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<b>let </b><font color="Maroon" title="c1">g0</font>, <font color="Maroon" title="c2">g1</font>, <font color="Maroon" title="c3">g2</font>, <font color="Maroon" title="c4">g3</font>, <font color="Maroon" title="c5">g4</font>, <font color="Maroon" title="c6">g5</font>, <font color="Maroon" title="c7">g6</font>, <font color="Maroon" title="c8">g7</font>, <font color="Maroon" title="c9">g8</font>, <font color="Maroon" title="c10">g9</font>, <font color="Maroon" title="c11">g10</font>, <font color="Maroon" title="c12">g11</font>, <font color="Maroon" title="c13">g12</font>, <font color="Maroon" title="c14">a0</font>, <font color="Maroon" title="c15">a1</font>, <font color="Maroon" title="c16">a2</font>, <font color="Maroon" title="c17">a3</font>, <font color="Maroon" title="c18">a4</font>, <font color="Maroon" title="c19">a5</font>, <font color="Maroon" title="c20">a6</font>, <font color="Maroon" title="c21">a7</font>, <font color="Maroon" title="c22">a8</font>, <font color="Maroon" title="c23">a9</font>, <font color="Maroon" title="c24">a10</font>, <font color="Maroon" title="c25">a11</font>, <font color="Maroon" title="c26">b0</font>, <font color="Maroon" title="c27">b1</font>, <font color="Maroon" title="c28">b2</font>, <font color="Maroon" title="c29">b3</font>, <font color="Maroon" title="c30">b4</font>, <font color="Maroon" title="c31">b5</font>, <font color="Maroon" title="c32">b6</font>, <font color="Maroon" title="c33">b7</font>, <font color="Maroon" title="c34">b8</font>, <font color="Maroon" title="c35">b9</font>, <font color="Maroon" title="c36">b10</font>, <font color="Maroon" title="c37">b11</font>, <font color="Maroon" title="c38">z</font>, <font color="Maroon" title="c39">p</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 <font color="Maroon" title="c1">g0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c13">g12</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c38">z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( not <font color="Maroon" title="c26">b0</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="c39">p</font>,<font color="Maroon" title="c25">a11</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="c39">p</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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="c14">a0</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c14">a0</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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="c15">a1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c15">a1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">b3</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="c16">a2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c16">a2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c30">b4</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="c17">a3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c17">a3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">b4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c31">b5</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="c18">a4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c18">a4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c31">b5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c32">b6</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="c19">a5</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c19">a5</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c32">b6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c33">b7</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="c20">a6</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c20">a6</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c33">b7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c34">b8</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="c21">a7</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c21">a7</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c34">b8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c35">b9</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="c22">a8</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c22">a8</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c35">b9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c36">b10</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="c23">a9</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c23">a9</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c36">b10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c37">b11</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">a10</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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">a10</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c37">b11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) implies ( ( not <font color="Maroon" title="c37">b11</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">a10</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">a10</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c37">b11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c36">b10</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a9</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a9</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c36">b10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c35">b9</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c35">b9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c34">b8</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c34">b8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c33">b7</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c33">b7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c32">b6</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c32">b6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c31">b5</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c31">b5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c30">b4</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">b4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) )</span><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:3"/><i><font color="Green" title="E1">A1</font></i>: 
( not <font color="Maroon" title="c1">g0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c13">g12</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c38">z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E2:3"/><i><font color="Green" title="E2">A2</font></i>: 
( not <font color="Maroon" title="c26">b0</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="c39">p</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E3:3"/><i><font color="Green" title="E3">A3</font></i>: 
( not <font color="Maroon" title="c27">b1</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="c14">a0</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E4:3"/><i><font color="Green" title="E4">A4</font></i>: 
( not <font color="Maroon" title="c28">b2</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="c15">a1</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E5:3"/><i><font color="Green" title="E5">A5</font></i>: 
( not <font color="Maroon" title="c29">b3</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="c16">a2</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E6:3"/><i><font color="Green" title="E6">A6</font></i>: 
( not <font color="Maroon" title="c30">b4</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="c17">a3</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E7:3"/><i><font color="Green" title="E7">A7</font></i>: 
( not <font color="Maroon" title="c31">b5</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="c18">a4</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E8:3"/><i><font color="Green" title="E8">A8</font></i>: 
( not <font color="Maroon" title="c32">b6</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="c19">a5</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E9:3"/><i><font color="Green" title="E9">A9</font></i>: 
( not <font color="Maroon" title="c33">b7</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="c20">a6</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E10:3"/><i><font color="Green" title="E10">A10</font></i>: 
( not <font color="Maroon" title="c34">b8</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="c21">a7</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E11:3"/><i><font color="Green" title="E11">A11</font></i>: 
( not <font color="Maroon" title="c35">b9</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="c22">a8</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E12:3"/><i><font color="Green" title="E12">A12</font></i>: 
( not <font color="Maroon" title="c36">b10</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="c23">a9</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c26">b0</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>and </b><br/><a NAME="E13:3"/><i><font color="Green" title="E13">A13</font></i>: 
