<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">c1</font>, <font color="Maroon" title="c2">x1</font>, <font color="Maroon" title="c3">y1</font>, <font color="Maroon" title="c4">x2</font>, <font color="Maroon" title="c5">y2</font>, <font color="Maroon" title="c6">x3</font>, <font color="Maroon" title="c7">y3</font>, <font color="Maroon" title="c8">x4</font>, <font color="Maroon" title="c9">y4</font>, <font color="Maroon" title="c10">c4</font>, <font color="Maroon" title="c11">q1</font>, <font color="Maroon" title="c12">p1</font>, <font color="Maroon" title="c13">sd1</font>, <font color="Maroon" title="c14">q2</font>, <font color="Maroon" title="c15">p2</font>, <font color="Maroon" title="c16">sd2</font>, <font color="Maroon" title="c17">q3</font>, <font color="Maroon" title="c18">p3</font>, <font color="Maroon" title="c19">sd3</font>, <font color="Maroon" title="c20">q4</font>, <font color="Maroon" title="c21">p4</font>, <font color="Maroon" title="c22">sd4</font>, <font color="Maroon" title="c23">cb1</font>, <font color="Maroon" title="c24">cb2</font>, <font color="Maroon" title="c25">l2</font>, <font color="Maroon" title="c26">t2</font>, <font color="Maroon" title="c27">l3</font>, <font color="Maroon" title="c28">m3</font>, <font color="Maroon" title="c29">t3</font>, <font color="Maroon" title="c30">l4</font>, <font color="Maroon" title="c31">m4</font>, <font color="Maroon" title="c32">n4</font>, <font color="Maroon" title="c33">t4</font>, <font color="Maroon" title="c34">l5</font>, <font color="Maroon" title="c35">m5</font>, <font color="Maroon" title="c36">n5</font>, <font color="Maroon" title="c37">o5</font>, <font color="Maroon" title="c38">s1</font>, <font color="Maroon" title="c39">s2</font>, <font color="Maroon" title="c40">s3</font>, <font color="Maroon" title="c41">s4</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="c11">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c11">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c12">p1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c12">p1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c13">sd1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c13">sd1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c14">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c14">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c16">sd2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c16">sd2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c17">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c17">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c19">sd3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c19">sd3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c20">q4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c20">q4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c21">p4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c21">p4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c22">sd4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c22">sd4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c23">cb1</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="c1">c1</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="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c24">cb2</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="c23">cb1</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="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c24">cb2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c38">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">cb2</font>,<font color="Maroon" title="c13">sd1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">cb2</font>,<font color="Maroon" title="c13">sd1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c38">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c25">l2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c23">cb1</font>,<font color="Maroon" title="c12">p1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c23">cb1</font>,<font color="Maroon" title="c12">p1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c25">l2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">t2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c25">l2</font>,<font color="Maroon" title="c11">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c25">l2</font>,<font color="Maroon" title="c11">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">t2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c26">t2</font>,<font color="Maroon" title="c16">sd2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c26">t2</font>,<font color="Maroon" title="c16">sd2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">l3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">q1</font>,<font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">q1</font>,<font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">l3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">m3</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="c15">p2</font>,<font color="Maroon" title="c12">p1</font>,<font color="Maroon" title="c23">cb1</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="c15">p2</font>,<font color="Maroon" title="c12">p1</font>,<font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">m3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">t3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K13" title="GATE_1:func.13">NOR3</a> <font color="Maroon" title="c27">l3</font>,<font