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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> ; <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><br/> for <font color="Olive" title="b3">FSeq</font> being   <a href="prob_3.html#M1" title="PROB_3:mode.1">FinSequence</a> of <font color="Olive" title="b1">Sigma</font> holds <br/> ( <font color="Olive" title="b2">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Olive" title="b3">FSeq</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Olive" title="b3">FSeq</font></span>)</span> &amp; ( <font color="Olive" title="b3">FSeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> implies <font color="Olive" title="b2">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Olive" title="b3">FSeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Olive" title="b3">FSeq</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><br/> for <font color="Olive" title="b2">FSeq</font> being   <a href="prob_3.html#M1" title="PROB_3:mode.1">FinSequence</a> of <font color="Maroon" title="c2">Sigma</font> holds <br/> ( <font color="Olive" title="b1">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Olive" title="b2">FSeq</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Olive" title="b2">FSeq</font></span>)</span> &amp; ( <font color="Olive" title="b2">FSeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> implies <font color="Olive" title="b1">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Olive" title="b2">FSeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Olive" title="b2">FSeq</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"> for <font color="Olive" title="b1">FSeq</font> being   <a href="prob_3.html#M1" title="PROB_3:mode.1">FinSequence</a> of <font color="Maroon" title="c2">Sigma</font> holds <br/> ( <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Olive" title="b1">FSeq</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Olive" title="b1">FSeq</font></span>)</span> &amp; ( <font color="Olive" title="b1">FSeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> implies <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Olive" title="b1">FSeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Olive" title="b1">FSeq</font></span>)</span> ) )</span><br/><b>let </b><font color="Maroon" title="c4">FSeq</font> be    <a href="prob_3.html#M1" title="PROB_3:mode.1">FinSequence</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"> ( <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Maroon" title="c4">FSeq</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Maroon" title="c4">FSeq</font></span>)</span> &amp; ( <font color="Maroon" title="c4">FSeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> implies <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Maroon" title="c4">FSeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Maroon" title="c4">FSeq</font></span>)</span> ) )</span><br/>







<b>consider </b><font color="Maroon" title="c5">ASeq</font> being    <a href="prob_1.html#M1" title="PROB_1:mode.1">SetSequence</a> of <font color="Maroon" title="c2">Sigma</font><b> such that </b><br/><a NAME="E2:68"/><i><font color="Green" title="E56">A1</font></i>: 
( ( for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">FSeq</font> holds <br/><font color="Maroon" title="c5">ASeq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">FSeq</font> <a href="prob_3.html#K11" title="PROB_3:func.11">.</a> <font color="Olive" title="b1">k</font> ) &amp; ( for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st not <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">FSeq</font> holds <br/><font color="Maroon" title="c5">ASeq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) )
 <b>by </b><i><a class="ref" href="prob_3.html#T61" target="_self" title="PROB_3:th.61">Th61</a></i>;<br/>
<a NAME="E3:68"/>
<font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Maroon" title="c5">ASeq</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> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Maroon" title="c4">FSeq</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:68"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="prob_3.html#T60" target="_self" title="PROB_3:th.60">Th60</a></i>;<br/>
<a NAME="E4:68"/><b>then </b>
<font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Maroon" title="c4">FSeq</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="series_1.html#K2" title="SERIES_1:func.2">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_1.html#K9" title="PROB_1:func.9">*</a> <font color="Maroon" title="c5">ASeq</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E2:68"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="prob_3.html#T69" target="_self" title="PROB_3:th.69">Th69</a></i>;<br/>
<b>hence </b><a NAME="E5:68"/>
<font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Maroon" title="c4">FSeq</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Maroon" title="c4">FSeq</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:68"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="prob_3.html#T69" target="_self" title="PROB_3:th.69">Th69</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">FSeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> implies <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Maroon" title="c4">FSeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Maroon" title="c4">FSeq</font></span>)</span> )</span><br/>

<a NAME="E6:68"/><i><font color="Green" title="E57">A2</font></i>: 
( <font color="Maroon" title="c4">FSeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> implies <font color="Maroon" title="c5">ASeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:68_1"/><i><font color="Green" title="E58">A3</font></i>: 
<font color="Maroon" title="c4">FSeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">ASeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a></span><br/>

<a NAME="E2:68_1"/>
for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">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>   st <font color="Olive" title="b1">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b2">n</font> holds <br/><font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Olive" title="b1">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Olive" title="b2">n</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c6">m</font>, <font color="Maroon" title="c7">n</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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">n</font> implies <font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font> )</span><br/>