( not <font color="Maroon" title="c37">b11</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">a10</font>,<span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c26">b0</font></span>)</span> 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="c37">b11</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">a10</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">a10</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c37">b11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c36">b10</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a9</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a9</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c36">b10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c35">b9</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c35">b9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c34">b8</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c34">b8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c33">b7</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c33">b7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c32">b6</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c32">b6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c31">b5</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c31">b5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c30">b4</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">b4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E14:3"/>
( ( ( ( ( not <font color="Maroon" title="c24">a10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c24">a10</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="c12">g11</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <!--HUMANRECFAILED-->( not <font color="Maroon" title="c24">a10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c24">a10</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="c12">g11</font>,<font color="Maroon" title="c25">a11</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="c12">g11</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">a10</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E15:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c24">a10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c12">g11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c12">g11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c24">a10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c12">g11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c12">g11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c24">a10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c12">g11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c24">a10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c12">g11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c12">g11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">a10</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E16:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c24">a10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c24">a10</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="c12">g11</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">a10</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E17:3"/>
( not <font color="Maroon" title="c37">b11</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c24">a10</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c12">g11</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E13:3"><i><font color="Green" title="E13">A13</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c36">b10</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a9</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a9</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c36">b10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c35">b9</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c35">b9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c34">b8</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c34">b8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c33">b7</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c33">b7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c32">b6</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c32">b6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c31">b5</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c31">b5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c30">b4</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">b4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E18:3"/>
( ( ( ( ( not <font color="Maroon" title="c23">a9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c23">a9</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">g10</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <!--HUMANRECFAILED-->( not <font color="Maroon" title="c23">a9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c23">a9</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">g10</font>,<font color="Maroon" title="c25">a11</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">g10</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a9</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E19:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c23">a9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c11">g10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c11">g10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c23">a9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c11">g10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c11">g10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c23">a9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c11">g10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c23">a9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c11">g10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c11">g10</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a9</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E20:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c23">a9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c23">a9</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">g10</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a9</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E21:3"/>
( not <font color="Maroon" title="c36">b10</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c23">a9</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c11">g10</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E12:3"><i><font color="Green" title="E12">A12</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c35">b9</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c35">b9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c34">b8</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c34">b8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c33">b7</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c33">b7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c32">b6</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c32">b6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c31">b5</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c31">b5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c30">b4</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">b4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E22:3"/>
( ( ( ( ( not <font color="Maroon" title="c22">a8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c22">a8</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="c10">g9</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <!--HUMANRECFAILED-->( not <font color="Maroon" title="c22">a8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c22">a8</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="c10">g9</font>,<font color="Maroon" title="c25">a11</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="c10">g9</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E23:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c22">a8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c10">g9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c10">g9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c22">a8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c10">g9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c10">g9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c22">a8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c10">g9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c22">a8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c10">g9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c10">g9</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E24:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c22">a8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c22">a8</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="c10">g9</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E25:3"/>
( not <font color="Maroon" title="c35">b9</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c22">a8</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c10">g9</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E11:3"><i><font color="Green" title="E11">A11</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c34">b8</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c34">b8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c33">b7</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c33">b7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c32">b6</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c32">b6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c31">b5</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c31">b5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c30">b4</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">b4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E26:3"/>
