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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">A</font> be    <a href="prob_1.html#M2">Event</a> of <font color="Maroon">Sigma</font>;<br/><b>let </b><font color="Maroon">A1</font> be    <a href="prob_1.html#M2">Event</a> of <font color="Maroon">Sigma</font>;<br/><b>let </b><font color="Maroon">A2</font> be    <a href="prob_1.html#M2">Event</a> of <font color="Maroon">Sigma</font>;<br/><b>let </b><font color="Maroon">A3</font> be    <a href="prob_1.html#M2">Event</a> of <font color="Maroon">Sigma</font>;<br/>













<b>assume </b><b>that </b><br/><a NAME="E1:43"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">A1</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A2</font>
 <b>and </b><br/><a NAME="E2:43"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">A3</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">A2</font></span>)</span> <a href="subset_1.html#K3">`</a> 
 <b>and </b><br/><a NAME="E3:43"/><i><font color="Green">E39</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A1</font>
 <b>and </b><br/><a NAME="E4:43"/><i><font color="Green">E41</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A2</font>
 <b>and </b><br/><a NAME="E5:43"/><i><font color="Green">E43</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A3</font>
 ;<br/>

<a NAME="E6:43"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A1</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A2</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T76">XBOOLE_1:76</a></i>;<br/>
<a NAME="E7:43"/>
<font color="Maroon">A1</font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">A2</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A3</font>
 
<b>by </b><i>, <a class="ref" href="subset_1.html#T44">SUBSET_1:44</a></i>;<br/>
<a NAME="E8:43"/><b>then </b><i><font color="Green">E45</font></i>: 
<font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">A2</font></span>)</span> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A3</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T76">XBOOLE_1:76</a></i>;<br/>
<i><font color="Green">E46</font></i>: <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">A2</font></span>)</span> <a href="prob_1.html#K7">\/</a> <font color="Maroon">A3</font> = 
 <a href="subset_1.html#K2">[#]</a> <font color="Maroon">Omega</font>
<b>by </b><i>, <a class="ref" href="subset_1.html#T25">SUBSET_1:25</a></i>
<br/>.= 
<font color="Maroon">Omega</font>
<b>by </b><i><a class="ref" href="subset_1.html#D4">SUBSET_1:def 4</a></i>
;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">P</font> <a href="prob_2.html#K4" target="_self">.|.</a> <font color="Maroon">A1</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">P</font> <a href="prob_2.html#K4" target="_self">.|.</a> <font color="Maroon">A2</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A2</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"><span class="p3">(<span class="default"><font color="Maroon">P</font> <a href="prob_2.html#K4" target="_self">.|.</a> <font color="Maroon">A3</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A3</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">P</font> <a href="prob_2.html#K4" target="_self">.|.</a> <font color="Maroon">A2</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A2</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"><span class="p3">(<span class="default"><font color="Maroon">P</font> <a href="prob_2.html#K4" target="_self">.|.</a> <font color="Maroon">A3</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A3</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A2</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"><span class="p3">(<span class="default"><font color="Maroon">P</font> <a href="prob_2.html#K4" target="_self">.|.</a> <font color="Maroon">A3</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A3</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A3</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A1</font></span>)</span> <a href="prob_1.html#K7">\/</a> <span class="p3">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A3</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="prob_1.html#D13">PROB_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <span class="p3">(<span class="default"><font color="Maroon">A1</font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">A2</font></span>)</span></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
<font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <span class="p3">(<span class="default"><font color="Maroon">A1</font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">A2</font></span>)</span></span>)</span> <a href="prob_1.html#K7">\/</a> <span class="p2">(<span class="default"><font color="Maroon">A</font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">A3</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="prob_1.html#D13">PROB_1:def 13</a></i>
<br/>.= 
<font color="Maroon">P</font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K8">/\</a> <font color="Maroon">Omega</font></span>)</span>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
<font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E11:43"/>
<font color="Maroon">P</font> <a href="prob_1.html#K10">.</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"><span class="p4">(<span class="default"><font color="Maroon">P</font> <a href="prob_2.html#K4" target="_self">.|.</a> <font color="Maroon">A1</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A1</font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">P</font> <a href="prob_2.html#K4" target="_self">.|.</a> <font color="Maroon">A2</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A2</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"><span class="p3">(<span class="default"><font color="Maroon">P</font> <a href="prob_2.html#K4" target="_self">.|.</a> <font color="Maroon">A3</font></span>)</span> <a href="prob_1.html#K10">.</a> <font color="Maroon">A</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">A3</font></span>)</span></span>)</span>
 ;<br/>


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