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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be   <a href="prob_1.html#NM3">SigmaField</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="prob_1.html#M3">Probability</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="prob_4.html#K8" target="_self">COM</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="prob_4.html#K2" target="_self">P2M</a> <span class="p1">(<span class="default"><a href="prob_4.html#K8" target="_self">COM</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> as    <a href="measure1.html#M3">sigma_Measure</a> of  <a href="measure3.html#K2">COM</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <b>by </b><i><a class="ref" href="prob_4.html#T28" target="_self">Th28</a></i>;<br/>
<a NAME="E2:54"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="measure3.html#M1">thin</a> of  <a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">c<sub>3</sub></font> holds <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Olive">b<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:54_1"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="measure3.html#M1">thin</a> of  <a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>7</sub></font> as    <a href="prob_4.html#M2" target="_self">thin</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="prob_4.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E3:54_1"/>
<span class="p1">(<span class="default"><a href="prob_4.html#K8" target="_self">COM</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="prob_4.html#E1:54_1"><i><font color="Green">E39</font></i></a>, <a class="ref" href="prob_4.html#D8" target="_self">Def8</a></i>;<br/>
<b>hence </b><a NAME="E4:54_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:54"/>
 <a href="prob_4.html#K8" target="_self">COM</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R1">=</a>  <a href="measure3.html#K4">COM</a> <span class="p1">(<span class="default"><a href="prob_4.html#K2" target="_self">P2M</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="measure3.html#D6">MEASURE3:def 6</a></i>;<br/>


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