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<b>let </b><font color="Maroon">Omega</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">Sigma</font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">Omega</font>;<br/><b>let </b><font color="Maroon">P</font> be    <a href="prob_1.html#M3">Probability</a> of <font color="Maroon">Sigma</font>;<br/>





<a NAME="E1:39"/><i><font color="Green">E24</font></i>: 
 <a href="prob_4.html#K4" target="_self">COM</a> <font color="Maroon">Sigma</font>,<font color="Maroon">P</font> <a href="tarski.html#R1">c=</a>  <a href="measure3.html#K2">COM</a> <font color="Maroon">Sigma</font>,<span class="p1">(<span class="default"><a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:39_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="prob_4.html#K4" target="_self">COM</a> <font color="Maroon">Sigma</font>,<font color="Maroon">P</font>
 ;<br/>

<b>consider </b><font color="Maroon">B</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:39_1"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp;  ex <font color="Olive">C</font> being   <a href="prob_4.html#M1" target="_self">thin</a> of <font color="Maroon">P</font> st <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">C</font> )
 <b>by </b><i>, </i>;<br/>
<b>consider </b><font color="Maroon">C</font> being    <a href="prob_4.html#M1" target="_self">thin</a> of <font color="Maroon">P</font><b> such that </b><br/><a NAME="E5:39_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">C1</font> = <font color="Maroon">C</font> as    <a href="measure3.html#M1">thin</a> of  <a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font> <b>by </b><i/>;<br/>
<a NAME="E7:39_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C1</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:39_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="measure3.html#K2">COM</a> <font color="Maroon">Sigma</font>,<span class="p1">(<span class="default"><a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="measure3.html#D4">MEASURE3:def 4</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:39"/>
 <a href="measure3.html#K2">COM</a> <font color="Maroon">Sigma</font>,<span class="p1">(<span class="default"><a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="prob_4.html#K4" target="_self">COM</a> <font color="Maroon">Sigma</font>,<font color="Maroon">P</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:39_2"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="measure3.html#K2">COM</a> <font color="Maroon">Sigma</font>,<span class="p1">(<span class="default"><a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font></span>)</span>
 ;<br/>

<b>consider </b><font color="Maroon">B</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:39_2"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp;  ex <font color="Olive">C</font> being   <a href="measure3.html#M1">thin</a> of  <a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font> st <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">C</font> )
 <b>by </b><i>, <a class="ref" href="measure3.html#D4">MEASURE3:def 4</a></i>;<br/>
<b>consider </b><font color="Maroon">C</font> being    <a href="measure3.html#M1">thin</a> of  <a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font><b> such that </b><br/><a NAME="E5:39_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C</font>
 <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">C1</font> = <font color="Maroon">C</font> as    <a href="prob_4.html#M1" target="_self">thin</a> of <font color="Maroon">P</font> <b>by </b><i/>;<br/>
<a NAME="E7:39_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C1</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:39_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="prob_4.html#K4" target="_self">COM</a> <font color="Maroon">Sigma</font>,<font color="Maroon">P</font>
 <b>by </b><i>, </i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:39"/>
 <a href="prob_4.html#K4" target="_self">COM</a> <font color="Maroon">Sigma</font>,<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="measure3.html#K2">COM</a> <font color="Maroon">Sigma</font>,<span class="p1">(<span class="default"><a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font></span>)</span>
 <b>by </b><i><a class="txt" href="prob_4.html#E1"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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