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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="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="rpr_1.html#NM2">Event</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:63"/><i><font color="Green">E32</font></i>: 
 <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:63"/>
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E3:63"/><b>then </b>
 <a href="rpr_1.html#K1" target="_self">prob</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 0
 
<b>by </b><i><a class="txt" href="rpr_1.html#E1:63"><i><font color="Green">E32</font></i></a>, <a class="ref" href="rpr_1.html#T44" target="_self">Th44</a></i>;<br/>
<a NAME="E4:63"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="rpr_1.html#K1" target="_self">prob</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="rpr_1.html#T43" target="_self">Th43</a></i>;<br/>
<a NAME="E5:63"/>
0 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> 0
 
;<br/>
<b>hence </b><a NAME="E6:63"/>
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="rpr_1.html#R1" target="_self">are_independent</a> 
 <b>by </b><i><a class="txt" href="rpr_1.html#E1:63"><i><font color="Green">E32</font></i></a>, <a class="txt" href="rpr_1.html#E4:63"><i><font color="Green">E33</font></i></a>, <a class="ref" href="rpr_1.html#D6" target="_self">Def6</a></i>;<br/>


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