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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">D</font> be    <a href="dynkin.html#M1" target="_self">Dynkin_System</a> of <font color="Maroon">Omega</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">D</font>, <font color="Maroon">y</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">D</font>;<br/>





<b>assume </b><a NAME="E1:31"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">x</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">y</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">e</font> =  <a href="xboole_0.html#K1">{}</a>  as    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">D</font> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">x1</font> = <font color="Maroon">x</font> as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">Omega</font> ;<br/>
<b>reconsider </b><font color="Maroon">y1</font> = <font color="Maroon">y</font> as   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">Omega</font> ;<br/>
<b>reconsider </b><font color="Maroon">r</font> = <font color="Maroon">x1</font>,<font color="Maroon">y1</font> <a href="dynkin.html#K3" target="_self">followed_by</a> <span class="p1">(<span class="default"><a href="subset_1.html#K1">{}</a> <font color="Maroon">Omega</font></span>)</span> as   <a href="prob_1.html#NM2">SetSequence</a> of <font color="Maroon">Omega</font> ;<br/>
<a NAME="E6:31"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">r</font> is <a href="prob_2.html#V1">disjoint_valued</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E7:31"/>
<font color="Maroon">x</font>,<font color="Maroon">y</font> <a href="dynkin.html#K3" target="_self">followed_by</a> <font color="Maroon">e</font> is   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,<font color="Maroon">D</font>
 
<b>by </b><i/>;<br/>
<a NAME="E8:31"/><b>then </b>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">r</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 
<b>by </b><i><a class="ref" href="relset_1.html#T12">RELSET_1:12</a></i>;<br/>
<a NAME="E9:31"/><b>then </b>
 <a href="prob_1.html#K2">Union</a> <font color="Maroon">r</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E10:31"/><b>then </b>
 <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">r</font></span>)</span> <a href="hidden.html#R2">in</a> <font color="Maroon">D</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="E11:31"/>
<font color="Maroon">x</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 <b>by </b><i/>;<br/>


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