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

<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Y</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Z</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<i><font color="Green">E13</font></i>: <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">X</font></span>)</span> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T22" target="_self">Th22</a></i>
<br/>.= 
<font color="Maroon">Y</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T22" target="_self">Th22</a></i>
;<br/>
<a NAME="E2:80"/>
( ( <font color="Maroon">X</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Y</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font> implies <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; ( <font color="Maroon">X</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">Y</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Maroon">X</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Y</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font> ) &amp; ( <font color="Maroon">Y</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font> implies <font color="Maroon">Y</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  ) &amp; ( <font color="Maroon">Y</font> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  implies <font color="Maroon">Y</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font> ) )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E3:80"/>
( <font color="Maroon">X</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">Y</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font> implies <font color="Maroon">Y</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">X</font> <a href="xboole_0.html#K4">\</a> <font color="Maroon">Z</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T41" target="_self">Th41</a></i>;<br/>


</div>
