<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><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#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#M2" title="PROB_1:mode.2">Probability</a> of <font color="Olive" title="b1">Sigma</font><br/>  for <font color="Olive" title="b3">A</font> being    <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="Olive" title="b1">Sigma</font>,<font color="Olive" title="b2">P</font>) holds   <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Olive" title="b3">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="Olive" title="b3">A</font></span>)</span></span><br/><span class="kw">let </span><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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">P</font> being    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font><br/>  for <font color="Olive" title="b2">A</font> being    <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="Olive" title="b1">P</font>) holds   <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Olive" title="b2">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="Olive" title="b2">A</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">P</font> be    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of <font color="Maroon" title="c2">Sigma</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">A</font> being    <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>) holds   <a href="prob_4.html#K6" title="PROB_4:func.6">ProbPart</a> <font color="Olive" title="b1">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="Olive" title="b1">A</font></span>)</span></span><br/><span class="kw">let </span><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>); <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <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></span><br/>







<a NAME="E1:37"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
 <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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="37_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <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> or <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> )</span><br/>

<span class="kw">assume </span><a NAME="E1:37_1"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
<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>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">xx</font> = <font color="Maroon" title="c5">x</font> as    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#T1" onmouseover="rs('tarski/T1')" onmouseout="rh()">TARSKI:1</a></span>;<br/>
<a NAME="E3:37_1"/>
<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="c6">xx</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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="measure3.html#D4" onmouseover="rs('measure3/D4')" onmouseout="rh()">MEASURE3:def 4</a></span>;<br/>
<a NAME="E4:37_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A3</font></span>: 
<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c6">xx</font> is    <a href="prob_4.html#M1" title="PROB_4:mode.1">thin</a> of <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_4.html#T23" target="_self" onmouseover="rs('prob_4/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<a NAME="E5:37_1"/>
( <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="c6">xx</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> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_1"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="ref" href="measure3.html#D4" onmouseover="rs('measure3/D4')" onmouseout="rh()">MEASURE3:def 4</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:37_1"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37_1"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="prob_4.html#D7" target="_self" onmouseover="rs('prob_4/D7')" onmouseout="rh()">Def7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E2:37"/>
 <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" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="37_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <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> or <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> )</span><br/>

<span class="kw">assume </span><a NAME="E1:37_2"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
<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>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <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></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c6">xx</font> = <font color="Maroon" title="c5">x</font> as    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#T1" onmouseover="rs('tarski/T1')" onmouseout="rh()">TARSKI:1</a></span>;<br/>
<a NAME="E3:37_2"/>
<font color="Maroon" title="c4">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <font color="Maroon" title="c6">xx</font> is    <a href="prob_4.html#M1" title="PROB_4:mode.1">thin</a> of <font color="Maroon" title="c3">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_2"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="prob_4.html#D7" target="_self" onmouseover="rs('prob_4/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<a NAME="E4:37_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A5</font></span>: 
<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="c6">xx</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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="prob_4.html#T23" target="_self" onmouseover="rs('prob_4/T23')" onmouseout="rh()">Th23</a></span>;<br/>
<a NAME="E5:37_2"/>
( <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="c6">xx</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">A</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37_2"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="ref" href="prob_4.html#D7" target="_self" onmouseover="rs('prob_4/D7')" onmouseout="rh()">Def7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:37_2"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37_2"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="ref" href="measure3.html#D4" onmouseover="rs('measure3/D4')" onmouseout="rh()">MEASURE3:def 4</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:37"/>
 <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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E29">A1</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