color="Maroon" title="c28">m3</font>,<font color="Maroon" title="c14">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K13" title="GATE_1:func.13">NOR3</a> <font color="Maroon" title="c27">l3</font>,<font color="Maroon" title="c28">m3</font>,<font color="Maroon" title="c14">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">t3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c29">t3</font>,<font color="Maroon" title="c19">sd3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c29">t3</font>,<font color="Maroon" title="c19">sd3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c30">l4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c14">q2</font>,<font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c14">q2</font>,<font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">l4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c31">m4</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="c11">q1</font>,<font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</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="c11">q1</font>,<font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c31">m4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c32">n4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c12">p1</font>,<font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c12">p1</font>,<font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c32">n4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c33">t4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K17" title="GATE_1:func.17">NOR4</a> <font color="Maroon" title="c30">l4</font>,<font color="Maroon" title="c31">m4</font>,<font color="Maroon" title="c32">n4</font>,<font color="Maroon" title="c17">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K17" title="GATE_1:func.17">NOR4</a> <font color="Maroon" title="c30">l4</font>,<font color="Maroon" title="c31">m4</font>,<font color="Maroon" title="c32">n4</font>,<font color="Maroon" title="c17">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c33">t4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c33">t4</font>,<font color="Maroon" title="c22">sd4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c33">t4</font>,<font color="Maroon" title="c22">sd4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c34">l5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q3</font>,<font color="Maroon" title="c21">p4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q3</font>,<font color="Maroon" title="c21">p4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c34">l5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c35">m5</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="c14">q2</font>,<font color="Maroon" title="c21">p4</font>,<font color="Maroon" title="c18">p3</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="c14">q2</font>,<font color="Maroon" title="c21">p4</font>,<font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c35">m5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c36">n5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c11">q1</font>,<font color="Maroon" title="c21">p4</font>,<font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c11">q1</font>,<font color="Maroon" title="c21">p4</font>,<font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c36">n5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c37">o5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K18" title="GATE_1:func.18">AND5</a> <font color="Maroon" title="c21">p4</font>,<font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c12">p1</font>,<font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K18" title="GATE_1:func.18">AND5</a> <font color="Maroon" title="c21">p4</font>,<font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c12">p1</font>,<font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c37">o5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K21" title="GATE_1:func.21">NOR5</a> <font color="Maroon" title="c20">q4</font>,<font color="Maroon" title="c34">l5</font>,<font color="Maroon" title="c35">m5</font>,<font color="Maroon" title="c36">n5</font>,<font color="Maroon" title="c37">o5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K21" title="GATE_1:func.21">NOR5</a> <font color="Maroon" title="c20">q4</font>,<font color="Maroon" title="c34">l5</font>,<font color="Maroon" title="c35">m5</font>,<font color="Maroon" title="c36">n5</font>,<font color="Maroon" title="c37">o5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <!--HUMANRECFAILED-->( ( not <font color="Maroon" title="c38">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#NK35" title="GATE_1:NK.35">ADD1</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#NK35" title="GATE_1:NK.35">ADD1</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c38">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K35" title="GATE_1:func.35">ADD2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K35" title="GATE_1:func.35">ADD2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K37" title="GATE_1:func.37">ADD3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K37" title="GATE_1:func.37">ADD3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c10">c4</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="E1:71"/><i><font color="Green" title="E35">A1</font></i>: 
( not <font color="Maroon" title="c11">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E2:71"/><i><font color="Green" title="E36">A2</font></i>: 