( ( ( ( ( not <font color="Maroon" title="c21">a7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c21">a7</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="c9">g8</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <!--HUMANRECFAILED-->( not <font color="Maroon" title="c21">a7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c21">a7</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="c9">g8</font>,<font color="Maroon" title="c25">a11</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="c9">g8</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E27:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c21">a7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c9">g8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c9">g8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c21">a7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c9">g8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c9">g8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c21">a7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c9">g8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c21">a7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c9">g8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c9">g8</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E28:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c21">a7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c21">a7</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="c9">g8</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E29:3"/>
( not <font color="Maroon" title="c34">b8</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c21">a7</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c9">g8</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E10:3"><i><font color="Green" title="E10">A10</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c33">b7</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c33">b7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c32">b6</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c32">b6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c31">b5</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c31">b5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c30">b4</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">b4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E30:3"/>
( ( ( ( ( not <font color="Maroon" title="c20">a6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c20">a6</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="c8">g7</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <!--HUMANRECFAILED-->( not <font color="Maroon" title="c20">a6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c20">a6</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="c8">g7</font>,<font color="Maroon" title="c25">a11</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="c8">g7</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E31:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c20">a6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c8">g7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c8">g7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c20">a6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c8">g7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c8">g7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c20">a6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c8">g7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c20">a6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c8">g7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c8">g7</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E32:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c20">a6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c20">a6</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="c8">g7</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E33:3"/>
( not <font color="Maroon" title="c33">b7</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c20">a6</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c8">g7</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E9:3"><i><font color="Green" title="E9">A9</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c32">b6</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c32">b6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c31">b5</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c31">b5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c30">b4</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">b4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E34:3"/>
( ( ( not <font color="Maroon" title="c19">a5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c19">a5</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="c7">g6</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( ( <font color="Maroon" title="c19">a5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; (  not <font color="Maroon" title="c19">a5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</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="c7">g6</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E35:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c19">a5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c7">g6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c7">g6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c19">a5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c7">g6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c7">g6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c19">a5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c7">g6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c19">a5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c7">g6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c7">g6</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E36:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c19">a5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c19">a5</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="c7">g6</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E37:3"/>
( not <font color="Maroon" title="c32">b6</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c19">a5</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c7">g6</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E8:3"><i><font color="Green" title="E8">A8</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c31">b5</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c31">b5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c30">b4</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">b4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E38:3"/>
( ( ( ( ( not <font color="Maroon" title="c18">a4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c18">a4</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="c6">g5</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <!--HUMANRECFAILED-->( not <font color="Maroon" title="c18">a4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c18">a4</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="c6">g5</font>,<font color="Maroon" title="c25">a11</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="c6">g5</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E39:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c18">a4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c6">g5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c6">g5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c18">a4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c6">g5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c6">g5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c18">a4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c6">g5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c18">a4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c6">g5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c6">g5</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E40:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c18">a4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c18">a4</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="c6">g5</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E41:3"/>
( not <font color="Maroon" title="c31">b5</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c18">a4</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c6">g5</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E7:3"><i><font color="Green" title="E7">A7</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c30">b4</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c30">b4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E42:3"/>
( ( ( not <font color="Maroon" title="c17">a3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c17">a3</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="c5">g4</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( ( <font color="Maroon" title="c17">a3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; (  not <font color="Maroon" title="c17">a3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</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="c5">g4</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E43:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c17">a3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c5">g4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c5">g4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c17">a3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c5">g4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c5">g4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c17">a3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c5">g4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c17">a3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c5">g4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c5">g4</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E44:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c17">a3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c17">a3</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="c5">g4</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E45:3"/>
