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<div class="add">

<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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">Sigma</font> being  <a href="prob_1.html#NM3" title="PROB_1:NM.3">SigmaField</a> of <font color="Maroon" title="c1">Omega</font><br/> for <font color="Olive" title="b2">P</font> being   <a href="prob_1.html#M3" title="PROB_1:mode.3">Probability</a> of <font color="Olive" title="b1">Sigma</font> holds   <a href="prob_4.html#K8" title="PROB_4:func.8">COM</a> <font color="Olive" title="b2">P</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="measure3.html#K4" title="MEASURE3:func.4">COM</a> <span class="p1">(<span class="default"><a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Olive" title="b2">P</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">P</font> being   <a href="prob_1.html#M3" title="PROB_1:mode.3">Probability</a> of <font color="Maroon" title="c2">Sigma</font> holds   <a href="prob_4.html#K8" title="PROB_4:func.8">COM</a> <font color="Olive" title="b1">P</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="measure3.html#K4" title="MEASURE3:func.4">COM</a> <span class="p1">(<span class="default"><a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <font color="Olive" title="b1">P</font></span>)</span></span><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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="prob_4.html#K8" title="PROB_4:func.8">COM</a> <font color="Maroon" title="c3">P</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="measure3.html#K4" title="MEASURE3:func.4">COM</a> <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></span><br/>





<b>set </b><font color="Maroon" title="c4">Y</font> =  <a href="prob_4.html#K8" title="PROB_4:func.8">COM</a> <font color="Maroon" title="c3">P</font>;<br/>
<a NAME="E1:50"/>
 <a href="prob_4.html#K7" title="PROB_4:func.7">COM</a> <font color="Maroon" title="c2">Sigma</font>,<font color="Maroon" title="c3">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> <font color="Maroon" title="c2">Sigma</font>,<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>
 
<b>by </b><i><a class="ref" href="prob_4.html#T28" target="_self" title="PROB_4:th.28">Th28</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">Y1</font> =  <a href="prob_4.html#K2" title="PROB_4:func.2">P2M</a> <span class="p1">(<span class="default"><a href="prob_4.html#K8" title="PROB_4:func.8">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> as   <a href="measure1.html#NM5" title="MEASURE1:NM.5">sigma_Measure</a> of  <a href="measure3.html#K2" title="MEASURE3:func.2">COM</a> <font color="Maroon" title="c2">Sigma</font>,<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> ;<br/>
<a NAME="E3:50"/>
for <font color="Olive" title="b1">B</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font> holds <br/>for <font color="Olive" title="b2">C</font> being   <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> holds  <font color="Maroon" title="c5">Y1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b2">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="b1">B</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">B</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font> implies for <font color="Olive" title="b1">C</font> being   <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> holds  <font color="Maroon" title="c5">Y1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="Maroon" title="c6">B</font> )</span><br/>

<b>assume </b><a NAME="E1:50_1"/><i><font color="Green" title="E38">A1</font></i>: 
<font color="Maroon" title="c6">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">Sigma</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">C</font> being   <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> holds  <font color="Maroon" title="c5">Y1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Olive" title="b1">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="Maroon" title="c6">B</font></span><br/>

<b>let </b><font color="Maroon" title="c7">C</font> be    <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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">Y1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="Maroon" title="c6">B</font></span><br/>

<b>reconsider </b><font color="Maroon" title="c8">C1</font> = <font color="Maroon" title="c7">C</font> as    <a href="prob_4.html#M2" title="PROB_4:mode.2">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/>
<a NAME="E3:50_1"/>
<span class="p1">(<span class="default"><a href="prob_4.html#K8" title="PROB_4:func.8">COM</a> <font color="Maroon" title="c3">P</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c8">C1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">B</font>
 
<b>by </b><i><a class="txt" href="#E1:50_1"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="prob_4.html#D8" target="_self" title="PROB_4:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E4:50_1"/>
<font color="Maroon" title="c5">Y1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">B</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c7">C</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="Maroon" title="c6">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:50"/>
 <a href="prob_4.html#K8" title="PROB_4:func.8">COM</a> <font color="Maroon" title="c3">P</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a>  <a href="measure3.html#K4" title="MEASURE3:func.4">COM</a> <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>
 <b>by </b><i><a class="ref" href="measure3.html#D6" title="MEASURE3:def.6">MEASURE3:def 6</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
