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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">P1</font> be    <a href="prob_1.html#M3">Probability</a> of <font color="Maroon">Sigma</font>;<br/>







<b>assume </b><a NAME="E1:9"/><i><font color="Green">E37</font></i>: 
for <font color="Olive">A</font> being   <a href="prob_1.html#M2">Event</a> of <font color="Maroon">Sigma</font> holds  <font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Olive">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P1</font> <a href="prob_1.html#K10">.</a> <font color="Olive">A</font>
 ;<br/>

<a NAME="E2:9"/>
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> holds <br/><font color="Maroon">P</font> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P1</font> <a href="seq_1.html#K2">.</a> <font color="Olive">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:9_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as    <a href="prob_1.html#M2">Event</a> of <font color="Maroon">Sigma</font> <b>by </b><i><a class="ref" href="prob_1.html#T48">PROB_1:48</a></i>;<br/>
<a NAME="E3:9_1"/>
<font color="Maroon">P</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P1</font> <a href="prob_1.html#K10">.</a> <font color="Maroon">x</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E4:9_1"/>
<font color="Maroon">P</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P1</font> <a href="seq_1.html#K2">.</a> <font color="Maroon">x</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:9"/>
<font color="Maroon">P</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">P1</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T18">FUNCT_2:18</a></i>;<br/>


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