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<b>let </b><font color="Maroon" title="c1">X'</font>, <font color="Maroon" title="c2">Y'</font>, <font color="Maroon" title="c3">X</font>, <font color="Maroon" title="c4">Y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>







<b>assume </b><a NAME="E1:71"/>
<font color="Maroon" title="c1">X'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">Y</font>
 ;<br/>

<a NAME="E2:71"/><b>then </b><i><font color="Green" title="E35">A1</font></i>: 
( <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y'</font> &amp; <font color="Maroon" title="c4">Y</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">X'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y'</font> &amp; <font color="Maroon" title="c1">X'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">Y</font> &amp; <font color="Maroon" title="c2">Y'</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">Y</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" target="_self" title="XBOOLE_1:th.7">Th7</a></i>;<br/>
<b>assume </b><a NAME="E3:71"/>
( <font color="Maroon" title="c3">X</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c1">X'</font> &amp; <font color="Maroon" title="c4">Y</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">Y'</font> )
 ;<br/>

<a NAME="E4:71"/><b>then </b><i><font color="Green" title="E36">A2</font></i>: 
( <font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c1">X'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c4">Y</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7" title="XBOOLE_0:def.7">XBOOLE_0:def 7</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c3">X</font> = 
<font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">X'</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c2">Y'</font></span>)</span>
<b>by </b><i><a class="txt" href="xboole_1.html#E2:71"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="xboole_1.html#T28" target="_self" title="XBOOLE_1:th.28">Th28</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c1">X'</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y'</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23" target="_self" title="XBOOLE_1:th.23">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c4">Y</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c2">Y'</font>
<b>by </b><i><a class="txt" href="xboole_1.html#E4:71"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="xboole_1.html#T23" target="_self" title="XBOOLE_1:th.23">Th23</a></i>
<br/>.= 
<font color="Maroon" title="c2">Y'</font>
<b>by </b><i><a class="txt" href="xboole_1.html#E2:71"><i><font color="Green" title="E35">A1</font></i></a>, <a class="ref" href="xboole_1.html#T28" target="_self" title="XBOOLE_1:th.28">Th28</a></i>
;<br/>


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