<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="prob_1.html#M2">Event</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="prob_1.html#M3">Probability</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>











<b>assume </b><a NAME="E1:37"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="prob_2.html#R1" target="_self">are_independent_respect_to</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="prob_2.html#R1" target="_self">are_independent_respect_to</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>5</sub></font> )
 ;<br/>

<a NAME="E2:37"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">c<sub>4</sub></font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T76">XBOOLE_1:76</a></i>;<br/>
<font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K6">/\</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> = 
<font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="prob_1.html#K7">\/</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T23">XBOOLE_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prob_2.html#E2:37"><i><font color="Green">E26</font></i></a>, <a class="ref" href="prob_1.html#D13">PROB_1:def 13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prob_1.html#K6">/\</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prob_2.html#E1:37"><i><font color="Green">E25</font></i></a>, <a class="ref" href="prob_2.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>4</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"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prob_2.html#E1:37"><i><font color="Green">E25</font></i></a>, <a class="ref" href="prob_2.html#D5" target="_self">Def5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="prob_1.html#K10">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="prob_2.html#E1:37"><i><font color="Green">E25</font></i></a>, <a class="ref" href="prob_1.html#D13">PROB_1:def 13</a></i>
;<br/>
<b>hence </b><a NAME="E4:37"/>
<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="prob_1.html#K7">\/</a> <font color="Maroon">c<sub>5</sub></font> <a href="prob_2.html#R1" target="_self">are_independent_respect_to</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="prob_2.html#D5" target="_self">Def5</a></i>;<br/>


</div>
