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<b>let </b><font color="Maroon" title="c1">I</font>, <font color="Maroon" title="c2">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="c2">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">F</font> being   <a href="kolmog01.html#M1" title="KOLMOG01:mode.1">ManySortedSigmaField</a> of <font color="Maroon" title="c1">I</font>,<font color="Olive" title="b1">Sigma</font><br/> for <font color="Olive" title="b4">J</font>, <font color="Olive" title="b5">K</font> being 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="c1">I</font>  st <font color="Olive" title="b3">F</font> <a href="kolmog01.html#R2" title="KOLMOG01:pred.2">is_independent_wrt</a> <font color="Olive" title="b2">P</font> &amp; <font color="Olive" title="b4">J</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <font color="Olive" title="b5">K</font> holds <br/>for <font color="Olive" title="b6">u</font>, <font color="Olive" title="b7">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="b6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Olive" title="b3">F</font>,<font color="Olive" title="b4">J</font> &amp; <font color="Olive" title="b7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Olive" title="b3">F</font>,<font color="Olive" title="b5">K</font> holds <br/><font color="Olive" title="b2">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b6">u</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b7">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">u</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b7">v</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">Sigma</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c2">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="c3">Sigma</font><br/> for <font color="Olive" title="b2">F</font> being   <a href="kolmog01.html#M1" title="KOLMOG01:mode.1">ManySortedSigmaField</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">Sigma</font><br/> for <font color="Olive" title="b3">J</font>, <font color="Olive" title="b4">K</font> being 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="c1">I</font>  st <font color="Olive" title="b2">F</font> <a href="kolmog01.html#R2" title="KOLMOG01:pred.2">is_independent_wrt</a> <font color="Olive" title="b1">P</font> &amp; <font color="Olive" title="b3">J</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <font color="Olive" title="b4">K</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="Maroon" title="c3">Sigma</font>  st <font color="Olive" title="b5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Olive" title="b2">F</font>,<font color="Olive" title="b3">J</font> &amp; <font color="Olive" title="b6">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Olive" title="b2">F</font>,<font color="Olive" title="b4">K</font> holds <br/><font color="Olive" title="b1">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">u</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b6">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">u</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b6">v</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">P</font> be    <a href="prob_1.html#M3" title="PROB_1:mode.3">Probability</a> of <font color="Maroon" title="c3">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">F</font> being   <a href="kolmog01.html#M1" title="KOLMOG01:mode.1">ManySortedSigmaField</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">Sigma</font><br/> for <font color="Olive" title="b2">J</font>, <font color="Olive" title="b3">K</font> being 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="c1">I</font>  st <font color="Olive" title="b1">F</font> <a href="kolmog01.html#R2" title="KOLMOG01:pred.2">is_independent_wrt</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Olive" title="b2">J</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <font color="Olive" title="b3">K</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="c3">Sigma</font>  st <font color="Olive" title="b4">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Olive" title="b1">F</font>,<font color="Olive" title="b2">J</font> &amp; <font color="Olive" title="b5">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Olive" title="b1">F</font>,<font color="Olive" title="b3">K</font> holds <br/><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">u</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b5">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">u</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">v</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c5">F</font> be    <a href="kolmog01.html#M1" title="KOLMOG01:mode.1">ManySortedSigmaField</a> of <font color="Maroon" title="c1">I</font>,<font color="Maroon" title="c3">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">J</font>, <font color="Olive" title="b2">K</font> being 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="c1">I</font>  st <font color="Maroon" title="c5">F</font> <a href="kolmog01.html#R2" title="KOLMOG01:pred.2">is_independent_wrt</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Olive" title="b1">J</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <font color="Olive" title="b2">K</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="c3">Sigma</font>  st <font color="Olive" title="b3">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Maroon" title="c5">F</font>,<font color="Olive" title="b1">J</font> &amp; <font color="Olive" title="b4">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Maroon" title="c5">F</font>,<font color="Olive" title="b2">K</font> holds <br/><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">u</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b4">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">u</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">v</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">J</font>, <font color="Maroon" title="c7">K</font> be  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="c1">I</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">F</font> <a href="kolmog01.html#R2" title="KOLMOG01:pred.2">is_independent_wrt</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c6">J</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <font color="Maroon" title="c7">K</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="c3">Sigma</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c6">J</font> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c7">K</font> holds <br/><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">u</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">v</font></span>)</span> )</span><br/>











<b>assume </b><a NAME="E1:28"/><i><font color="Green" title="E22">A0</font></i>: 
( <font color="Maroon" title="c5">F</font> <a href="kolmog01.html#R2" title="KOLMOG01:pred.2">is_independent_wrt</a> <font color="Maroon" title="c4">P</font> &amp; <font color="Maroon" title="c6">J</font> <a href="subset_1.html#R1" title="SUBSET_1:pred.1">misses</a> <font color="Maroon" title="c7">K</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="c3">Sigma</font>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c6">J</font> &amp; <font color="Olive" title="b2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c7">K</font> holds <br/><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">u</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Olive" title="b2">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">u</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">v</font></span>)</span></span><br/>

<b>let </b><font color="Maroon" title="c8">u</font>, <font color="Maroon" title="c9">v</font> be    <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c3">Sigma</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c6">J</font> &amp; <font color="Maroon" title="c9">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c7">K</font> implies <font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">u</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c9">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">u</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font></span>)</span> )</span><br/>