( not <font color="Maroon" title="c12">p1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E3:71"/><i><font color="Green" title="E37">A3</font></i>: 
( not <font color="Maroon" title="c13">sd1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E4:71"/><i><font color="Green" title="E38">A4</font></i>: 
( not <font color="Maroon" title="c14">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E5:71"/><i><font color="Green" title="E39">A5</font></i>: 
( not <font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E6:71"/><i><font color="Green" title="E40">A6</font></i>: 
( not <font color="Maroon" title="c16">sd2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E7:71"/><i><font color="Green" title="E41">A7</font></i>: 
( not <font color="Maroon" title="c17">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E8:71"/><i><font color="Green" title="E42">A8</font></i>: 
( not <font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E9:71"/><i><font color="Green" title="E43">A9</font></i>: 
( not <font color="Maroon" title="c19">sd3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E10:71"/><i><font color="Green" title="E44">A10</font></i>: 
( not <font color="Maroon" title="c20">q4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E11:71"/><i><font color="Green" title="E45">A11</font></i>: 
( not <font color="Maroon" title="c21">p4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K6" title="GATE_1:func.6">NAND2</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E12:71"/><i><font color="Green" title="E46">A12</font></i>: 
( not <font color="Maroon" title="c22">sd4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K34" title="GATE_1:func.34">MODADD2</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E13:71"/><i><font color="Green" title="E47">A13</font></i>: 
( not <font color="Maroon" title="c23">cb1</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="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E14:71"/><i><font color="Green" title="E48">A14</font></i>: 
( not <font color="Maroon" title="c24">cb2</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="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E15:71"/><i><font color="Green" title="E49">A15</font></i>: 
( not <font color="Maroon" title="c38">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">cb2</font>,<font color="Maroon" title="c13">sd1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E16:71"/><i><font color="Green" title="E50">A16</font></i>: 
( not <font color="Maroon" title="c25">l2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c23">cb1</font>,<font color="Maroon" title="c12">p1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E17:71"/><i><font color="Green" title="E51">A17</font></i>: 
( not <font color="Maroon" title="c26">t2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K7" title="GATE_1:func.7">NOR2</a> <font color="Maroon" title="c25">l2</font>,<font color="Maroon" title="c11">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E18:71"/><i><font color="Green" title="E52">A18</font></i>: 
( not <font color="Maroon" title="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c26">t2</font>,<font color="Maroon" title="c16">sd2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E19:71"/><i><font color="Green" title="E53">A19</font></i>: 
( not <font color="Maroon" title="c27">l3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">q1</font>,<font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E20:71"/><i><font color="Green" title="E54">A20</font></i>: 
( not <font color="Maroon" title="c28">m3</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="c15">p2</font>,<font color="Maroon" title="c12">p1</font>,<font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E21:71"/><i><font color="Green" title="E55">A21</font></i>: 
( not <font color="Maroon" title="c29">t3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K13" title="GATE_1:func.13">NOR3</a> <font color="Maroon" title="c27">l3</font>,<font color="Maroon" title="c28">m3</font>,<font color="Maroon" title="c14">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E22:71"/><i><font color="Green" title="E56">A22</font></i>: 
( not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c29">t3</font>,<font color="Maroon" title="c19">sd3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E23:71"/><i><font color="Green" title="E57">A23</font></i>: 
( not <font color="Maroon" title="c30">l4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c14">q2</font>,<font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E24:71"/><i><font color="Green" title="E58">A24</font></i>: 
( not <font color="Maroon" title="c31">m4</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="c11">q1</font>,<font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E25:71"/><i><font color="Green" title="E59">A25</font></i>: 
( not <font color="Maroon" title="c32">n4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c12">p1</font>,<font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E26:71"/><i><font color="Green" title="E60">A26</font></i>: 
( not <font color="Maroon" title="c33">t4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K17" title="GATE_1:func.17">NOR4</a> <font color="Maroon" title="c30">l4</font>,<font color="Maroon" title="c31">m4</font>,<font color="Maroon" title="c32">n4</font>,<font color="Maroon" title="c17">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E27:71"/><i><font color="Green" title="E61">A27</font></i>: 
