title="E3">A3</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font></span>)</span>,<font color="Maroon" title="c34">q2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E4:6"/><i><font color="Green" title="E4">A4</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font></span>)</span>,<font color="Maroon" title="c34">q2</font>,<font color="Maroon" title="c33">q1</font> )
 <b>and </b><br/><a NAME="E5:6"/><i><font color="Green" title="E5">A5</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font></span>)</span>,<font color="Maroon" title="c35">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E6:6"/><i><font color="Green" title="E6">A6</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font></span>)</span>,<font color="Maroon" title="c35">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font></span>)</span>,<font color="Maroon" title="c33">q1</font> )
 <b>and </b><br/><a NAME="E7:6"/><i><font color="Green" title="E7">A7</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font></span>)</span>,<font color="Maroon" title="c35">q3</font>,<font color="Maroon" title="c34">q2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E8:6"/><i><font color="Green" title="E8">A8</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font></span>)</span>,<font color="Maroon" title="c35">q3</font>,<font color="Maroon" title="c34">q2</font>,<font color="Maroon" title="c33">q1</font> )
 <b>and </b><br/><a NAME="E9:6"/><i><font color="Green" title="E9">A9</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">s8</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c36">q4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E10:6"/><i><font color="Green" title="E10">A10</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">s9</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c36">q4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font></span>)</span>,<font color="Maroon" title="c33">q1</font> )
 <b>and </b><br/><a NAME="E11:6"/><i><font color="Green" title="E11">A11</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">s10</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c36">q4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font></span>)</span>,<font color="Maroon" title="c34">q2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E12:6"/><i><font color="Green" title="E12">A12</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">s11</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c36">q4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font></span>)</span>,<font color="Maroon" title="c34">q2</font>,<font color="Maroon" title="c33">q1</font> )
 <b>and </b><br/><a NAME="E13:6"/><i><font color="Green" title="E13">A13</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">s12</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c36">q4</font>,<font color="Maroon" title="c35">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E14:6"/><i><font color="Green" title="E14">A14</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">s13</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c36">q4</font>,<font color="Maroon" title="c35">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font></span>)</span>,<font color="Maroon" title="c33">q1</font> )
 <b>and </b><br/><a NAME="E15:6"/><i><font color="Green" title="E15">A15</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">s14</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c36">q4</font>,<font color="Maroon" title="c35">q3</font>,<font color="Maroon" title="c34">q2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E16:6"/><i><font color="Green" title="E16">A16</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">s15</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c36">q4</font>,<font color="Maroon" title="c35">q3</font>,<font color="Maroon" title="c34">q2</font>,<font color="Maroon" title="c33">q1</font> )
 <b>and </b><br/><a NAME="E17:6"/><i><font color="Green" title="E17">A17</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">ns0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E18:6"/><i><font color="Green" title="E18">A18</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">ns1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font></span>)</span>,<font color="Maroon" title="c37">nq1</font> )
 <b>and </b><br/><a NAME="E19:6"/><i><font color="Green" title="E19">A19</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">ns2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font></span>)</span>,<font color="Maroon" title="c38">nq2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E20:6"/><i><font color="Green" title="E20">A20</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">ns3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font></span>)</span>,<font color="Maroon" title="c38">nq2</font>,<font color="Maroon" title="c37">nq1</font> )
 <b>and </b><br/><a NAME="E21:6"/><i><font color="Green" title="E21">A21</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">ns4</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font></span>)</span>,<font color="Maroon" title="c39">nq3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E22:6"/><i><font color="Green" title="E22">A22</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">ns5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font></span>)</span>,<font color="Maroon" title="c39">nq3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font></span>)</span>,<font color="Maroon" title="c37">nq1</font> )
 <b>and </b><br/><a NAME="E23:6"/><i><font color="Green" title="E23">A23</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c23">ns6</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font></span>)</span>,<font color="Maroon" title="c39">nq3</font>,<font color="Maroon" title="c38">nq2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E24:6"/><i><font color="Green" title="E24">A24</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">ns7</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font></span>)</span>,<font color="Maroon" title="c39">nq3</font>,<font color="Maroon" title="c38">nq2</font>,<font color="Maroon" title="c37">nq1</font> )
 <b>and </b><br/><a NAME="E25:6"/><i><font color="Green" title="E25">A25</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c25">ns8</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c40">nq4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E26:6"/><i><font color="Green" title="E26">A26</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c26">ns9</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c40">nq4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font></span>)</span>,<font color="Maroon" title="c37">nq1</font> )
 <b>and </b><br/><a NAME="E27:6"/><i><font color="Green" title="E27">A27</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c27">ns10</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c40">nq4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font></span>)</span>,<font color="Maroon" title="c38">nq2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E28:6"/><i><font color="Green" title="E28">A28</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c28">ns11</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c40">nq4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font></span>)</span>,<font color="Maroon" title="c38">nq2</font>,<font color="Maroon" title="c37">nq1</font> )
 <b>and </b><br/><a NAME="E29:6"/><i><font color="Green" title="E29">A29</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c29">ns12</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c40">nq4</font>,<font color="Maroon" title="c39">nq3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E30:6"/><i><font color="Green" title="E30">A30</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c30">ns13</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c40">nq4</font>,<font color="Maroon" title="c39">nq3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font></span>)</span>,<font color="Maroon" title="c37">nq1</font> )
 <b>and </b><br/><a NAME="E31:6"/><i><font color="Green" title="E31">A31</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c31">ns14</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c40">nq4</font>,<font color="Maroon" title="c39">nq3</font>,<font color="Maroon" title="c38">nq2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E32:6"/><i><font color="Green" title="E32">A32</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c32">ns15</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c40">nq4</font>,<font color="Maroon" title="c39">nq3</font>,<font color="Maroon" title="c38">nq2</font>,<font color="Maroon" title="c37">nq1</font> )
 <b>and </b><br/><a NAME="E33:6"/><i><font color="Green" title="E33">A33</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">nq1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font></span>)</span>,<font color="Maroon" title="c41">R</font> )
 <b>and </b><br/><a NAME="E34:6"/><i><font color="Green" title="E34">A34</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">nq2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c33">q1</font>,<font color="Maroon" title="c41">R</font> )
 <b>and </b><br/><a NAME="E35:6"/><i><font color="Green" title="E35">A35</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">nq3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c34">q2</font>,<font color="Maroon" title="c41">R</font> )
 <b>and </b><br/><a NAME="E36:6"/><i><font color="Green" title="E36">A36</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">nq4</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c35">q3</font>,<font color="Maroon" title="c41">R</font> )
 ;<br/>