<b>assume </b><a NAME="E2:28"/><i><font color="Green" title="E23">A1</font></i>: 
( <font color="Maroon" title="c8">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c6">J</font> &amp; <font color="Maroon" title="c9">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K4" title="KOLMOG01:func.4">sigUn</a> <font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c7">K</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">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">u</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c9">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">u</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font></span>)</span></span><br/>

<a NAME="E3:28"/><i><font color="Green" title="E24">A2</font></i>: 
 <a href="kolmog01.html#K7" title="KOLMOG01:func.7">MeetSections</a> <font color="Maroon" title="c6">J</font>,<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="c3">Sigma</font>
 
<b>by </b><i><a class="ref" href="kolmog01.html#T13" target="_self" title="KOLMOG01:th.13">Th11</a></i>;<br/>
<a NAME="E4:28"/><i><font color="Green" title="E25">A4</font></i>: 
 <a href="kolmog01.html#K7" title="KOLMOG01:func.7">MeetSections</a> <font color="Maroon" title="c7">K</font>,<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="c3">Sigma</font>
 
<b>by </b><i><a class="ref" href="kolmog01.html#T13" target="_self" title="KOLMOG01:th.13">Th11</a></i>;<br/>
<a NAME="E5:28"/><i><font color="Green" title="E26">A6</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="c3">Sigma</font>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K7" title="KOLMOG01:func.7">MeetSections</a> <font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c5">F</font> &amp; <font color="Olive" title="b2">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K7" title="KOLMOG01:func.7">MeetSections</a> <font color="Maroon" title="c7">K</font>,<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="c4">P</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c10">p</font>, <font color="Maroon" title="c11">q</font> be    <a href="prob_1.html#M2" title="PROB_1:mode.2">Event</a> of <font color="Maroon" title="c3">Sigma</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c10">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K7" title="KOLMOG01:func.7">MeetSections</a> <font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c5">F</font> &amp; <font color="Maroon" title="c11">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K7" title="KOLMOG01:func.7">MeetSections</a> <font color="Maroon" title="c7">K</font>,<font color="Maroon" title="c5">F</font> implies <font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c11">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c4">P</font> )</span><br/>



<b>assume </b><a NAME="E1:28_1"/><i><font color="Green" title="E27">B0</font></i>: 
( <font color="Maroon" title="c10">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K7" title="KOLMOG01:func.7">MeetSections</a> <font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c5">F</font> &amp; <font color="Maroon" title="c11">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="kolmog01.html#K7" title="KOLMOG01:func.7">MeetSections</a> <font color="Maroon" title="c7">K</font>,<font color="Maroon" title="c5">F</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c11">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c4">P</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c12">p</font> = <font color="Maroon" title="c10">p</font>, <font color="Maroon" title="c13">q</font> = <font color="Maroon" title="c11">q</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c2">Omega</font> ;<br/>
<a NAME="E3:28_1"/>
<font color="Maroon" title="c4">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">p</font> <a href="finsub_1.html#K3" title="FINSUB_1:func.3">/\</a> <font color="Maroon" title="c13">q</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c12">p</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c13">q</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:28"><i><font color="Green" title="E22">A0</font></i></a>, <a class="txt" href="#E1:28_1"><i><font color="Green" title="E27">B0</font></i></a>, <a class="ref" href="kolmog01.html#T12" target="_self" title="KOLMOG01:th.12">Th10</a></i>;<br/>
<b>hence </b><a NAME="E4:28_1"/>
<font color="Maroon" title="c10">p</font>,<font color="Maroon" title="c11">q</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c4">P</font>
 <b>by </b><i><a class="ref" href="prob_2.html#D5" title="PROB_2:def.5">PROB_2:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E6:28"/>
( <font color="Maroon" title="c8">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> <span class="p1">(<span class="default"><a href="kolmog01.html#K7" title="KOLMOG01:func.7">MeetSections</a> <font color="Maroon" title="c6">J</font>,<font color="Maroon" title="c5">F</font></span>)</span> &amp; <font color="Maroon" title="c9">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> <span class="p1">(<span class="default"><a href="kolmog01.html#K7" title="KOLMOG01:func.7">MeetSections</a> <font color="Maroon" title="c7">K</font>,<font color="Maroon" title="c5">F</font></span>)</span> )
 
<b>by </b><i><a class="txt" href="#E2:28"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="kolmog01.html#T11" target="_self" title="KOLMOG01:th.11">Th9</a></i>;<br/>
<a NAME="E7:28"/><b>then </b>
<font color="Maroon" title="c8">u</font>,<font color="Maroon" title="c9">v</font> <a href="prob_2.html#R1" title="PROB_2:pred.1">are_independent_respect_to</a> <font color="Maroon" title="c4">P</font>
 
<b>by </b><i><a class="txt" href="#E3:28"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="#E4:28"><i><font color="Green" title="E25">A4</font></i></a>, <a class="txt" href="#E5:28"><i><font color="Green" title="E26">A6</font></i></a>, <a class="ref" href="kolmog01.html#T10" target="_self" title="KOLMOG01:th.10">Th8</a></i>;<br/>
<b>hence </b><a NAME="E8:28"/>
<font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">u</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c9">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">u</font></span>)</span> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">v</font></span>)</span>
 <b>by </b><i><a class="ref" href="prob_2.html#D5" title="PROB_2:def.5">PROB_2:def 5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