( not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c33">t4</font>,<font color="Maroon" title="c22">sd4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E28:71"/><i><font color="Green" title="E62">A28</font></i>: 
( not <font color="Maroon" title="c34">l5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c17">q3</font>,<font color="Maroon" title="c21">p4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E29:71"/><i><font color="Green" title="E63">A29</font></i>: 
( not <font color="Maroon" title="c35">m5</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="c14">q2</font>,<font color="Maroon" title="c21">p4</font>,<font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E30:71"/><i><font color="Green" title="E64">A30</font></i>: 
( not <font color="Maroon" title="c36">n5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K14" title="GATE_1:func.14">AND4</a> <font color="Maroon" title="c11">q1</font>,<font color="Maroon" title="c21">p4</font>,<font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E31:71"/><i><font color="Green" title="E65">A31</font></i>: 
( not <font color="Maroon" title="c37">o5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K18" title="GATE_1:func.18">AND5</a> <font color="Maroon" title="c21">p4</font>,<font color="Maroon" title="c18">p3</font>,<font color="Maroon" title="c15">p2</font>,<font color="Maroon" title="c12">p1</font>,<font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E32:71"/><i><font color="Green" title="E66">A32</font></i>: 
( not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K21" title="GATE_1:func.21">NOR5</a> <font color="Maroon" title="c20">q4</font>,<font color="Maroon" title="c34">l5</font>,<font color="Maroon" title="c35">m5</font>,<font color="Maroon" title="c36">n5</font>,<font color="Maroon" title="c37">o5</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="c38">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#NK35" title="GATE_1:NK.35">ADD1</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#NK35" title="GATE_1:NK.35">ADD1</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c38">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K35" title="GATE_1:func.35">ADD2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K35" title="GATE_1:func.35">ADD2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K37" title="GATE_1:func.37">ADD3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K37" title="GATE_1:func.37">ADD3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E33:71"/><i><font color="Green" title="E67">A33</font></i>: 
( not <font color="Maroon" title="c11">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E1:71"><i><font color="Green" title="E35">A1</font></i></a></i>;<br/>
<a NAME="E34:71"/><i><font color="Green" title="E68">A34</font></i>: 
( not <font color="Maroon" title="c12">p1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:71"><i><font color="Green" title="E36">A2</font></i></a></i>;<br/>
<a NAME="E35:71"/><i><font color="Green" title="E69">A35</font></i>: 
( not <font color="Maroon" title="c13">sd1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( (  not <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) )
 
<b>by </b><i><a class="txt" href="#E3:71"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="gate_1.html#D34" target="_self" title="GATE_1:def.34">Def34</a></i>;<br/>
<a NAME="E36:71"/><i><font color="Green" title="E70">A36</font></i>: 
( not <font color="Maroon" title="c14">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( <font color="Maroon" title="c4">x2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E4:71"><i><font color="Green" title="E38">A4</font></i></a></i>;<br/>
<a NAME="E37:71"/><i><font color="Green" title="E71">A37</font></i>: 
( not <font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c4">x2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff <font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E5:71"><i><font color="Green" title="E39">A5</font></i></a></i>;<br/>
<a NAME="E38:71"/><i><font color="Green" title="E72">A38</font></i>: 
( not <font color="Maroon" title="c16">sd2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( (  not <font color="Maroon" title="c4">x2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c4">x2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) )
 
<b>by </b><i><a class="txt" href="#E6:71"><i><font color="Green" title="E40">A6</font></i></a>, <a class="ref" href="gate_1.html#D34" target="_self" title="GATE_1:def.34">Def34</a></i>;<br/>
<a NAME="E39:71"/><i><font color="Green" title="E73">A39</font></i>: 
( not <font color="Maroon" title="c17">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( <font color="Maroon" title="c6">x3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E7:71"><i><font color="Green" title="E41">A7</font></i></a></i>;<br/>
<a NAME="E40:71"/><i><font color="Green" title="E74">A40</font></i>: 
( not <font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c6">x3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff <font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E8:71"><i><font color="Green" title="E42">A8</font></i></a></i>;<br/>
<a NAME="E41:71"/><i><font color="Green" title="E75">A41</font></i>: 
( not <font color="Maroon" title="c19">sd3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( (  not <font color="Maroon" title="c6">x3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c6">x3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) )
 
