
diff -r f83271c585d2 -r 664322da08fe thys2/Journal/Paper.tex
--- a/thys2/Journal/Paper.tex	Thu Nov 04 13:31:17 2021 +0000
+++ b/thys2/Journal/Paper.tex	Thu Nov 04 13:52:17 2021 +0000
@@ -89,13 +89,34 @@
 regular expressions that can grow exponentially.
 For example, the regular expression $(a+aa)^*$ after taking
 derivative against just 10 $a$s will have size 8192.
+
 %TODO: add figure for this?
+
+
+Therefore, we insert a simplification phase
+after each derivation step, as defined below:
+\begin{lemma}
+\isa{blexer{\isacharunderscore}{\kern0pt}simp\ r\ s\ {\isasymequiv}\ \textrm{if}\ nullable\mbox{$_b$}\ {\isacharparenleft}{\kern0pt}bders{\isacharunderscore}{\kern0pt}simp\ {\isacharparenleft}{\kern0pt}r\mbox{$^\uparrow$}{\isacharparenright}{\kern0pt}\ s{\isacharparenright}{\kern0pt}\ \textrm{then}\ decode\ {\isacharparenleft}{\kern0pt}mkeps\mbox{$_b$}\ {\isacharparenleft}{\kern0pt}bders{\isacharunderscore}{\kern0pt}simp\ {\isacharparenleft}{\kern0pt}r\mbox{$^\uparrow$}{\isacharparenright}{\kern0pt}\ s{\isacharparenright}{\kern0pt}{\isacharparenright}{\kern0pt}\ r\ \textrm{else}\ None}
+\end{lemma}
+
+The simplification function is given as follows:
+
 \begin{center}
   \begin{tabular}{lcl}
   \isa{bsimp\ {\isacharparenleft}{\kern0pt}ASEQ\ bs\ r\isactrlsub {\isadigit{1}}\ r\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}} & $\dn$ & \isa{bsimp{\isacharunderscore}{\kern0pt}ASEQ\ bs\ {\isacharparenleft}{\kern0pt}bsimp\ r\isactrlsub {\isadigit{1}}{\isacharparenright}{\kern0pt}\ {\isacharparenleft}{\kern0pt}bsimp\ r\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}}\\
   \isa{bsimp\ {\isacharparenleft}{\kern0pt}AALTs\ bs{\isadigit{1}}{\isachardot}{\kern0pt}{\isadigit{0}}\ rs{\isacharparenright}{\kern0pt}} & $\dn$ & \isa{bsimp{\isacharunderscore}{\kern0pt}AALTs\ bs{\isadigit{1}}{\isachardot}{\kern0pt}{\isadigit{0}}\ {\isacharparenleft}{\kern0pt}distinctBy\ {\isacharparenleft}{\kern0pt}flts\ {\isacharparenleft}{\kern0pt}map\ bsimp\ rs{\isacharparenright}{\kern0pt}{\isacharparenright}{\kern0pt}\ erase\ {\isasymemptyset}{\isacharparenright}{\kern0pt}}\\
   \isa{bsimp\ AZERO} & $\dn$ & \isa{AZERO}\\
-  \isa{{\isacharparenleft}{\kern0pt}r\isactrlsub {\isadigit{1}}\ {\isacharplus}{\kern0pt}\ r\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}\mbox{$^\uparrow$}} & $\dn$ & \isa{AALT\ {\isacharbrackleft}{\kern0pt}{\isacharbrackright}{\kern0pt}\ {\isacharparenleft}{\kern0pt}fuse\ {\isacharbrackleft}{\kern0pt}Z{\isacharbrackright}{\kern0pt}\ {\isacharparenleft}{\kern0pt}r\isactrlsub {\isadigit{1}}\mbox{$^\uparrow$}{\isacharparenright}{\kern0pt}{\isacharparenright}{\kern0pt}\ {\isacharparenleft}{\kern0pt}fuse\ {\isacharbrackleft}{\kern0pt}S{\isacharbrackright}{\kern0pt}\ {\isacharparenleft}{\kern0pt}r\isactrlsub {\isadigit{2}}\mbox{$^\uparrow$}{\isacharparenright}{\kern0pt}{\isacharparenright}{\kern0pt}}\\
+
+\end{tabular}
+\end{center}
+
+And the two helper functions are:
+\begin{center}
+  \begin{tabular}{lcl}