<a NAME="E37:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">ns1</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E18:6"><i><font color="Green" title="E18">A18</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E38:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">ns1</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E39:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">ns1</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E40:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">ns1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">s0</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E1:6"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E41:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">ns3</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E20:6"><i><font color="Green" title="E20">A20</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E42:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">ns3</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E43:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">ns3</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E44:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">ns3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E2:6"><i><font color="Green" title="E2">A2</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E45:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">ns7</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E24:6"><i><font color="Green" title="E24">A24</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E46:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">ns7</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E47:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">ns7</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E48:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c24">ns7</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">s3</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E4:6"><i><font color="Green" title="E4">A4</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E49:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c32">ns15</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E32:6"><i><font color="Green" title="E32">A32</font></i></a>, <a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<b>hence </b><a NAME="E50:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c32">ns15</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">s7</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E8:6"><i><font color="Green" title="E8">A8</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E51:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c31">ns14</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E31:6"><i><font color="Green" title="E31">A31</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E52:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c31">ns14</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E53:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c31">ns14</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E54:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c31">ns14</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c16">s15</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E16:6"><i><font color="Green" title="E16">A16</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E55:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c29">ns12</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E29:6"><i><font color="Green" title="E29">A29</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E56:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c29">ns12</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E57:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c29">ns12</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E58:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c29">ns12</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c15">s14</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E15:6"><i><font color="Green" title="E15">A15</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E59:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c25">ns8</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E25:6"><i><font color="Green" title="E25">A25</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E60:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c25">ns8</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E61:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c25">ns8</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E62:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c25">ns8</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c13">s12</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E13:6"><i><font color="Green" title="E13">A13</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E63:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">ns0</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E17:6"><i><font color="Green" title="E17">A17</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E64:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">ns0</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E65:6"/><b>then </b>
( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">ns0</font> )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<a NAME="E66:6"/><b>then </b>
( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">s8</font>,<font color="Maroon" title="c41">R</font> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c41">R</font> ) iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">ns0</font> )
 
