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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="rpr_1.html#NM2">Event</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:57"/><i><font color="Green">E30</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">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:57"/><i><font color="Green">E31</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">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E3:57"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:57"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E5:57"/>
<font color="Maroon">c<sub>4</sub></font> <a href="subset_1.html#K7">\</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="rpr_1.html#E3:57"><i><font color="Green">E32</font></i></a>, <a class="ref" href="xboole_1.html#T40">XBOOLE_1:40</a></i>;<br/>
<a NAME="E6:57"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="subset_1.html#K6">\</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="rpr_1.html#E4:57"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xboole_1.html#T83">XBOOLE_1:83</a></i>;<br/>
<a NAME="E7:57"/><b>then </b><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> 
 
<b>by </b><i><a class="ref" href="subset_1.html#D5">SUBSET_1:def 5</a></i>;<br/>
<a NAME="E8:57"/>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="rpr_1.html#K1" target="_self">prob</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a> </span>)</span>
 
<b>by </b><i><a class="txt" href="rpr_1.html#E2:57"><i><font color="Green">E31</font></i></a>, <a class="txt" href="rpr_1.html#E6:57"><i><font color="Green">E34</font></i></a>, <a class="ref" href="subset_1.html#D5">SUBSET_1:def 5</a></i>;<br/>
<a NAME="E9:57"/><b>then </b>
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="rpr_1.html#T48" target="_self">Th48</a></i>;<br/>
<a NAME="E10:57"/><b>then </b>
1 <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T46">XREAL_1:46</a></i>;<br/>
<b>hence </b><a NAME="E11:57"/>
 <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</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">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></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">c<sub>3</sub></font></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">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></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">c<sub>4</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rpr_1.html#E1:57"><i><font color="Green">E30</font></i></a>, <a class="txt" href="rpr_1.html#E7:57"><i><font color="Green">E35</font></i></a>, <a class="ref" href="rpr_1.html#T79" target="_self">Th79</a></i>;<br/>


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