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

<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/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:32_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">P</font> <a href="prob_4.html#R1" target="_self">is_complete</a> <font color="Maroon">Sigma</font>
 ;<br/><a NAME="E2:32_1"/>
for <font color="Olive">A</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">Omega</font><br/> for <font color="Olive">B</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp; <font color="Olive">A</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> &amp; <span class="p1">(<span class="default"><a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">B</font> <a href="hidden.html#R1">=</a>  <a href="supinf_2.html#K1">0.</a>  holds <br/><font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font>
 <b>by </b><i><a class="txt" href="prob_4.html#E1:32_1"><i><font color="Green">E24</font></i></a>, , <a class="ref" href="supinf_2.html#D1">SUPINF_2:def 1</a></i>;<br/><b>hence </b><a NAME="E3:32_1"/>
 <a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font> <a href="measure3.html#R1">is_complete</a> <font color="Maroon">Sigma</font>
 <b>by </b><i><a class="ref" href="measure3.html#D2">MEASURE3:def 2</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:32"/><i><font color="Green">E36</font></i>: 
 <a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">P</font> <a href="measure3.html#R1">is_complete</a> <font color="Maroon">Sigma</font>
 ;<br/>

<a NAME="E3:32"/>
for <font color="Olive">A</font> being  <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">Omega</font><br/> for <font color="Olive">B</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp; <font color="Olive">A</font> <a href="tarski.html#R1">c=</a> <font color="Olive">B</font> &amp; <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <font color="Olive">B</font> <a href="hidden.html#R1">=</a> 0 holds <br/><font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font>
 
<b>by </b><i>, <a class="ref" href="measure3.html#D2">MEASURE3:def 2</a>, <a class="ref" href="supinf_2.html#D1">SUPINF_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:32"/>
<font color="Maroon">P</font> <a href="prob_4.html#R1" target="_self">is_complete</a> <font color="Maroon">Sigma</font>
 <b>by </b><i/>;<br/>


</div>