<b>by </b><i><a class="txt" href="gate_3.html#E9:6"><i><font color="Green" title="E9">A9</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<b>hence </b><a NAME="E67:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">ns0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">s8</font>,<font color="Maroon" title="c41">R</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c41">R</font></span>)</span> )
 <b>by </b><i><a class="ref" href="gate_1.html#T7" title="GATE_1:th.7">GATE_1:7</a></i>;<br/>

<a NAME="E68:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">ns5</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E22:6"><i><font color="Green" title="E22">A22</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E69:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">ns5</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E70:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">ns5</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E71:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">ns5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E3:6"><i><font color="Green" title="E3">A3</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E72:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c28">ns11</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E28:6"><i><font color="Green" title="E28">A28</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E73:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c28">ns11</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E74:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c28">ns11</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E75:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c28">ns11</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">s5</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E6:6"><i><font color="Green" title="E6">A6</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E76:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c23">ns6</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E23:6"><i><font color="Green" title="E23">A23</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E77:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c23">ns6</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E78:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c23">ns6</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E79:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c23">ns6</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">s11</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E12:6"><i><font color="Green" title="E12">A12</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E80:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c30">ns13</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E30:6"><i><font color="Green" title="E30">A30</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E81:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c30">ns13</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E82:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c30">ns13</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E83:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c30">ns13</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">s6</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E7:6"><i><font color="Green" title="E7">A7</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E84:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c27">ns10</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E27:6"><i><font color="Green" title="E27">A27</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E85:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c27">ns10</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E86:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c27">ns10</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E87:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c27">ns10</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c14">s13</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E14:6"><i><font color="Green" title="E14">A14</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E88:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">ns4</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E21:6"><i><font color="Green" title="E21">A21</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E89:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">ns4</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E90:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">ns4</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E91:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">ns4</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">s10</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E11:6"><i><font color="Green" title="E11">A11</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E92:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c26">ns9</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E26:6"><i><font color="Green" title="E26">A26</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E93:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c26">ns9</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E94:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c26">ns9</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E95:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c26">ns9</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">s4</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E5:6"><i><font color="Green" title="E5">A5</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>

<a NAME="E96:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">ns2</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c40">nq4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c39">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c38">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c37">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E19:6"><i><font color="Green" title="E19">A19</font></i></a>, <a class="ref" href="gate_1.html#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>
<a NAME="E97:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">ns2</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c36">q4</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c35">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c34">q2</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E33:6"><i><font color="Green" title="E33">A33</font></i></a>, <a class="txt" href="gate_3.html#E34:6"><i><font color="Green" title="E34">A34</font></i></a>, <a class="txt" href="gate_3.html#E35:6"><i><font color="Green" title="E35">A35</font></i></a>, <a class="txt" href="gate_3.html#E36:6"><i><font color="Green" title="E36">A36</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T6" title="GATE_1:th.6">GATE_1:6</a></i>;<br/>
<a NAME="E98:6"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">ns2</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c36">q4</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c35">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c34">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c33">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c41">R</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<b>hence </b><a NAME="E99:6"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">ns2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">s9</font>,<font color="Maroon" title="c41">R</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E10:6"><i><font color="Green" title="E10">A10</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#T22" title="GATE_1:th.22">GATE_1:22</a></i>;<br/>


</div>
