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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/><b>let </b><font color="Maroon">B1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">B2</font> be    <a href="hidden.html#M1">set</a> ;<br/>







<b>assume </b><a NAME="E1:36"/><i><font color="Green">E24</font></i>: 
( <font color="Maroon">B1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp; <font color="Maroon">B2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> )
 ;<br/>

<b>let </b><font color="Maroon">C1</font> be    <a href="prob_4.html#M1" target="_self">thin</a> of <font color="Maroon">P</font>, <font color="Maroon">C2</font> be    <a href="prob_4.html#M1" target="_self">thin</a> of <font color="Maroon">P</font>;<br/>

<b>assume </b><a NAME="E2:36"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">B1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C2</font>
 ;<br/>

<b>consider </b><font color="Maroon">D1</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:36"/><i><font color="Green">E39</font></i>: 
( <font color="Maroon">D1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp; <font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D1</font> &amp; <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D1</font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="txt" href="prob_4.html#E1:36"><i><font color="Green">E24</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">D2</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:36"/><i><font color="Green">E48</font></i>: 
( <font color="Maroon">D2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp; <font color="Maroon">C2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D2</font> &amp; <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">D2</font> <a href="hidden.html#R1">=</a> 0 )
 <b>by </b><i><a class="txt" href="prob_4.html#E1:36"><i><font color="Green">E24</font></i></a></i>;<br/>
<a NAME="E7:36"/>
( <font color="Maroon">B1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C2</font> &amp; <font color="Maroon">B2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">D2</font> )
 
<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_1.html#T7">XBOOLE_1:7</a>, <a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/>
<a NAME="E8:36"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">B1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B2</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">D2</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E9:36"/>
( <font color="Maroon">B2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C1</font> &amp; <font color="Maroon">B1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">C1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">D1</font> )
 
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a>, <a class="ref" href="xboole_1.html#T9">XBOOLE_1:9</a></i>;<br/>
<a NAME="E10:36"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">B2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B1</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">D1</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<b>reconsider </b><font color="Maroon">B1</font> = <font color="Maroon">B1</font>, <font color="Maroon">B2</font> = <font color="Maroon">B2</font>, <font color="Maroon">D1</font> = <font color="Maroon">D1</font>, <font color="Maroon">D2</font> = <font color="Maroon">D2</font> as    <a href="prob_1.html#M2">Event</a> of <font color="Maroon">Sigma</font> <b>by </b><i>, , <a class="txt" href="prob_4.html#E1"><i><font color="Green">Lemma31</font></i></a>, <a class="ref" href="prob_1.html#D10">PROB_1:def 10</a></i>;<br/>
<a NAME="E12:36"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">B1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">D2</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="prob_1.html#T70">PROB_1:70</a></i>;<br/>
<a NAME="E13:36"/>
<font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">D2</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">B2</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">D2</font></span>)</span>
 
<b>by </b><i><a class="ref" href="prob_1.html#T75">PROB_1:75</a></i>;<br/>
<a NAME="E14:36"/><b>then </b><i><font color="Green">E52</font></i>: 
<font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">B1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">B2</font>
 
<b>by </b><i><a class="txt" href="prob_4.html#E1"><i><font color="Green">Lemma31</font></i></a>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E15:36"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">B2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">D1</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="prob_1.html#T70">PROB_1:70</a></i>;<br/>
<a NAME="E16:36"/><i><font color="Green">E55</font></i>: 
<font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">D1</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">B1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">D1</font></span>)</span>
 
<b>by </b><i><a class="ref" href="prob_1.html#T75">PROB_1:75</a></i>;<br/>
<a NAME="E17:36"/>
<font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">B2</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">B1</font>
 
<b>by </b><i>, <a class="txt" href="prob_4.html#E2:36"><i><font color="Green">E36</font></i></a>, <a class="ref" href="prob_4.html#T2" target="_self">Th2</a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E18:36"/>
<font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">B2</font>
 <b>by </b><i><a class="ref" href="prob_4.html#T1" target="_self">Th1</a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


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