<b>by </b><i><a class="txt" href="#E9:71"><i><font color="Green" title="E43">A9</font></i></a>, <a class="ref" href="gate_1.html#D34" target="_self" title="GATE_1:def.34">Def34</a></i>;<br/>
<a NAME="E42:71"/><i><font color="Green" title="E76">A42</font></i>: 
( not <font color="Maroon" title="c20">q4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( <font color="Maroon" title="c8">x4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E10:71"><i><font color="Green" title="E44">A10</font></i></a></i>;<br/>
<a NAME="E43:71"/><i><font color="Green" title="E77">A43</font></i>: 
( not <font color="Maroon" title="c21">p4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c8">x4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff <font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E11:71"><i><font color="Green" title="E45">A11</font></i></a></i>;<br/>
<a NAME="E44:71"/><i><font color="Green" title="E78">A44</font></i>: 
( not <font color="Maroon" title="c22">sd4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( (  not <font color="Maroon" title="c8">x4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c8">x4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c9">y4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) )
 
<b>by </b><i><a class="txt" href="#E12:71"><i><font color="Green" title="E46">A12</font></i></a>, <a class="ref" href="gate_1.html#D34" target="_self" title="GATE_1:def.34">Def34</a></i>;<br/>
<a NAME="E45:71"/><i><font color="Green" title="E79">A45</font></i>: 
( not <font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff <font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E13:71"><i><font color="Green" title="E47">A13</font></i></a></i>;<br/>
<a NAME="E46:71"/><i><font color="Green" title="E80">A47</font></i>: 
( ( ( not <font color="Maroon" title="c24">cb2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c13">sd1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c24">cb2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c13">sd1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) iff  not <font color="Maroon" title="c38">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E15:71"><i><font color="Green" title="E49">A15</font></i></a></i>;<br/>
<a NAME="E47:71"/><i><font color="Green" title="E81">A49</font></i>: 
( not <font color="Maroon" title="c26">t2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( <font color="Maroon" title="c25">l2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c11">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E17:71"><i><font color="Green" title="E51">A17</font></i></a></i>;<br/>
<a NAME="E48:71"/><i><font color="Green" title="E82">A50</font></i>: 
( ( ( not <font color="Maroon" title="c26">t2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c16">sd2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c26">t2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c16">sd2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) iff  not <font color="Maroon" title="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E18:71"><i><font color="Green" title="E52">A18</font></i></a></i>;<br/>
<a NAME="E49:71"/><i><font color="Green" title="E83">A52</font></i>: 
( not <font color="Maroon" title="c28">m3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c12">p1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E20:71"><i><font color="Green" title="E54">A20</font></i></a></i>;<br/>
<a NAME="E50:71"/><i><font color="Green" title="E84">A53</font></i>: 
( not <font color="Maroon" title="c29">t3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( <font color="Maroon" title="c27">l3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c28">m3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c14">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E21:71"><i><font color="Green" title="E55">A21</font></i></a>, <a class="ref" href="gate_1.html#D13" target="_self" title="GATE_1:def.13">Def13</a></i>;<br/>
<a NAME="E51:71"/><i><font color="Green" title="E85">A54</font></i>: 
( ( ( not <font color="Maroon" title="c29">t3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c19">sd3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c29">t3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c19">sd3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) iff  not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E22:71"><i><font color="Green" title="E56">A22</font></i></a></i>;<br/>
<a NAME="E52:71"/><i><font color="Green" title="E86">A56</font></i>: 
( not <font color="Maroon" title="c31">m4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c11">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E24:71"><i><font color="Green" title="E58">A24</font></i></a></i>;<br/>
<a NAME="E53:71"/><i><font color="Green" title="E87">A57</font></i>: 
( not <font color="Maroon" title="c32">n4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c12">p1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E25:71"><i><font color="Green" title="E59">A25</font></i></a>, <a class="ref" href="gate_1.html#D14" target="_self" title="GATE_1:def.14">Def14</a></i>;<br/>
<a NAME="E54:71"/><i><font color="Green" title="E88">A58</font></i>: 