( not <font color="Maroon" title="c30">b4</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c17">a3</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c5">g4</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E6:3"><i><font color="Green" title="E6">A6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c29">b3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E46:3"/>
( ( ( not <font color="Maroon" title="c16">a2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c16">a2</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="c4">g3</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( ( <font color="Maroon" title="c16">a2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; (  not <font color="Maroon" title="c16">a2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</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="c4">g3</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E47:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c16">a2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c4">g3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c4">g3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c16">a2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c4">g3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c4">g3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c16">a2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c4">g3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c16">a2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c4">g3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c4">g3</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E48:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c16">a2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c16">a2</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="c4">g3</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E49:3"/>
( not <font color="Maroon" title="c29">b3</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c16">a2</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c4">g3</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E5:3"><i><font color="Green" title="E5">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c28">b2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E50:3"/>
( ( ( ( ( not <font color="Maroon" title="c15">a1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c15">a1</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="c3">g2</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <!--HUMANRECFAILED-->( not <font color="Maroon" title="c15">a1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c15">a1</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="c3">g2</font>,<font color="Maroon" title="c25">a11</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="c3">g2</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E51:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c15">a1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c3">g2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c3">g2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c15">a1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c3">g2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c3">g2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c15">a1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c3">g2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c15">a1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c3">g2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c3">g2</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E52:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c15">a1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c15">a1</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="c3">g2</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E53:3"/>
( not <font color="Maroon" title="c28">b2</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c15">a1</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c3">g2</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E4:3"><i><font color="Green" title="E4">A4</font></i></a></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="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c27">b1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> 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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>

<a NAME="E54:3"/>
( ( ( ( ( not <font color="Maroon" title="c14">a0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c14">a0</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="c2">g1</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( not <!--HUMANRECFAILED-->( not <font color="Maroon" title="c14">a0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <!--HUMANRECFAILED-->( <font color="Maroon" title="c14">a0</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="c2">g1</font>,<font color="Maroon" title="c25">a11</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="c2">g1</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E55:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c14">a0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c2">g1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c2">g1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c14">a0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c2">g1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c2">g1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c14">a0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c2">g1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c14">a0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c2">g1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c2">g1</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<a NAME="E56:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c14">a0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c26">b0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c14">a0</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="c2">g1</font>,<font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E57:3"/>
( not <font color="Maroon" title="c27">b1</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c14">a0</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c2">g1</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E3:3"><i><font color="Green" title="E3">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )</span><br/>

<a NAME="E58:3"/>
( ( ( not <font color="Maroon" title="c38">z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c38">z</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="c1">g0</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp;  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( ( <font color="Maroon" title="c38">z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; (  not <font color="Maroon" title="c38">z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</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="c1">g0</font>,<font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
<b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a></i>;<br/>
<a NAME="E59:3"/><b>then </b>
( ( ( not <font color="Maroon" title="c38">z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c1">g0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( <font color="Maroon" title="c1">g0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( <font color="Maroon" title="c38">z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c1">g0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( <font color="Maroon" title="c1">g0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c39">p</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) or ( ( <font color="Maroon" title="c38">z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c1">g0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; (  not <font color="Maroon" title="c38">z</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c1">g0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c25">a11</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; not <font color="Maroon" title="c1">g0</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <font color="Maroon" title="c39">p</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 
;<br/>
<b>hence </b><a NAME="E60:3"/>
( not <font color="Maroon" title="c26">b0</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> <span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c25">a11</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K4" title="GATE_1:func.4">XOR2</a> <font color="Maroon" title="c38">z</font>,<span class="p2">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">g0</font>,<font color="Maroon" title="c39">p</font></span>)</span></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> )
 <b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">A1</font></i></a>, <a class="txt" href="#E2:3"><i><font color="Green" title="E2">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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