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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">d</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"> ( (  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c2">b</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c2">b</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font></span>)</span>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font></span>)</span>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( not <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">c</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">c</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp;  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )</span><br/>







<a NAME="E1:3"/><i><font color="Green" title="E1">B1</font></i>: 
(  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 
;<br/>
<a NAME="E2:3"/><i><font color="Green" title="E2">B2</font></i>: 
( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( (  not <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; (  not <font color="Maroon" title="c3">c</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) )
 
;<br/>
<a NAME="E3:3"/>
( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> iff ( (  not <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; (  not <font color="Maroon" title="c3">c</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; (  not <font color="Maroon" title="c4">d</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or  not <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) )
 
;<br/>
<b>hence </b><a NAME="E4:3"/>
( (  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c2">b</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c1">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="gate_1.html#K1" title="GATE_1:func.1">NOT1</a> <font color="Maroon" title="c2">b</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  <a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K2" title="GATE_1:func.2">AND2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font></span>)</span>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font></span>)</span>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <span class="p1">(<span class="default"><a href="gate_1.html#K8" title="GATE_1:func.8">AND3</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c4">d</font></span>)</span>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies ( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c4">d</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) ) &amp; not <!--HUMANRECFAILED-->( not  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; ( not <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c3">c</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not <font color="Maroon" title="c3">c</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies  not <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp;  <a href="gate_1.html#K3" title="GATE_1:func.3">OR2</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) )
 <b>by </b><i><a class="txt" href="#E1:3"><i><font color="Green" title="E1">B1</font></i></a>, <a class="txt" href="#E2:3"><i><font color="Green" title="E2">B2</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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