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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">ns0</font>, <font color="Maroon" title="c10">ns1</font>, <font color="Maroon" title="c11">ns2</font>, <font color="Maroon" title="c12">ns3</font>, <font color="Maroon" title="c13">ns4</font>, <font color="Maroon" title="c14">ns5</font>, <font color="Maroon" title="c15">ns6</font>, <font color="Maroon" title="c16">ns7</font>, <font color="Maroon" title="c17">q1</font>, <font color="Maroon" title="c18">q2</font>, <font color="Maroon" title="c19">q3</font>, <font color="Maroon" title="c20">nq1</font>, <font color="Maroon" title="c21">nq2</font>, <font color="Maroon" title="c22">nq3</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:1"/><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#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">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="c18">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="c17">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E2:1"/><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#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">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="c18">q2</font></span>)</span>,<font color="Maroon" title="c17">q1</font> )
 <b>and </b><br/><a NAME="E3:1"/><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#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font></span>)</span>,<font color="Maroon" title="c18">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="c17">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E4:1"/><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#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font></span>)</span>,<font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c17">q1</font> )
 <b>and </b><br/><a NAME="E5:1"/><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#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c19">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="c18">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="c17">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E6:1"/><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#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c19">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="c18">q2</font></span>)</span>,<font color="Maroon" title="c17">q1</font> )
 <b>and </b><br/><a NAME="E7:1"/><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#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c19">q3</font>,<font color="Maroon" title="c18">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="c17">q1</font></span>)</span> )
 <b>and </b><br/><a NAME="E8:1"/><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#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c19">q3</font>,<font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c17">q1</font> )
 <b>and </b><br/><a NAME="E9:1"/><i><font color="Green" title="E9">A9</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">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="c21">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="c20">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E10:1"/><i><font color="Green" title="E10">A10</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">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="c21">nq2</font></span>)</span>,<font color="Maroon" title="c20">nq1</font> )
 <b>and </b><br/><a NAME="E11:1"/><i><font color="Green" title="E11">A11</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font></span>)</span>,<font color="Maroon" title="c21">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="c20">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E12:1"/><i><font color="Green" title="E12">A12</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font></span>)</span>,<font color="Maroon" title="c21">nq2</font>,<font color="Maroon" title="c20">nq1</font> )
 <b>and </b><br/><a NAME="E13:1"/><i><font color="Green" title="E13">A13</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c22">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="c21">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="c20">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E14:1"/><i><font color="Green" title="E14">A14</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c22">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="c21">nq2</font></span>)</span>,<font color="Maroon" title="c20">nq1</font> )
 <b>and </b><br/><a NAME="E15:1"/><i><font color="Green" title="E15">A15</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c22">nq3</font>,<font color="Maroon" title="c21">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="c20">nq1</font></span>)</span> )
 <b>and </b><br/><a NAME="E16:1"/><i><font color="Green" title="E16">A16</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c22">nq3</font>,<font color="Maroon" title="c21">nq2</font>,<font color="Maroon" title="c20">nq1</font> )
 <b>and </b><br/><a NAME="E17:1"/><i><font color="Green" title="E17">A17</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">nq1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> )
 <b>and </b><br/><a NAME="E18:1"/><i><font color="Green" title="E18">A18</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">nq2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">q1</font>,<font color="Maroon" title="c18">q2</font> )
 <b>and </b><br/><a NAME="E19:1"/><i><font color="Green" title="E19">A19</font></i>: 
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">nq3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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="c19">q3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font></span>)</span></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="c17">q1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font></span>)</span></span>)</span> )
 ;<br/>

<a NAME="E20:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E10:1"><i><font color="Green" title="E10">A10</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>
<a NAME="E21:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">q1</font>,<font color="Maroon" title="c18">q2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E17:1"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_2.html#E18:1"><i><font color="Green" title="E18">A18</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<a NAME="E22:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> iff ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c19">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="c17">q1</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E19:1"><i><font color="Green" title="E19">A19</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#T7" title="GATE_1:th.7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<a NAME="E23:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font> ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E24:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</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="E25:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">s0</font> )
 <b>by </b><i><a class="txt" href="gate_2.html#E1:1"><i><font color="Green" title="E1">A1</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>

<a NAME="E26:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E11:1"><i><font color="Green" title="E11">A11</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>
<a NAME="E27:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> iff ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c19">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="c17">q1</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E17:1"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_2.html#E18:1"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_2.html#E19:1"><i><font color="Green" title="E19">A19</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#T7" title="GATE_1:th.7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<a NAME="E28:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font> ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E29:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E30:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E31:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">s1</font> )
 <b>by </b><i><a class="txt" href="gate_2.html#E2:1"><i><font color="Green" title="E2">A2</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>

