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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   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="prob_1.html#M1">SetSequence</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="prob_1.html#M3">Probability</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:40"/>
<font color="Maroon">c<sub>3</sub></font> is <a href="prob_2.html#V1">disjoint_valued</a>
 ;<br/>

<a NAME="E2:40"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prob_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="series_1.html#K1">Partial_Sums</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prob_1.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="prob_3.html#T48" target="_self">Th48</a></i>;<br/>
<b>hence </b><a NAME="E3:40"/>
<font color="Maroon">c<sub>4</sub></font> <a href="prob_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="prob_3.html#K5" target="_self">@Partial_Union</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="series_1.html#K1">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prob_1.html#K9">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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