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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Sigma</font> being  <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font><br/> for <font color="Olive" title="b2">P</font> being   <a href="prob_1.html#M3" title="PROB_1:mode.3">Probability</a> of <font color="Olive" title="b1">Sigma</font><br/> for <font color="Olive" title="b3">E</font>, <font color="Olive" title="b4">F</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font>  st <font color="Olive" title="b3">E</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">Sigma</font> &amp; <font color="Olive" title="b3">E</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> &amp; <font color="Olive" title="b4">F</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">Sigma</font> &amp; <font color="Olive" title="b4">F</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> &amp; ( for <font color="Olive" title="b5">p</font>, <font color="Olive" title="b6">q</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Olive" title="b1">Sigma</font>  st <font color="Olive" title="b5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">E</font> &amp; <font color="Olive" title="b6">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b4">F</font> holds <br/><font color="Olive" title="b5">p</font>,<font color="Olive" title="b6">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Olive" title="b2">P</font> ) holds <br/>for <font color="Olive" title="b5">u</font>, <font color="Olive" title="b6">v</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Olive" title="b1">Sigma</font>  st <font color="Olive" title="b5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Olive" title="b3">E</font> &amp; <font color="Olive" title="b6">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Olive" title="b4">F</font> holds <br/><font color="Olive" title="b5">u</font>,<font color="Olive" title="b6">v</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Olive" title="b2">P</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">P</font> being   <a href="prob_1.html#M3" title="PROB_1:mode.3">Probability</a> of <font color="Maroon" title="c2">Sigma</font><br/> for <font color="Olive" title="b2">E</font>, <font color="Olive" title="b3">F</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font>  st <font color="Olive" title="b2">E</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Olive" title="b2">E</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> &amp; <font color="Olive" title="b3">F</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Olive" title="b3">F</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> &amp; ( for <font color="Olive" title="b4">p</font>, <font color="Olive" title="b5">q</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b4">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">E</font> &amp; <font color="Olive" title="b5">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b3">F</font> holds <br/><font color="Olive" title="b4">p</font>,<font color="Olive" title="b5">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Olive" title="b1">P</font> ) holds <br/>for <font color="Olive" title="b4">u</font>, <font color="Olive" title="b5">v</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b4">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Olive" title="b2">E</font> &amp; <font color="Olive" title="b5">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Olive" title="b3">F</font> holds <br/><font color="Olive" title="b4">u</font>,<font color="Olive" title="b5">v</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Olive" title="b1">P</font></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">E</font>, <font color="Olive" title="b2">F</font> being  <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font>  st <font color="Olive" title="b1">E</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Olive" title="b1">E</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> &amp; <font color="Olive" title="b2">F</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Olive" title="b2">F</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> &amp; ( for <font color="Olive" title="b3">p</font>, <font color="Olive" title="b4">q</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b3">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b4">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Olive" title="b2">F</font> holds <br/><font color="Olive" title="b3">p</font>,<font color="Olive" title="b4">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> ) holds <br/>for <font color="Olive" title="b3">u</font>, <font color="Olive" title="b4">v</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b3">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Olive" title="b1">E</font> &amp; <font color="Olive" title="b4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Olive" title="b2">F</font> holds <br/><font color="Olive" title="b3">u</font>,<font color="Olive" title="b4">v</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font></span><br/><b>let </b><font color="Maroon" title="c4">E</font>, <font color="Maroon" title="c5">F</font> be   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">E</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Maroon" title="c4">E</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> &amp; <font color="Maroon" title="c5">F</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Maroon" title="c5">F</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> &amp; ( for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font> holds <br/><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> ) implies for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c5">F</font> holds <br/><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> )</span><br/>









<b>assume </b><a NAME="E1:11"/><i><font color="Green" title="E12">A0</font></i>: 
<font color="Maroon" title="c4">E</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">E</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> or  not <font color="Maroon" title="c5">F</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> or  not <font color="Maroon" title="c5">F</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> or  ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font> st <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font> &amp; not <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> ) or for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c5">F</font> holds <br/><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> )</span><br/>

<b>assume </b><a NAME="E2:11"/><i><font color="Green" title="E13">A1</font></i>: 
<font color="Maroon" title="c4">E</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">F</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> or  not <font color="Maroon" title="c5">F</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> or  ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font> st <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font> &amp; not <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> ) or for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c5">F</font> holds <br/><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> )</span><br/>

<b>assume </b><a NAME="E3:11"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c5">F</font> is  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">F</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a> or  ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font> st <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font> &amp; not <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> ) or for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c5">F</font> holds <br/><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> )</span><br/>

<b>assume </b><a NAME="E4:11"/><i><font color="Green" title="E15">A3</font></i>: 
<font color="Maroon" title="c5">F</font> is <a href="finsub_1.html#V2" title="FINSUB_1:attr.2">intersection_stable</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  ex <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font> st <br/>( <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font> &amp; not <font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> ) or for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c5">F</font> holds <br/><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font> )</span><br/>

<b>assume </b><a NAME="E5:11"/><i><font color="Green" title="E16">A4</font></i>: 
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">q</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">F</font> holds <br/><font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c5">F</font> holds <br/><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c3">P</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c6">E</font> = <font color="Maroon" title="c4">E</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> <b>by </b><i><a class="txt" href="#E1:11"><i><font color="Green" title="E12">A0</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">F</font> = <font color="Maroon" title="c5">F</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> <b>by </b><i><a class="txt" href="#E3:11"><i><font color="Green" title="E14">A2</font></i></a></i>;<br/>
<a NAME="E8:11"/><i><font color="Green" title="E17">A5</font></i>: 
<font color="Maroon" title="c6">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="kolmog01.html#K1" title="KOLMOG01:func.1">Indep</a> <font color="Maroon" title="c7">F</font>,<font color="Maroon" title="c3">P</font>
 
<b>by </b><i><a class="txt" href="#E5:11"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="kolmog01.html#T7" target="_self" title="KOLMOG01:th.7">Th5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">E</font> = <font color="Maroon" title="c6">E</font>, <font color="Maroon" title="c9">F</font> = <font color="Maroon" title="c7">F</font> as   <a href="setfam_1.html#NM1" title="SETFAM_1:NM.1">Subset-Family</a> of <font color="Maroon" title="c1">Omega</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c10">sF</font> =  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c9">F</font>, <font color="Maroon" title="c11">sE</font> =  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c8">E</font> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Sigma</font> <b>by </b><i><a class="ref" href="prob_1.html#D14" title="PROB_1:def.14">PROB_1:def 14</a></i>;<br/>
<a NAME="E11:11"/>
 <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c8">E</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="kolmog01.html#K1" title="KOLMOG01:func.1">Indep</a> <font color="Maroon" title="c10">sF</font>,<font color="Maroon" title="c3">P</font>
 
<b>by </b><i><a class="txt" href="#E2:11"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="#E4:11"><i><font color="Green" title="E15">A3</font></i></a>, <a class="txt" href="#E8:11"><i><font color="Green" title="E17">A5</font></i></a>, <a class="ref" href="kolmog01.html#T9" target="_self" title="KOLMOG01:th.9">Th7</a></i>;<br/>
<b>hence </b><a NAME="E12:11"/>
for <font color="Olive" title="b1">u</font>, <font color="Olive" title="b2">v</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c4">E</font> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_1.html#K10" title="PROB_1:func.10">sigma</a> <font color="Maroon" title="c5">F</font> holds <br/><font color="Olive" title="b1">u</font>,<font color="Olive" title="b2">v</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="ref" href="kolmog01.html#T7" target="_self" title="KOLMOG01:th.7">Th5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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