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<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/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:9_1"/>
<font color="Maroon">X</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">Y</font>
 ;<br/><a NAME="E2:9_1"/><b>then </b>
<font color="Maroon">X</font> <a href="xboole_0.html#K3" target="_self">/\</a> <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1" target="_self">{}</a> 
 <b>by </b><i/>;<br/><b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:9_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3" target="_self">/\</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/><b>take </b><font color="Maroon">x</font> = <font color="Maroon">x</font>;<br/><b>thus </b><a NAME="E5:9_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 <b>by </b><i>, </i>;<br/></div>
<b>end;</b></div>

<b>given </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><a NAME="E2:9"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 ;<br/>

<a NAME="E3:9"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> <a href="xboole_0.html#K3" target="_self">/\</a> <font color="Maroon">Y</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:9"/><b>then </b>
<font color="Maroon">X</font> <a href="xboole_0.html#K3" target="_self">/\</a> <font color="Maroon">Y</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1" target="_self">{}</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:9"/>
<font color="Maroon">X</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/>


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