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<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#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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">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/><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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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">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/><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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>







<span class="kw">consider </span><font color="Maroon" title="c5">ASeq</font> being   <a href="prob_1.html#NM4" title="PROB_1:NM.4">SetSequence</a> of <font color="Maroon" title="c2">Sigma</font><span class="kw"> such that </span><br/><a NAME="E2:68"/><span class="lab"><font color="Green" title="E56">A1</font></span>: 
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#K1" title="RELSET_1:func.1">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>
 <span class="kw">and </span><br/><a NAME="E3:68"/><span class="lab"><font color="Green" title="E57">A2</font></span>: 
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#K1" title="RELSET_1:func.1">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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_3.html#T61" target="_self" title="PROB_3:th.61">Th61</a></span>;<br/>
<a NAME="E4:68"/>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="ref" href="prob_3.html#T60" target="_self" title="PROB_3:th.60">Th60</a></span>;<br/>
<a NAME="E5:68"/><span class="kw">then </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="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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="ref" href="prob_3.html#T69" target="_self" title="PROB_3:th.69">Th69</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:68"/>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="ref" href="prob_3.html#T69" target="_self" title="PROB_3:th.69">Th69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E7:68"/><span class="lab"><font color="Green" title="E58">A3</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<a NAME="E8:68"/><span class="lab"><font color="Green" title="E59">A4</font></span>: 
( <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"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:68_1"/><span class="lab"><font color="Green" title="E60">A5</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><a NAME="E1:68_1_1"/><span class="lab"><font color="Green" title="E61">A6</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></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#K1" title="RELSET_1:func.1">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#K1" title="RELSET_1:func.1">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#K1" title="RELSET_1:func.1">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#K1" title="RELSET_1:func.1">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"><span class="kw">suppose </span></a><a NAME="E1:68_1_1_1_1"/><span class="lab"><font color="Green" title="E62">A7</font></span>: 
( <font color="Maroon" title="c6">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="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#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">FSeq</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:68_1"><span class="lab"><font color="Green" title="E60">A5</font></span></a>, <a class="txt" href="#E1:68_1_1"><span class="lab"><font color="Green" title="E61">A6</font></span></a>, <a class="ref" href="prob_2.html#D3" title="PROB_2:def.3">PROB_2:def 3</a></span>;<br/><a NAME="E3:68_1_1_1_1"/><span class="kw">then </span>
<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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E1:68_1_1_1_1"><span class="lab"><font color="Green" title="E62">A7</font></span></a></span>;<br/><span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E1:68_1_1_1_1"><span class="lab"><font color="Green" title="E62">A7</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="68_1_1_1_2"><span class="kw">suppose </span></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#K1" title="RELSET_1:func.1">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#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">FSeq</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"/><span class="kw">then </span>
( <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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E57">A2</font></span></a></span>;<br/><span class="kw">hence </span><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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T65" title="XBOOLE_1:th.65">XBOOLE_1:65</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">hence </span><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> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_2.html#D4" title="PROB_2:def.4">PROB_2:def 4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">thus </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="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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="ref" href="prob_3.html#T60" target="_self" title="PROB_3:th.60">Th60</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:68"><span class="lab"><font color="Green" title="E59">A4</font></span></a>, <a class="txt" href="#E7:68"><span class="lab"><font color="Green" title="E58">A3</font></span></a>, <a class="ref" href="prob_3.html#T51" target="_self" title="PROB_3:th.51">Th51</a></span>
<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>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:68"><span class="lab"><font color="Green" title="E56">A1</font></span></a>, <a class="txt" href="#E3:68"><span class="lab"><font color="Green" title="E57">A2</font></span></a>, <a class="ref" href="prob_3.html#T69" target="_self" title="PROB_3:th.69">Th69</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
