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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <!--HUMANRECFAILED-->( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">s0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font></span>)</span> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">s0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">s1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font></span>)</span>,<font color="Maroon" title="c17">q1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">s1</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font></span>)</span>,<font color="Maroon" title="c18">q2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font></span>)</span> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font></span>)</span>,<font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c17">q1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c19">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font></span>)</span> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c19">q3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font></span>)</span>,<font color="Maroon" title="c17">q1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c19">q3</font>,<font color="Maroon" title="c18">q2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font></span>)</span> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c19">q3</font>,<font color="Maroon" title="c18">q2</font>,<font color="Maroon" title="c17">q1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font></span>)</span> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font></span>)</span>,<font color="Maroon" title="c20">nq1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font></span>)</span>,<font color="Maroon" title="c21">nq2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font></span>)</span> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font></span>)</span>,<font color="Maroon" title="c21">nq2</font>,<font color="Maroon" title="c20">nq1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c22">nq3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font></span>)</span> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c22">nq3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font></span>)</span>,<font color="Maroon" title="c20">nq1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c22">nq3</font>,<font color="Maroon" title="c21">nq2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font></span>)</span> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a>  <a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c22">nq3</font>,<font color="Maroon" title="c21">nq2</font>,<font color="Maroon" title="c20">nq1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">nq1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">nq1</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">nq2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c21">nq2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">nq3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c18">q2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c22">nq3</font> ) &amp; not <!--HUMANRECFAILED-->( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">s0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">s0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">s1</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">s1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> ) ) )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:3"/><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="E2:3"/><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="E3:3"/><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="E4:3"/><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="E5:3"/><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="E6:3"/><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="E7:3"/><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="E8:3"/><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="E9:3"/><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="E10:3"/><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="E11:3"/><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="E12:3"/><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="E13:3"/><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="E14:3"/><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="E15:3"/><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="E16:3"/><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="E17:3"/><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="c19">q3</font> )
 <b>and </b><br/><a NAME="E18:3"/><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> <font color="Maroon" title="c17">q1</font> )
 <b>and </b><br/><a NAME="E19:3"/><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> <font color="Maroon" title="c18">q2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">s0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c1">s0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c10">ns1</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">s1</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">s1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> ) )</span><br/>

<a NAME="E20:3"/>
(  <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_3.html#E10:3"><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="E21:3"/><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="txt" href="gate_3.html#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><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></i>;<br/>
<b>hence </b><a NAME="E22:3"/>
(  <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_3.html#E1:3"><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">s1</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c2">s1</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c12">ns3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> ) )</span><br/>

<a NAME="E23:3"/>
(  <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">$</a> <font color="Maroon" title="c21">nq2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c20">nq1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E12:3"><i><font color="Green" title="E12">A12</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>;<br/>
<a NAME="E24:3"/><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">$</a>  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><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></i>;<br/>
<b>hence </b><a NAME="E25:3"/>
(  <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="c2">s1</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E2:3"><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c4">s3</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c16">ns7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> ) )</span><br/>

<b>thus </b><a NAME="E26:3"/>
(  <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="c4">s3</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E4:3"><i><font color="Green" title="E4">A4</font></i></a>, <a class="txt" href="gate_3.html#E16:3"><i><font color="Green" title="E16">A16</font></i></a>, <a class="txt" href="gate_3.html#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><i><font color="Green" title="E19">A19</font></i></a>, <a class="ref" href="gate_1.html#T16" title="GATE_1:th.16">GATE_1:16</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c8">s7</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c15">ns6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> ) )</span><br/>

<a NAME="E27:3"/>
(  <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_3.html#E15:3"><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="E28:3"/><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">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c17">q1</font> ) )
 
<b>by </b><i><a class="txt" href="gate_3.html#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><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></i>;<br/>
<b>hence </b><a NAME="E29:3"/>
(  <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="c8">s7</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E8:3"><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c7">s6</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c13">ns4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> ) )</span><br/>

<a NAME="E30:3"/>
(  <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_3.html#E13:3"><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="E31:3"/><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">$</a> <font color="Maroon" title="c18">q2</font> &amp;  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</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="txt" href="gate_3.html#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><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></i>;<br/>
<b>hence </b><a NAME="E32:3"/>
(  <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="c7">s6</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E7:3"><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c5">s4</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c9">ns0</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> ) )</span><br/>

<a NAME="E33:3"/>
(  <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_3.html#E9:3"><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="E34:3"/><b>then </b>
(  <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="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="txt" href="gate_3.html#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><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></i>;<br/>
<b>hence </b><a NAME="E35:3"/>
(  <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="c5">s4</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E5:3"><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c6">s5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c11">ns2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> ) &amp; (  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c3">s2</font> implies  <a href="gate_1.html#NR1" title="GATE_1:NR.1">$</a> <font color="Maroon" title="c14">ns5</font> ) )</span><br/>

<a NAME="E36:3"/>
(  <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_3.html#E11:3"><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="E37:3"/><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> <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="txt" href="gate_3.html#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><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></i>;<br/>
<b>hence </b><a NAME="E38:3"/>
(  <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="c6">s5</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E6:3"><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <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="c3">s2</font> )</span><br/>

<a NAME="E39:3"/>
(  <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_3.html#E14:3"><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="E40:3"/><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#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="txt" href="gate_3.html#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="gate_3.html#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="gate_3.html#E19:3"><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></i>;<br/>
<b>hence </b><a NAME="E41:3"/>
(  <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="c3">s2</font> )
 <b>by </b><i><a class="txt" href="gate_3.html#E3:3"><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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