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<div class="add">

<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">bool</a> <font color="Maroon" title="c1">E</font>) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  =  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> $1;<br/>
<span class="kw">consider </span><font color="Maroon" title="c2">EP</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">E</font></span>)</span>,<a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a><span class="kw"> such that </span><br/><a NAME="E2:30_1_1"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">E</font> holds  <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S4" title="FUNCT_2:sch.4">FUNCT_2:sch 4</a>();<br/></span>
<a NAME="E3:30_1_1"/><span class="lab"><font color="Green" title="E25">A2</font></span>: 
 for <font color="Olive" title="b1">A</font>, <font color="Olive" title="b2">B</font> being    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">E</font>  st <font color="Olive" title="b1">A</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Olive" title="b2">B</font> holds <br/><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="measure1.html#K1" title="MEASURE1:func.1">\/</a> <font color="Olive" title="b2">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b2">B</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">A</font>, <font color="Maroon" title="c4">B</font> be    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">B</font> implies <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="measure1.html#K1" title="MEASURE1:func.1">\/</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">B</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:30_1_1_1"/><span class="lab"><font color="Green" title="E26">A3</font></span>: 
<font color="Maroon" title="c3">A</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="measure1.html#K1" title="MEASURE1:func.1">\/</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">B</font></span>)</span></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="measure1.html#K1" title="MEASURE1:func.1">\/</a> <font color="Maroon" title="c4">B</font></span>)</span> = 
 <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="measure1.html#K1" title="MEASURE1:func.1">\/</a> <font color="Maroon" title="c4">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30_1_1"><span class="lab"><font color="Green" title="E24">A1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">A</font> <a href="measure1.html#K2" title="MEASURE1:func.2">/\</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rpr_1.html#T20" title="RPR_1:th.20">RPR_1:20</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:30_1_1_1"><span class="lab"><font color="Green" title="E26">A3</font></span></a>, <a class="ref" href="rpr_1.html#T16" title="RPR_1:th.16">RPR_1:16</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c4">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30_1_1"><span class="lab"><font color="Green" title="E24">A1</font></span></a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">B</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30_1_1"><span class="lab"><font color="Green" title="E24">A1</font></span></a></span>
; <a class="txt" 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="E4:30_1_1"/><span class="lab"><font color="Green" title="E26">A4</font></span>: 
 for <font color="Olive" title="b1">A</font> being    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">E</font> holds   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">A</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">A</font> be    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font></span><br/>

<a NAME="E1:30_1_1_2"/>
<font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Maroon" title="c3">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30_1_1"><span class="lab"><font color="Green" title="E24">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:30_1_1_2"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c3">A</font>
 ; <a class="txt" 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">take </span>
<font color="Maroon" title="c2">EP</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">EP</font> is    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">E</font> &amp; (  for <font color="Olive" title="b1">A</font> being   <a href="rpr_1.html#NM1" title="RPR_1:NM.1">Event</a> of <font color="Maroon" title="c1">E</font> holds  <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b1">A</font> ) )</span><br/>