<b>assume </b><a NAME="E1:68_1_1"/><i><font color="Green" title="E59">A4</font></i>: 
<font color="Maroon" title="c6">m</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c7">n</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">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font></span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:68_1_1_1"/>
( ( <font color="Maroon" title="c6">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">FSeq</font> &amp; <font color="Maroon" title="c7">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">FSeq</font> ) or  not <font color="Maroon" title="c6">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">FSeq</font> or  not <font color="Maroon" title="c7">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">FSeq</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_1_1_1_1"><b>suppose </b></a><a NAME="E1:68_1_1_1_1"/><i><font color="Green" title="E60">A5</font></i>: 
( <font color="Maroon" title="c6">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">FSeq</font> &amp; <font color="Maroon" title="c7">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">FSeq</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">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font></span><br/><div class="add"><a NAME="E2:68_1_1_1_1"/>
<font color="Maroon" title="c4">FSeq</font> <a href="prob_3.html#K11" title="PROB_3:func.11">.</a> <font color="Maroon" title="c6">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">FSeq</font> <a href="prob_3.html#K11" title="PROB_3:func.11">.</a> <font color="Maroon" title="c7">n</font>
 <b>by </b><i><a class="txt" href="#E1:68_1"><i><font color="Green" title="E58">A3</font></i></a>, <a class="txt" href="#E1:68_1_1"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="prob_2.html#D3" title="PROB_2:def.3">PROB_2:def 3</a></i>;<br/><a NAME="E3:68_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c4">FSeq</font> <a href="prob_3.html#K11" title="PROB_3:func.11">.</a> <font color="Maroon" title="c7">n</font>
 <b>by </b><i><a class="txt" href="#E2:68"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="#E1:68_1_1_1_1"><i><font color="Green" title="E60">A5</font></i></a></i>;<br/><b>hence </b><a NAME="E4:68_1_1_1_1"/>
<font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font>
 <b>by </b><i><a class="txt" href="#E2:68"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="#E1:68_1_1_1_1"><i><font color="Green" title="E60">A5</font></i></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><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_1_1_1_2"><b>suppose </b></a><a NAME="E1:68_1_1_1_2"/>
(  not <font color="Maroon" title="c6">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">FSeq</font> or  not <font color="Maroon" title="c7">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c4">FSeq</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">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font></span><br/><div class="add"><a NAME="E2:68_1_1_1_2"/><b>then </b>
( <font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  or <font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="txt" href="#E2:68"><i><font color="Green" title="E56">A1</font></i></a></i>;<br/><b>hence </b><a NAME="E3:68_1_1_1_2"/>
<font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c6">m</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c5">ASeq</font> <a href="prob_2.html#K1" title="PROB_2:func.1">.</a> <font color="Maroon" title="c7">n</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T65" title="XBOOLE_1:th.65">XBOOLE_1:65</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><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div>
<b>hence </b><a NAME="E3:68_1"/>
<font color="Maroon" title="c5">ASeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a>
 <b>by </b><i><a class="ref" href="prob_2.html#D4" title="PROB_2:def.4">PROB_2:def 4</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><b>end;</b></div>
<b>assume </b><a NAME="E7:68"/><i><font color="Green" title="E58">A6</font></i>: 
<font color="Maroon" title="c4">FSeq</font> is <a href="prob_2.html#V1" title="PROB_2:attr.1">disjoint_valued</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Maroon" title="c4">FSeq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Maroon" title="c4">FSeq</font></span>)</span></span><br/>

<b>thus </b><font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="prob_3.html#K8" title="PROB_3:func.8">Union</a> <font color="Maroon" title="c4">FSeq</font></span>)</span> = 
<font color="Maroon" title="c3">P</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="kurato_2.html#K1" title="KURATO_2:func.1">Union</a> <font color="Maroon" title="c5">ASeq</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:68"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="prob_3.html#T60" target="_self" title="PROB_3:th.60">Th60</a></i>
<br/>.= 
 <a href="series_1.html#K2" title="SERIES_1:func.2">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_1.html#K9" title="PROB_1:func.9">*</a> <font color="Maroon" title="c5">ASeq</font></span>)</span>
<b>by </b><i><a class="txt" href="#E6:68"><i><font color="Green" title="E57">A2</font></i></a>, <a class="txt" href="#E7:68"><i><font color="Green" title="E58">A6</font></i></a>, <a class="ref" href="prob_3.html#T51" target="_self" title="PROB_3:th.51">Th51</a></i>
<br/>.= 
 <a href="rvsum_1.html#K18" title="RVSUM_1:func.18">Sum</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">P</font> <a href="prob_3.html#K13" title="PROB_3:func.13">*</a> <font color="Maroon" title="c4">FSeq</font></span>)</span>
<b>by </b><i><a class="txt" href="#E2:68"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="prob_3.html#T69" target="_self" title="PROB_3:th.69">Th69</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>