( not <font color="Maroon" title="c33">t4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( <font color="Maroon" title="c30">l4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c31">m4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c32">n4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c17">q3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E26:71"><i><font color="Green" title="E60">A26</font></i></a>, <a class="ref" href="gate_1.html#D17" target="_self" title="GATE_1:def.17">Def17</a></i>;<br/>
<a NAME="E55:71"/><i><font color="Green" title="E89">A59</font></i>: 
( ( ( not <font color="Maroon" title="c33">t4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c22">sd4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c33">t4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c22">sd4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) iff  not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E27:71"><i><font color="Green" title="E61">A27</font></i></a></i>;<br/>
<a NAME="E56:71"/><i><font color="Green" title="E90">A61</font></i>: 
( not <font color="Maroon" title="c35">m5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c14">q2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c21">p4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E29:71"><i><font color="Green" title="E63">A29</font></i></a></i>;<br/>
<a NAME="E57:71"/><i><font color="Green" title="E91">A62</font></i>: 
( not <font color="Maroon" title="c36">n5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c11">q1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c21">p4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E30:71"><i><font color="Green" title="E64">A30</font></i></a>, <a class="ref" href="gate_1.html#D14" target="_self" title="GATE_1:def.14">Def14</a></i>;<br/>
<a NAME="E58:71"/><i><font color="Green" title="E92">A63</font></i>: 
( not <font color="Maroon" title="c37">o5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( not <font color="Maroon" title="c21">p4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c18">p3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c15">p2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c12">p1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c23">cb1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E31:71"><i><font color="Green" title="E65">A31</font></i></a>, <a class="ref" href="gate_1.html#D18" target="_self" title="GATE_1:def.18">Def18</a></i>;<br/>
<a NAME="E59:71"/><i><font color="Green" title="E93">A64</font></i>: 
( not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( <font color="Maroon" title="c20">q4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c34">l5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c35">m5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c36">n5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c37">o5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
<b>by </b><i><a class="txt" href="#E32:71"><i><font color="Green" title="E66">A32</font></i></a>, <a class="ref" href="gate_1.html#D21" target="_self" title="GATE_1:def.21">Def21</a></i>;<br/>
<b>thus </b><a NAME="E60:71"/>
( not <font color="Maroon" title="c38">s1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#NK35" title="GATE_1:NK.35">ADD1</a> <font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E35:71"><i><font color="Green" title="E69">A35</font></i></a>, <a class="txt" href="#E45:71"><i><font color="Green" title="E79">A45</font></i></a>, <a class="txt" href="#E14:71"><i><font color="Green" title="E48">A14</font></i></a>, <a class="txt" href="#E46:71"><i><font color="Green" title="E80">A47</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="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K35" title="GATE_1:func.35">ADD2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K35" title="GATE_1:func.35">ADD2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K37" title="GATE_1:func.37">ADD3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K37" title="GATE_1:func.37">ADD3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<b>thus </b><a NAME="E61:71"/>
( not <font color="Maroon" title="c39">s2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K35" title="GATE_1:func.35">ADD2</a> <font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E33:71"><i><font color="Green" title="E67">A33</font></i></a>, <a class="txt" href="#E34:71"><i><font color="Green" title="E68">A34</font></i></a>, <a class="txt" href="#E38:71"><i><font color="Green" title="E72">A38</font></i></a>, <a class="txt" href="#E45:71"><i><font color="Green" title="E79">A45</font></i></a>, <a class="txt" href="#E16:71"><i><font color="Green" title="E50">A16</font></i></a>, <a class="txt" href="#E47:71"><i><font color="Green" title="E81">A49</font></i></a>, <a class="txt" href="#E48:71"><i><font color="Green" title="E82">A50</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="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K37" title="GATE_1:func.37">ADD3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K37" title="GATE_1:func.37">ADD3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<b>thus </b><a NAME="E62:71"/>