<a NAME="E32:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">q1</font>,<font color="Maroon" title="c18">q2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E12:1"><i><font color="Green" title="E12">A12</font></i></a>, <a class="txt" href="gate_2.html#E17:1"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_2.html#E18:1"><i><font color="Green" title="E18">A18</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#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>
<a NAME="E33:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> iff ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c19">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="c17">q1</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font></span>)</span> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E19:1"><i><font color="Green" title="E19">A19</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#T7" title="GATE_1:th.7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<a NAME="E34:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E35:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</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="E36:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> )
 <b>by </b><i><a class="txt" href="gate_2.html#E3:1"><i><font color="Green" title="E3">A3</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>

<a NAME="E37:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E13:1"><i><font color="Green" title="E13">A13</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>
<a NAME="E38:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> iff ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c19">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="c17">q1</font></span>)</span> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font></span>)</span> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E17:1"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_2.html#E18:1"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_2.html#E19:1"><i><font color="Green" title="E19">A19</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#T7" title="GATE_1:th.7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<a NAME="E39:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> iff ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font> ) ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E40:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> iff ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<a NAME="E41:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E42:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> )
 <b>by </b><i><a class="txt" href="gate_2.html#E4:1"><i><font color="Green" title="E4">A4</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>

<a NAME="E43:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E14:1"><i><font color="Green" title="E14">A14</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>
<a NAME="E44:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">nq3</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">q1</font>,<font color="Maroon" title="c18">q2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E17:1"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_2.html#E18:1"><i><font color="Green" title="E18">A18</font></i></a>, <a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a></i>;<br/>
<a NAME="E45:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> iff ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c19">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="c17">q1</font></span>)</span> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font></span>)</span> ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E19:1"><i><font color="Green" title="E19">A19</font></i></a>, <a class="ref" href="gate_1.html#T7" title="GATE_1:th.7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<a NAME="E46:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><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/>
<b>hence </b><a NAME="E47:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> )
 <b>by </b><i><a class="txt" href="gate_2.html#E5:1"><i><font color="Green" title="E5">A5</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>

<a NAME="E48:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E15:1"><i><font color="Green" title="E15">A15</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>
<a NAME="E49:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> iff ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c19">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="c17">q1</font></span>)</span> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font></span>)</span> ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E17:1"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_2.html#E18:1"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_2.html#E19:1"><i><font color="Green" title="E19">A19</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#T7" title="GATE_1:th.7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<a NAME="E50:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> iff ( ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> ) or (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font> ) ) &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E51:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E52:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E53:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> )
 <b>by </b><i><a class="txt" href="gate_2.html#E6:1"><i><font color="Green" title="E6">A6</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>

<a NAME="E54:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">q1</font>,<font color="Maroon" title="c18">q2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E16:1"><i><font color="Green" title="E16">A16</font></i></a>, <a class="txt" href="gate_2.html#E17:1"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_2.html#E18:1"><i><font color="Green" title="E18">A18</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#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>
<a NAME="E55:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> iff ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c19">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="c17">q1</font></span>)</span> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font></span>)</span> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E19:1"><i><font color="Green" title="E19">A19</font></i></a>, <a class="ref" href="gate_1.html#T7" title="GATE_1:th.7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<a NAME="E56:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><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/>
<b>hence </b><a NAME="E57:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> )
 <b>by </b><i><a class="txt" href="gate_2.html#E7:1"><i><font color="Green" title="E7">A7</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>

<a NAME="E58:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> iff (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E9:1"><i><font color="Green" title="E9">A9</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>
<a NAME="E59:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> iff ( not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c19">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="c17">q1</font></span>)</span> &amp; not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font></span>)</span> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_2.html#E17:1"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_2.html#E18:1"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_2.html#E19:1"><i><font color="Green" title="E19">A19</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#T7" title="GATE_1:th.7">GATE_1:7</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<a NAME="E60:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> ) &amp; (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> or  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c19">q3</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</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="E61:1"/><b>then </b>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> iff ( (  not  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> or  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c19">q3</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="ref" href="gate_1.html#T4" title="GATE_1:th.4">GATE_1:4</a>, <a class="ref" href="gate_1.html#T8" title="GATE_1:th.8">GATE_1:8</a></i>;<br/>
<b>hence </b><a NAME="E62:1"/>
(  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> iff  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> )
 <b>by </b><i><a class="txt" href="gate_2.html#E8:1"><i><font color="Green" title="E8">A8</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>


</div>
