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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">C</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="setfam_1.html#NM1">Subset-Family</a> of <font color="Maroon">Omega</font>;<br/>







<b>assume </b><a NAME="E1:52"/><i><font color="Green">E24</font></i>: 
for <font color="Olive">A</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> iff  ex <font color="Olive">A1</font>, <font color="Olive">A2</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">A1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp; <font color="Olive">A2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp; <font color="Olive">A1</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A</font> &amp; <font color="Olive">A</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A2</font> &amp; <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">A2</font> <a href="subset_1.html#K6">\</a> <font color="Olive">A1</font></span>)</span> <a href="hidden.html#R1">=</a> 0 ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="52_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">A</font> be    <a href="hidden.html#M1">set</a> ;<br/><a NAME="E1:52_1"/>
( <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> iff  ex <font color="Olive">A1</font>, <font color="Olive">A2</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Olive">A1</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp; <font color="Olive">A2</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Sigma</font> &amp; <font color="Olive">A1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A2</font> &amp; <font color="Maroon">P</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">A2</font> <a href="subset_1.html#K6">\</a> <font color="Olive">A1</font></span>)</span> <a href="hidden.html#R1">=</a> 0 ) )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E2:52_1"/>
( <font color="Maroon">A</font> <a href="hidden.html#R2">in</a> <font color="Maroon">C</font> iff <font color="Maroon">A</font> <a href="hidden.html#R2">in</a>  <a href="prob_4.html#K7" target="_self">COM</a> <font color="Maroon">Sigma</font>,<font color="Maroon">P</font> )
 <b>by </b><i><a class="ref" href="prob_4.html#T2" target="_self">Th2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:52"/>
<font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="prob_4.html#K7" target="_self">COM</a> <font color="Maroon">Sigma</font>,<font color="Maroon">P</font>
 <b>by </b><i><a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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