<a NAME="E5:30_1_1"/><span class="lab"><font color="Green" title="E27">A5</font></span>: 
 for <font color="Olive" title="b1">ASeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">E</font>  st <font color="Olive" title="b1">ASeq</font> is  <a href="prob_1.html#V2" title="PROB_1:attr.2">non-ascending</a>  holds <br/>( <font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Olive" title="b1">ASeq</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>  &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Olive" title="b1">ASeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_1.html#K3" title="PROB_1:func.3">Intersection</a> <font color="Olive" title="b1">ASeq</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">ASeq</font> be   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">E</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">ASeq</font> is  <a href="prob_1.html#V2" title="PROB_1:attr.2">non-ascending</a>  implies ( <font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Maroon" title="c3">ASeq</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>  &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_1.html#K3" title="PROB_1:func.3">Intersection</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:30_1_1_3"/>
<font color="Maroon" title="c3">ASeq</font> is  <a href="prob_1.html#V2" title="PROB_1:attr.2">non-ascending</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Maroon" title="c3">ASeq</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>  &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_1.html#K3" title="PROB_1:func.3">Intersection</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> )</span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">N</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <span class="kw"> such that </span><br/><a NAME="E3:30_1_1_3"/><span class="lab"><font color="Green" title="E28">A6</font></span>: 
 for <font color="Olive" title="b1">m</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon" title="c4">N</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">m</font> holds <br/> <a href="prob_1.html#K3" title="PROB_1:func.3">Intersection</a> <font color="Maroon" title="c3">ASeq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">ASeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Olive" title="b1">m</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="random_1.html#T15" target="_self" title="RANDOM_1:th.15">Th15</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_3_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c5">m</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">N</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">m</font> implies <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_1.html#K3" title="PROB_1:func.3">Intersection</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> )</span><br/><span class="kw">assume </span><a NAME="E1:30_1_1_3_1"/><span class="lab"><font color="Green" title="E29">A7</font></span>: 
<font color="Maroon" title="c4">N</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c5">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_1.html#K3" title="PROB_1:func.3">Intersection</a> <font color="Maroon" title="c3">ASeq</font></span>)</span></span><br/><a NAME="E2:30_1_1_3_1"/>
<font color="Maroon" title="c5">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 ;<br/><a NAME="E3:30_1_1_3_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">ASeq</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/><span class="kw">hence </span><span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c5">m</font> = 
<font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">ASeq</font> <a href="prob_4.html#K1" title="PROB_4:func.1">.</a> <font color="Maroon" title="c5">m</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T13" title="FUNCT_1:th.13">FUNCT_1:13</a></span>
<br/>.= 
<font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_1.html#K3" title="PROB_1:func.3">Intersection</a> <font color="Maroon" title="c3">ASeq</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:30_1_1_3"><span class="lab"><font color="Green" title="E28">A6</font></span></a>, <a class="txt" href="#E1:30_1_1_3_1"><span class="lab"><font color="Green" title="E29">A7</font></span></a></span>
;<br/> <a class="txt" 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="E5:30_1_1_3"/>
( <font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Maroon" title="c3">ASeq</font> is  <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a>  &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">EP</font> <a href="prob_1.html#K8" title="PROB_1:func.8">*</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_1.html#K3" title="PROB_1:func.3">Intersection</a> <font color="Maroon" title="c3">ASeq</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#T1" title="PROB_1:th.1">PROB_1:1</a></span>; <a class="txt" 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>
<font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c1">E</font> = 
 <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <span class="p1">(<span class="default"><a href="subset_1.html#K2" title="SUBSET_1:func.2">[#]</a> <font color="Maroon" title="c1">E</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30_1_1"><span class="lab"><font color="Green" title="E24">A1</font></span></a></span>
<br/>.= 
1
<span class="kw">by</span> <span class="lab"><a class="ref" href="rpr_1.html#T15" title="RPR_1:th.15">RPR_1:15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:30_1_1"/>
( <font color="Maroon" title="c2">EP</font> is    <a href="prob_1.html#M2" title="PROB_1:mode.2">Probability</a> of  <a href="random_1.html#K1" title="RANDOM_1:func.1">Trivial-SigmaField</a> <font color="Maroon" title="c1">E</font> &amp; (  for <font color="Olive" title="b1">A</font> being   <a href="rpr_1.html#NM1" title="RPR_1:NM.1">Event</a> of <font color="Maroon" title="c1">E</font> holds  <font color="Maroon" title="c2">EP</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rpr_1.html#K1" title="RPR_1:func.1">prob</a> <font color="Olive" title="b1">A</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:30_1_1"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E4:30_1_1"><span class="lab"><font color="Green" title="E26">A4</font></span></a>, <a class="txt" href="#E3:30_1_1"><span class="lab"><font color="Green" title="E25">A2</font></span></a>, <a class="txt" href="#E5:30_1_1"><span class="lab"><font color="Green" title="E27">A5</font></span></a>, <a class="ref" href="prob_1.html#D8" title="PROB_1:def.8">PROB_1:def 8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
