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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/><b>let </b><font color="Maroon" title="c4">A</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="prob_4.html#K4" title="PROB_4:func.4">COM</a> <font color="Maroon" title="c2">Sigma</font>,<font color="Maroon" title="c3">P</font>;<br/>







<a NAME="E1:43"/><i><font color="Green" title="E33">A1</font></i>: 
 <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Maroon" title="c4">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="measure3.html#K3" title="MEASURE3:func.3">MeasPart</a> <span class="p1">(<span class="default"><a href="prob_4.html#K5" title="PROB_4:func.5">P_COM2M_COM</a> <font color="Maroon" title="c4">A</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:43_1"/><i><font color="Green" title="E34">A2</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Maroon" title="c4">A</font>
 ;<br/>

<a NAME="E2:43_1"/><i><font color="Green" title="E35">A3</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Maroon" title="c5">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font> &amp; <font color="Maroon" title="c4">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c5">x</font> is    <a href="prob_4.html#M1" title="PROB_4:mode.1">thin</a> of <font color="Maroon" title="c3">P</font> )
 
<b>by </b><i><a class="txt" href="prob_4.html#E1:43_1"><i><font color="Green" title="E34">A2</font></i></a>, <a class="ref" href="prob_4.html#D7" target="_self" title="PROB_4:def.7">Def7</a></i>;<br/>
<a NAME="E3:43_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="prob_4.html#K5" title="PROB_4:func.5">P_COM2M_COM</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c5">x</font> is    <a href="measure3.html#M1" title="MEASURE3:mode.1">thin</a> of  <a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c3">P</font>
 
<b>by </b><i><a class="ref" href="prob_4.html#T24" target="_self" title="PROB_4:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E4:43_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure3.html#K3" title="MEASURE3:func.3">MeasPart</a> <span class="p1">(<span class="default"><a href="prob_4.html#K5" title="PROB_4:func.5">P_COM2M_COM</a> <font color="Maroon" title="c4">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="prob_4.html#E2:43_1"><i><font color="Green" title="E35">A3</font></i></a>, <a class="ref" href="measure3.html#D5" title="MEASURE3:def.5">MEASURE3:def 5</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:43"/>
 <a href="measure3.html#K3" title="MEASURE3:func.3">MeasPart</a> <span class="p1">(<span class="default"><a href="prob_4.html#K5" title="PROB_4:func.5">P_COM2M_COM</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Maroon" title="c4">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:43_2"/><i><font color="Green" title="E34">A4</font></i>: 
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="measure3.html#K3" title="MEASURE3:func.3">MeasPart</a> <span class="p1">(<span class="default"><a href="prob_4.html#K5" title="PROB_4:func.5">P_COM2M_COM</a> <font color="Maroon" title="c4">A</font></span>)</span>
 ;<br/>

<a NAME="E2:43_2"/><i><font color="Green" title="E35">A5</font></i>: 
( <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font> &amp; <font color="Maroon" title="c5">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="prob_4.html#K5" title="PROB_4:func.5">P_COM2M_COM</a> <font color="Maroon" title="c4">A</font> &amp; <span class="p1">(<span class="default"><a href="prob_4.html#K5" title="PROB_4:func.5">P_COM2M_COM</a> <font color="Maroon" title="c4">A</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c5">x</font> is    <a href="measure3.html#M1" title="MEASURE3:mode.1">thin</a> of  <a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Maroon" title="c3">P</font> )
 
<b>by </b><i><a class="txt" href="prob_4.html#E1:43_2"><i><font color="Green" title="E34">A4</font></i></a>, <a class="ref" href="measure3.html#D5" title="MEASURE3:def.5">MEASURE3:def 5</a></i>;<br/>
<a NAME="E3:43_2"/><b>then </b>
<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c5">x</font> is    <a href="prob_4.html#M1" title="PROB_4:mode.1">thin</a> of <font color="Maroon" title="c3">P</font>
 
<b>by </b><i><a class="ref" href="prob_4.html#T24" target="_self" title="PROB_4:th.24">Th24</a></i>;<br/>
<b>hence </b><a NAME="E4:43_2"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="txt" href="prob_4.html#E2:43_2"><i><font color="Green" title="E35">A5</font></i></a>, <a class="ref" href="prob_4.html#D7" target="_self" title="PROB_4:def.7">Def7</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:43"/>
 <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="measure3.html#K3" title="MEASURE3:func.3">MeasPart</a> <span class="p1">(<span class="default"><a href="prob_4.html#K5" title="PROB_4:func.5">P_COM2M_COM</a> <font color="Maroon" title="c4">A</font></span>)</span>
 <b>by </b><i><a class="txt" href="prob_4.html#E1:43"><i><font color="Green" title="E33">A1</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>


</div>
