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<b>let </b><font color="Maroon">Omega</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">E</font> be   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">Omega</font>;<br/>



<b>assume </b><a NAME="E1:39"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">E</font> is <a href="finsub_1.html#V2">intersection_stable</a>
 ;<br/>

<b>reconsider </b><font color="Maroon">G</font> =  <a href="dynkin.html#K7" target="_self">generated_Dynkin_System</a> <font color="Maroon">E</font> as   <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">Omega</font> ;<br/>
<a NAME="E3:39"/>
for <font color="Olive">a</font>, <font color="Olive">b</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> &amp; <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font> holds <br/><font color="Olive">a</font> <a href="xboole_0.html#K3">/\</a> <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">G</font>
 
<b>by </b><i>, <a class="ref" href="dynkin.html#T1" target="_self">Th1</a></i>;<br/>
<b>hence </b><a NAME="E4:39"/>
 <a href="dynkin.html#K7" target="_self">generated_Dynkin_System</a> <font color="Maroon">E</font> is <a href="finsub_1.html#V2">intersection_stable</a>
 <b>by </b><i><a class="ref" href="finsub_1.html#D2">FINSUB_1:def 2</a></i>;<br/>


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