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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">B</font> be   <a href="rpr_1.html#NM2">Event</a> of <font color="Maroon">E</font>;<br/>



<b>assume </b><a NAME="E1:40"/><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">B</font>
 ;<br/>

<a NAME="E2:40"/><b>then </b><i><font color="Green">E25</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span> <a href="real_1.html#K2">"</a> 
 
<b>by </b><i><a class="ref" href="xreal_1.html#T124">XREAL_1:124</a></i>;<br/>
<a NAME="E3:40"/>
<font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E4:40"/><b>then </b>
 <a href="rpr_1.html#K1" target="_self">prob</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:40"/><b>then </b>
<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">B</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<a NAME="E6:40"/><b>then </b>
<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">B</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rpr_1.html#K1" target="_self">prob</a> <font color="Maroon">B</font></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1
 
<b>by </b><i>, <a class="ref" href="xcmplx_0.html#D7">XCMPLX_0:def 7</a></i>;<br/>
<b>hence </b><a NAME="E7:40"/>
 <a href="rpr_1.html#K2" target="_self">prob</a> <font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="xxreal_0.html#R1">&lt;=</a> 1
 <b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>;<br/>


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