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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:30"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is    <a href="dynkin.html#M1" target="_self">Dynkin_System</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="finsub_1.html#V2">intersection_stable</a> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E2:30"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:30"/><b>then </b><i><font color="Green">E25</font></i>: 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="dynkin.html#K6" target="_self">disjointify</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="dynkin.html#E1:30"><i><font color="Green">E24</font></i></a>, <a class="ref" href="dynkin.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E4:30"/>
 <a href="dynkin.html#K6" target="_self">disjointify</a> <font color="Maroon">c<sub>3</sub></font> is <a href="prob_2.html#V1">disjoint_valued</a>
 
<b>by </b><i><a class="ref" href="dynkin.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E5:30"/><b>then </b>
 <a href="prob_1.html#K2">Union</a> <span class="p1">(<span class="default"><a href="dynkin.html#K6" target="_self">disjointify</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="dynkin.html#E1:30"><i><font color="Green">E24</font></i></a>, <a class="txt" href="dynkin.html#E3:30"><i><font color="Green">E25</font></i></a>, <a class="ref" href="dynkin.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E6:30"/><b>then </b>
 <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="dynkin.html#K6" target="_self">disjointify</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="card_3.html#D4">CARD_3:def 4</a></i>;<br/>
<b>hence </b><a NAME="E7:30"/>
 <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="dynkin.html#T10" target="_self">Th10</a></i>;<br/>


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