+  \isa{bsimp{\isacharunderscore}{\kern0pt}AALTs\ bs\isactrlsub {\isadigit{1}}\ {\isacharbrackleft}{\kern0pt}r{\isacharbrackright}{\kern0pt}} & $\dn$ & \isa{bsimp{\isacharunderscore}{\kern0pt}ASEQ\ bs\isactrlsub {\isadigit{1}}\ {\isacharparenleft}{\kern0pt}bsimp\ r{\isacharparenright}{\kern0pt}\ {\isacharparenleft}{\kern0pt}bsimp\ r{\isadigit{2}}{\isachardot}{\kern0pt}{\isadigit{0}}{\isacharparenright}{\kern0pt}}\\
+  \isa{bsimp{\isacharunderscore}{\kern0pt}AALTs\ bs{\isadigit{1}}{\isachardot}{\kern0pt}{\isadigit{0}}\ {\isacharbrackleft}{\kern0pt}r{\isacharbrackright}{\kern0pt}} & $\dn$ & \isa{bsimp{\isacharunderscore}{\kern0pt}AALTs\ bs{\isadigit{1}}{\isachardot}{\kern0pt}{\isadigit{0}}\ {\isacharparenleft}{\kern0pt}distinctBy\ {\isacharparenleft}{\kern0pt}flts\ {\isacharparenleft}{\kern0pt}map\ bsimp\ rs{\isacharparenright}{\kern0pt}{\isacharparenright}{\kern0pt}\ erase\ {\isasymemptyset}{\isacharparenright}{\kern0pt}}\\
+  \isa{bsimp{\isacharunderscore}{\kern0pt}AALTs\ bs{\isadigit{1}}{\isachardot}{\kern0pt}{\isadigit{0}}\ {\isacharparenleft}{\kern0pt}v\mbox{$\,$}{\isacharcolon}{\kern0pt}{\isacharcolon}{\kern0pt}\mbox{$\,$}vb\mbox{$\,$}{\isacharcolon}{\kern0pt}{\isacharcolon}{\kern0pt}\mbox{$\,$}vc{\isacharparenright}{\kern0pt}} & $\dn$ & \isa{AZERO}\\
+
 \end{tabular}
 \end{center}
 
@@ -122,8 +143,7 @@
   \isa{\mbox{}\inferrule{\mbox{r\ {\isasymleadsto}\ r{\isacharprime}{\kern0pt}}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub {\isadigit{1}}\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}r{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub {\isadigit{1}}\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}r{\isacharprime}{\kern0pt}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}}}}\\
   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ AZERO\mbox{$\,$}{\isacharcolon}{\kern0pt}{\isacharcolon}{\kern0pt}\mbox{$\,$}rs\isactrlsub b{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ rs\isactrlsub b{\isacharparenright}{\kern0pt}}}}\\
   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ AALTs\ bs\isactrlsub {\isadigit{1}}\ rs\isactrlsub {\isadigit{1}}\mbox{$\,$}{\isacharcolon}{\kern0pt}{\isacharcolon}{\kern0pt}\mbox{$\,$}rs\isactrlsub b{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ map\ {\isacharparenleft}{\kern0pt}fuse\ bs\isactrlsub {\isadigit{1}}{\isacharparenright}{\kern0pt}\ rs\isactrlsub {\isadigit{1}}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b{\isacharparenright}{\kern0pt}}}}\\
-  \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}map\ {\isacharparenleft}{\kern0pt}fuse\ r\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}\ rs{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ {\isacharparenleft}{\kern0pt}bs\ {\isacharat}{\kern0pt}\ r\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}\ rs}}}\\
-  \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ {\isacharparenleft}{\kern0pt}bs\ {\isacharat}{\kern0pt}\ r\isactrlsub {\isadigit{1}}{\isacharparenright}{\kern0pt}\ rs\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}map\ {\isacharparenleft}{\kern0pt}fuse\ r\isactrlsub {\isadigit{1}}{\isacharparenright}{\kern0pt}\ rs{\isacharparenright}{\kern0pt}}}}\\