( not <font color="Maroon" title="c40">s3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K37" title="GATE_1:func.37">ADD3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E33:71"><i><font color="Green" title="E67">A33</font></i></a>, <a class="txt" href="#E34:71"><i><font color="Green" title="E68">A34</font></i></a>, <a class="txt" href="#E36:71"><i><font color="Green" title="E70">A36</font></i></a>, <a class="txt" href="#E37:71"><i><font color="Green" title="E71">A37</font></i></a>, <a class="txt" href="#E41:71"><i><font color="Green" title="E75">A41</font></i></a>, <a class="txt" href="#E45:71"><i><font color="Green" title="E79">A45</font></i></a>, <a class="txt" href="#E19:71"><i><font color="Green" title="E53">A19</font></i></a>, <a class="txt" href="#E49:71"><i><font color="Green" title="E83">A52</font></i></a>, <a class="txt" href="#E50:71"><i><font color="Green" title="E84">A53</font></i></a>, <a class="txt" href="#E51:71"><i><font color="Green" title="E85">A54</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="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<b>set </b><font color="Maroon" title="c42">b</font> =  <a href="gate_1.html#K38" title="GATE_1:func.38">CARR3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font>;<br/>
<a NAME="E63:71"/><i><font color="Green" title="E94">A69</font></i>: 
( ( ( not <font color="Maroon" title="c6">x3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c7">y3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( ( not <font color="Maroon" title="c4">x2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( ( not <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) ) or ( ( ( not <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; not <font color="Maroon" title="c4">x2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) ) or ( ( ( not <font color="Maroon" title="c4">x2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c5">y2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( ( not <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) ) or ( ( ( not <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c3">y1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c2">x1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; not <font color="Maroon" title="c4">x2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; not <font color="Maroon" title="c6">x3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) iff  not  <a href="gate_1.html#K38" title="GATE_1:func.38">CARR3</a> <font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<b>thus </b><a NAME="E64:71"/>
( not <font color="Maroon" title="c41">s4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K39" title="GATE_1:func.39">ADD4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E44:71"><i><font color="Green" title="E78">A44</font></i></a>, <a class="txt" href="#E45:71"><i><font color="Green" title="E79">A45</font></i></a>, <a class="txt" href="#E23:71"><i><font color="Green" title="E57">A23</font></i></a>, <a class="txt" href="#E52:71"><i><font color="Green" title="E86">A56</font></i></a>, <a class="txt" href="#E53:71"><i><font color="Green" title="E87">A57</font></i></a>, <a class="txt" href="#E54:71"><i><font color="Green" title="E88">A58</font></i></a>, <a class="txt" href="#E55:71"><i><font color="Green" title="E89">A59</font></i></a>, <a class="txt" href="#E33:71"><i><font color="Green" title="E67">A33</font></i></a>, <a class="txt" href="#E34:71"><i><font color="Green" title="E68">A34</font></i></a>, <a class="txt" href="#E36:71"><i><font color="Green" title="E70">A36</font></i></a>, <a class="txt" href="#E37:71"><i><font color="Green" title="E71">A37</font></i></a>, <a class="txt" href="#E39:71"><i><font color="Green" title="E73">A39</font></i></a>, <a class="txt" href="#E40:71"><i><font color="Green" title="E74">A40</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="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )</span><br/>

<b>thus </b><a NAME="E65:71"/>
( not <font color="Maroon" title="c10">c4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff  not  <a href="gate_1.html#K40" title="GATE_1:func.40">CARR4</a> <font color="Maroon" title="c8">x4</font>,<font color="Maroon" title="c9">y4</font>,<font color="Maroon" title="c6">x3</font>,<font color="Maroon" title="c7">y3</font>,<font color="Maroon" title="c4">x2</font>,<font color="Maroon" title="c5">y2</font>,<font color="Maroon" title="c2">x1</font>,<font color="Maroon" title="c3">y1</font>,<font color="Maroon" title="c1">c1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E28:71"><i><font color="Green" title="E62">A28</font></i></a>, <a class="txt" href="#E56:71"><i><font color="Green" title="E90">A61</font></i></a>, <a class="txt" href="#E57:71"><i><font color="Green" title="E91">A62</font></i></a>, <a class="txt" href="#E58:71"><i><font color="Green" title="E92">A63</font></i></a>, <a class="txt" href="#E59:71"><i><font color="Green" title="E93">A64</font></i></a>, <a class="txt" href="#E13:71"><i><font color="Green" title="E47">A13</font></i></a>, <a class="txt" href="#E33:71"><i><font color="Green" title="E67">A33</font></i></a>, <a class="txt" href="#E34:71"><i><font color="Green" title="E68">A34</font></i></a>, <a class="txt" href="#E36:71"><i><font color="Green" title="E70">A36</font></i></a>, <a class="txt" href="#E37:71"><i><font color="Green" title="E71">A37</font></i></a>, <a class="txt" href="#E39:71"><i><font color="Green" title="E73">A39</font></i></a>, <a class="txt" href="#E40:71"><i><font color="Green" title="E74">A40</font></i></a>, <a class="txt" href="#E42:71"><i><font color="Green" title="E76">A42</font></i></a>, <a class="txt" href="#E43:71"><i><font color="Green" title="E77">A43</font></i></a>, <a class="txt" href="#E63:71"><i><font color="Green" title="E94">A69</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/>


</div>
