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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="E1:40"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">E</font> is <a href="finsub_1.html#V2">intersection_stable</a>
 ;<br/>

<b>let </b><font color="Maroon">D</font> be    <a href="dynkin.html#M1" target="_self">Dynkin_System</a> of <font color="Maroon">Omega</font>;<br/>

<b>assume </b><a NAME="E2:40"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">E</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 ;<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="dynkin.html#M1" target="_self">Dynkin_System</a> of <font color="Maroon">Omega</font> ;<br/>
<a NAME="E4:40"/>
<font color="Maroon">G</font> is <a href="finsub_1.html#V2">intersection_stable</a>
 
<b>by </b><i><a class="txt" href="dynkin.html#E2:40"><i><font color="Green">E32</font></i></a>, <a class="txt" href="dynkin.html#E1:40"><i><font color="Green">E31</font></i></a></i>;<br/>
<a NAME="E5:40"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">G</font> is   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">Omega</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:40"/>
<font color="Maroon">E</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:40"/><b>then </b><i><font color="Green">E41</font></i>: 
 <a href="prob_1.html#K11">sigma</a> <font color="Maroon">E</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">G</font>
 
<b>by </b><i>, <a class="ref" href="prob_1.html#D14">PROB_1:def 14</a></i>;<br/>
<a NAME="E8:40"/>
<font color="Maroon">G</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="dynkin.html#T2" target="_self">Th2</a>, </i>;<br/>
<b>hence </b><a NAME="E9:40"/>
 <a href="prob_1.html#K11">sigma</a> <font color="Maroon">E</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>


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