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<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="E1:58_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="measure1.html#V2" target="_self">sigma-additive</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="prob_1.html#V1">compl-closed</a> )
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  <a href="prob_1.html#V1">compl-closed</a> <a href="measure1.html#V2" target="_self">sigma-additive</a> <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E3:58_1_1"/>
<font color="Maroon">c<sub>3</sub></font> is   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<b>hence </b><a NAME="E4:58_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="finsub_1.html#V1">cup-closed</a>
 ;<br/>


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