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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-->( ( not <font color="Maroon" title="c1">s0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c1">s0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c2">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c2">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c10">ns1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c10">ns1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c20">nq1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c20">nq1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c21">nq2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c17">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c17">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c21">nq2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c22">nq3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c18">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c18">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c22">nq3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <!--HUMANRECFAILED-->( ( not <font color="Maroon" title="c10">ns1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c1">s0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c1">s0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c10">ns1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c2">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c2">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:3"/><i><font color="Green" title="E1">A1</font></i>: 
( not <font color="Maroon" title="c1">s0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E2:3"/><i><font color="Green" title="E2">A2</font></i>: 
( not <font color="Maroon" title="c2">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E3:3"/><i><font color="Green" title="E3">A3</font></i>: 
( not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E4:3"/><i><font color="Green" title="E4">A4</font></i>: 
( not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E5:3"/><i><font color="Green" title="E5">A5</font></i>: 
( not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E6:3"/><i><font color="Green" title="E6">A6</font></i>: 
( not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E7:3"/><i><font color="Green" title="E7">A7</font></i>: 
( not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E8:3"/><i><font color="Green" title="E8">A8</font></i>: 
( not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E9:3"/><i><font color="Green" title="E9">A9</font></i>: 
( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E10:3"/><i><font color="Green" title="E10">A10</font></i>: 
( not <font color="Maroon" title="c10">ns1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E11:3"/><i><font color="Green" title="E11">A11</font></i>: 
( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E12:3"/><i><font color="Green" title="E12">A12</font></i>: 
( not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E13:3"/><i><font color="Green" title="E13">A13</font></i>: 
( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E14:3"/><i><font color="Green" title="E14">A14</font></i>: 
( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E15:3"/><i><font color="Green" title="E15">A15</font></i>: 
( not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E16:3"/><i><font color="Green" title="E16">A16</font></i>: 
( not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <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> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E17:3"/><i><font color="Green" title="E17">A17</font></i>: 
( not <font color="Maroon" title="c20">nq1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E18:3"/><i><font color="Green" title="E18">A18</font></i>: 
( not <font color="Maroon" title="c21">nq2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c17">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E19:3"/><i><font color="Green" title="E19">A19</font></i>: 
( not <font color="Maroon" title="c22">nq3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c18">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c10">ns1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c1">s0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c1">s0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c10">ns1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c2">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c2">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E20:3"/>
( not <font color="Maroon" title="c10">ns1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c20">nq1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E10:3"><i><font color="Green" title="E10">A10</font></i></a></i>;<br/>
<a NAME="E21:3"/><b>then </b>
( not <font color="Maroon" title="c10">ns1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="#E19:3"><i><font color="Green" title="E19">A19</font></i></a></i>;<br/>
<b>hence </b><a NAME="E22:3"/>
( not <font color="Maroon" title="c10">ns1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c1">s0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c2">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c2">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E23:3"/>
( not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c21">nq2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c20">nq1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E12:3"><i><font color="Green" title="E12">A12</font></i></a></i>;<br/>
<a NAME="E24:3"/><b>then </b>
( not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c17">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="#E19:3"><i><font color="Green" title="E19">A19</font></i></a></i>;<br/>
<b>hence </b><a NAME="E25:3"/>
( not <font color="Maroon" title="c12">ns3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c2">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<b>thus </b><a NAME="E26:3"/>
( not <font color="Maroon" title="c16">ns7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c4">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E4:3"><i><font color="Green" title="E4">A4</font></i></a>, <a class="txt" href="#E16:3"><i><font color="Green" title="E16">A16</font></i></a>, <a class="txt" href="#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="#E19:3"><i><font color="Green" title="E19">A19</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E27:3"/>
( not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c22">nq3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c21">nq2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E15:3"><i><font color="Green" title="E15">A15</font></i></a></i>;<br/>
<a NAME="E28:3"/><b>then </b>
( not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c19">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c18">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c17">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="#E19:3"><i><font color="Green" title="E19">A19</font></i></a></i>;<br/>
<b>hence </b><a NAME="E29:3"/>
( not <font color="Maroon" title="c15">ns6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c8">s7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E8:3"><i><font color="Green" title="E8">A8</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E30:3"/>
( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c22">nq3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E13:3"><i><font color="Green" title="E13">A13</font></i></a></i>;<br/>
<a NAME="E31:3"/><b>then </b>
( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c19">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c18">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="#E19:3"><i><font color="Green" title="E19">A19</font></i></a></i>;<br/>
<b>hence </b><a NAME="E32:3"/>
( not <font color="Maroon" title="c13">ns4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c7">s6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E7:3"><i><font color="Green" title="E7">A7</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E33:3"/>
( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E9:3"><i><font color="Green" title="E9">A9</font></i></a></i>;<br/>
<a NAME="E34:3"/><b>then </b>
( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c19">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="#E19:3"><i><font color="Green" title="E19">A19</font></i></a></i>;<br/>
<b>hence </b><a NAME="E35:3"/>
( not <font color="Maroon" title="c9">ns0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c5">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E5:3"><i><font color="Green" title="E5">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E36:3"/>
( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c22">nq3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c21">nq2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c20">nq1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E11:3"><i><font color="Green" title="E11">A11</font></i></a></i>;<br/>
<a NAME="E37:3"/><b>then </b>
( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c19">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c18">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c17">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="#E19:3"><i><font color="Green" title="E19">A19</font></i></a></i>;<br/>
<b>hence </b><a NAME="E38:3"/>
( not <font color="Maroon" title="c11">ns2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c6">s5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E6:3"><i><font color="Green" title="E6">A6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )</span><br/>

<a NAME="E39:3"/>
( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c22">nq3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c21">nq2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c20">nq1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E14:3"><i><font color="Green" title="E14">A14</font></i></a></i>;<br/>
<a NAME="E40:3"/><b>then </b>
( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c19">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c18">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c17">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E17:3"><i><font color="Green" title="E17">A17</font></i></a>, <a class="txt" href="#E18:3"><i><font color="Green" title="E18">A18</font></i></a>, <a class="txt" href="#E19:3"><i><font color="Green" title="E19">A19</font></i></a></i>;<br/>
<b>hence </b><a NAME="E41:3"/>
( not <font color="Maroon" title="c14">ns5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not <font color="Maroon" title="c3">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E3:3"><i><font color="Green" title="E3">A3</font></i></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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