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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</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  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  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="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#K4" title="GATE_1:func.4">XOR2</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#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<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#K4" title="GATE_1:func.4">XOR2</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#K4" title="GATE_1:func.4">XOR2</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#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<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#K10" title="GATE_1:func.10">XOR3</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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#K4" title="GATE_1:func.4">XOR2</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#K4" title="GATE_1:func.4">XOR2</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#K10" title="GATE_1:func.10">XOR3</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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> ) )</span><br/>

<a NAME="E1:1"/>
( (  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; 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="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <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#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; (  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> or ( not <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; 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="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <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#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; (  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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> or ( not <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; 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="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; <font color="Maroon" title="c2">b</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) or ( <font color="Maroon" title="c1">a</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> &amp; not <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#K10" title="GATE_1:func.10">XOR3</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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> ) )
 
;<br/>
<b>hence </b><a NAME="E2:1"/>
( ( not  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  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="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#K4" title="GATE_1:func.4">XOR2</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#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> ) &amp; ( not  <a href="gate_1.html#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<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#K4" title="GATE_1:func.4">XOR2</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#K4" title="GATE_1:func.4">XOR2</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#K10" title="GATE_1:func.10">XOR3</a> <font color="Maroon" title="c1">a</font>,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> ,<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#K10" title="GATE_1:func.10">XOR3</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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#K4" title="GATE_1:func.4">XOR2</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#K4" title="GATE_1:func.4">XOR2</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#K10" title="GATE_1:func.10">XOR3</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</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> ) )
 ; <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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