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<b>let </b><font color="Maroon" title="c1">Omega</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">Sigma</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font>;<br/><b>let </b><font color="Maroon" title="c3">P</font> be    <a href="prob_1.html#M3" title="PROB_1:mode.3">Probability</a> of <font color="Maroon" title="c2">Sigma</font>;<br/><b>let </b><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">E</font> be    <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>;<br/>









<b>assume </b><a NAME="E1:33"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c5">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ;<br/>

<font color="Maroon" title="c3">P</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <font color="Maroon" title="c2">Sigma</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_1.html#K10" title="PROB_1:func.10">.</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> 0
<b>by </b><i><a class="ref" href="prob_1.html#T64" title="PROB_1:th.64">PROB_1:64</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_1.html#K10" title="PROB_1:func.10">.</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="real_1.html#K4" title="REAL_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <span class="p2">(<span class="default"><a href="subset_1.html#K1" title="SUBSET_1:func.1">{}</a> <font color="Maroon" title="c2">Sigma</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="prob_1.html#T64" title="PROB_1:th.64">PROB_1:64</a></i>
;<br/>
<b>hence </b><a NAME="E3:33"/>
<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">E</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font>
 <b>by </b><i><a class="txt" href="prob_2.html#E1:33"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="prob_2.html#D5" target="_self" title="PROB_2:def.5">Def5</a></i>;<br/>


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