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<b>let </b><font color="Maroon" title="c1">Omega</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">Sigma</font> be   <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font>;<br/><b>let </b><font color="Maroon" title="c3">P</font> be    <a href="prob_1.html#M3" title="PROB_1:mode.3">Probability</a> of <font color="Maroon" title="c2">Sigma</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:32_1"/>
<font color="Maroon" title="c3">P</font> <a href="prob_4.html#R1" title="PROB_4:pred.1">is_complete</a> <font color="Maroon" title="c2">Sigma</font>
 ;<br/><a NAME="E2:32_1"/><b>then </b>
for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Omega</font><br/> for <font color="Olive" title="b2">B</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">B</font> &amp; <span class="p1">(<span class="default"><a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="supinf_2.html#K1" title="SUPINF_2:func.1">0.</a>  holds <br/><font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font>
 <b>by </b><i><a class="ref" href="prob_4.html#D3" target="_self" title="PROB_4:def.3">Def3</a></i>;<br/><b>hence </b><a NAME="E3:32_1"/>
 <a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c3">P</font> <a href="measure3.html#R1" title="MEASURE3:pred.1">is_complete</a> <font color="Maroon" title="c2">Sigma</font>
 <b>by </b><i><a class="ref" href="measure3.html#D2" title="MEASURE3:def.2">MEASURE3:def 2</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:32"/>
 <a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c3">P</font> <a href="measure3.html#R1" title="MEASURE3:pred.1">is_complete</a> <font color="Maroon" title="c2">Sigma</font>
 ;<br/>

<a NAME="E3:32"/><b>then </b>
for <font color="Olive" title="b1">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">Omega</font><br/> for <font color="Olive" title="b2">B</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Olive" title="b1">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b2">B</font> &amp; <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  holds <br/><font color="Olive" title="b1">A</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font>
 
<b>by </b><i><a class="ref" href="measure3.html#D2" title="MEASURE3:def.2">MEASURE3:def 2</a></i>;<br/>
<b>hence </b><a NAME="E4:32"/>
<font color="Maroon" title="c3">P</font> <a href="prob_4.html#R1" title="PROB_4:pred.1">is_complete</a> <font color="Maroon" title="c2">Sigma</font>
 <b>by </b><i><a class="ref" href="prob_4.html#D3" target="_self" title="PROB_4:def.3">Def3</a></i>;<br/>


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