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<b>let </b><font color="Maroon">E</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">A</font> be   <a href="rpr_1.html#NM2">Event</a> of <font color="Maroon">E</font>, <font color="Maroon">B1</font> be   <a href="rpr_1.html#NM2">Event</a> of <font color="Maroon">E</font>, <font color="Maroon">B2</font> be   <a href="rpr_1.html#NM2">Event</a> of <font color="Maroon">E</font>, <font color="Maroon">B3</font> be   <a href="rpr_1.html#NM2">Event</a> of <font color="Maroon">E</font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:56"/><i><font color="Green">E22</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B1</font>
 <b>and </b><br/><a NAME="E2:56"/><i><font color="Green">E25</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B2</font>
 <b>and </b><br/><a NAME="E3:56"/><i><font color="Green">E26</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B3</font>
 <b>and </b><br/><a NAME="E4:56"/><i><font color="Green">E49</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B2</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">E</font>
 <b>and </b><br/><a NAME="E5:56"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">B1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B2</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E6:56"/><i><font color="Green">E62</font></i>: 
<font color="Maroon">B1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B3</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>and </b><br/><a NAME="E7:56"/><i><font color="Green">E65</font></i>: 
<font color="Maroon">B2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B3</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a><br/>

<a NAME="E8:56"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B2</font></span>)</span> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B3</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="rpr_1.html#T11" target="_self">Th11</a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/>
<a NAME="E9:56"/><b>then </b><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">B3</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E10:56"/>
<span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B3</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><font color="Maroon">B2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B3</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">B2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B3</font>
 
<b>by </b><i><a class="txt" href="rpr_1.html#E35"><i><font color="Green">Lemma33</font></i></a></i>;<br/>
<a NAME="E11:56"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B3</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="rpr_1.html#E36"><i><font color="Green">Lemma34</font></i></a>, <a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E12:56"/><b>then </b>
<font color="Maroon">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B2</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B3</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E13:56"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B3</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T76">XBOOLE_1:76</a></i>;<br/>
<a NAME="E14:56"/><b>then </b>
 <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">B2</font></span>)</span> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><font color="Maroon">B3</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="rpr_1.html#T39" target="_self">Th39</a>, </i>;<br/>
<a NAME="E15:56"/><b>then </b><i><font color="Green">E67</font></i>: 
 <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">B1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><font color="Maroon">B2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><font color="Maroon">B3</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>;<br/>
<a NAME="E16:56"/>
<font color="Maroon">B1</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B2</font>
 
<b>by </b><i><a class="ref" href="rpr_1.html#T34" target="_self">Th34</a>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E17:56"/><b>then </b>
<font color="Maroon">B1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">B2</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T76">XBOOLE_1:76</a></i>;<br/>
<a NAME="E18:56"/><b>then </b>
 <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B3</font></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E19:56"/><b>then </b>
 <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K2" target="_self">prob</a> <font color="Maroon">A</font>,<font color="Maroon">B1</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B3</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E20:56"/><b>then </b>
 <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K2" target="_self">prob</a> <font color="Maroon">A</font>,<font color="Maroon">B1</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K2" target="_self">prob</a> <font color="Maroon">A</font>,<font color="Maroon">B2</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B3</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<b>hence </b><a NAME="E21:56"/>
 <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K2" target="_self">prob</a> <font color="Maroon">A</font>,<font color="Maroon">B1</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rpr_1.html#K2" target="_self">prob</a> <font color="Maroon">A</font>,<font color="Maroon">B2</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rpr_1.html#K2" target="_self">prob</a> <font color="Maroon">A</font>,<font color="Maroon">B3</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B3</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rpr_1.html#T7" target="_self">Th7</a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>


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