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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#M2" title="PROB_1:mode.2">Probability</a> of <font color="Olive" title="b1">Sigma</font><br/> for <font color="Olive" title="b3">A</font>, <font color="Olive" title="b4">B</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of <font color="Olive" title="b1">Sigma</font>  st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b4">B</font> &amp; <font color="Olive" title="b2">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b4">B</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <font color="Olive" title="b4">B</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">A</font> <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="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Olive" title="b1">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Olive" title="b4">B</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">A</font> holds <br/><font color="Olive" title="b3">A</font>,<font color="Olive" title="b4">B</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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">P</font> being   <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font><br/> for <font color="Olive" title="b2">A</font>, <font color="Olive" title="b3">B</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">B</font> &amp; <font color="Olive" title="b1">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b3">B</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 &amp; <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <font color="Olive" title="b3">B</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">A</font> <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="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Olive" title="b3">B</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">A</font> holds <br/><font color="Olive" title="b2">A</font>,<font color="Olive" title="b3">B</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/><span class="kw">let </span><font color="Maroon" title="c3">P</font> be    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being   <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of <font color="Maroon" title="c2">Sigma</font>  st  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">B</font> &amp; <font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">B</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <font color="Olive" title="b2">B</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Olive" title="b2">B</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">B</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/><span class="kw">let </span><font color="Maroon" title="c4">A</font>, <font color="Maroon" title="c5">B</font> be    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of <font color="Maroon" title="c2">Sigma</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font> &amp; <font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">A</font> implies <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</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/>









<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:54"/><span class="lab"><font color="Green" title="E25">A1</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font>
 <span class="kw">and </span><br/><a NAME="E2:54"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
<font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1
 <span class="kw">and </span><br/><a NAME="E3:54"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</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/>

<a NAME="E4:54"/>
(  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_2.html#K4" title="PROB_2:func.4">.|.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="txt" href="#E3:54"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="prob_2.html#D7" target="_self" title="PROB_2:def.7">Def7</a>, <a class="ref" href="prob_2.html#T27" target="_self" title="PROB_2:th.27">Th27</a></span>;<br/>
<a NAME="E5:54"/><span class="kw">then </span><span class="lab"><font color="Green" title="E28">A4</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K10" title="REAL_1:func.10">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_2.html#D7" target="_self" title="PROB_2:def.7">Def7</a></span>;<br/>
<a NAME="E6:54"/><span class="lab"><font color="Green" title="E29">A5</font></span>: 
<font color="Maroon" title="c5">B</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font>
 
;<br/>
<a NAME="E7:54"/>
<font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:54"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="prob_2.html#T27" target="_self" title="PROB_2:th.27">Th27</a></span>;<br/>
<a NAME="E8:54"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:54"><span class="lab"><font color="Green" title="E25">A1</font></span></a>, <a class="txt" href="#E5:54"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="prob_2.html#T4" target="_self" title="PROB_2:th.4">Th4</a></span>;<br/>
<a NAME="E9:54"/><span class="kw">then </span>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#T68" title="PROB_1:th.68">PROB_1:68</a></span>;<br/>
<span class="kw">then </span><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">B</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="prob_1.html#K5" title="PROB_1:func.5">[#]</a> <font color="Maroon" title="c2">Sigma</font></span>)</span> <a href="prob_1.html#K8" title="PROB_1:func.8">\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">A</font> <a href="prob_1.html#K6" title="PROB_1:func.6">/\</a> <font color="Maroon" title="c5">B</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:54"><span class="lab"><font color="Green" title="E29">A5</font></span></a>, <a class="ref" href="prob_2.html#T24" target="_self" title="PROB_2:th.24">Th24</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E11:54"/>
<font color="Maroon" title="c4">A</font>,<font color="Maroon" title="c5">B</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 class="kw">by</span> <span class="lab"><a class="ref" href="prob_2.html#D5" target="_self" title="PROB_2:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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