+  \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ {\isacharparenleft}{\kern0pt}bs\ {\isacharat}{\kern0pt}\ bs\isactrlsub {\isadigit{1}}{\isacharparenright}{\kern0pt}\ rs\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}map\ {\isacharparenleft}{\kern0pt}fuse\ bs\isactrlsub {\isadigit{1}}{\isacharparenright}{\kern0pt}\ rs{\isacharparenright}{\kern0pt}}}}\\
   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharbrackleft}{\kern0pt}{\isacharbrackright}{\kern0pt}\ {\isasymleadsto}\ AZERO}}}\\
   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharbrackleft}{\kern0pt}r\isactrlsub {\isadigit{1}}{\isacharbrackright}{\kern0pt}\ {\isasymleadsto}\ fuse\ bs\ r\isactrlsub {\isadigit{1}}}}}\\
   \isa{\mbox{}\inferrule{\mbox{a\isactrlsub {\isadigit{1}}\mbox{$^\downarrow$}\ {\isacharequal}{\kern0pt}\ a\isactrlsub {\isadigit{2}}\mbox{$^\downarrow$}}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}a\isactrlsub {\isadigit{1}}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}a\isactrlsub {\isadigit{2}}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub c{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}a\isactrlsub {\isadigit{1}}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b\ {\isacharat}{\kern0pt}\ rs\isactrlsub c{\isacharparenright}{\kern0pt}}}}\\
@@ -168,8 +188,10 @@
 
 And that yields the correctness result:
 \begin{lemma}
-\isa{blexer{\isacharunderscore}{\kern0pt}simp\ r\ s\ {\isacharequal}{\kern0pt}\ lexer\ r\ s}
-\end{lemma}%
+\isa{lexer\ r\ s\ {\isacharequal}{\kern0pt}\ blexer{\isacharunderscore}{\kern0pt}simp\ r\ s}
+\end{lemma}
+
+The nice thing about the aove%
 \end{isamarkuptext}\isamarkuptrue%
 %
 \isadelimdocument
@@ -1813,33 +1835,33 @@
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 %:%171=245%:%
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-%:%199=264%:%
-%:%200=265%:%
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-%:%213=278%:%
-%:%214=279%:%
-%:%215=280%:%
-%:%216=281%:%
-%:%217=282%:%
+%:%173=247%:%
+%:%174=248%:%
+%:%175=249%:%
+%:%176=250%:%
+%:%177=251%:%
+%:%178=252%:%
+%:%179=253%:%
+%:%180=254%:%
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+%:%182=256%:%
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+%:%184=258%:%
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+%:%186=260%:%
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+%:%188=262%:%
+%:%189=263%:%
+%:%190=264%:%
+%:%191=265%:%
+%:%192=266%:%
+%:%193=267%:%
+%:%194=268%:%
+%:%203=273%:%
+%:%215=279%:%
+%:%216=280%:%
+%:%217=281%:%
+%:%218=282%:%
 %:%218=283%:%
 %:%219=284%:%
 %:%220=285%:%
@@ -1883,28 +1905,28 @@
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 %:%259=324%:%
 %:%260=325%:%
-%:%260=326%:%
-%:%261=327%:%
-%:%262=328%:%
-%:%263=329%:%
-%:%264=330%:%
-%:%265=331%:%
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-%:%267=333%:%
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-%:%275=341%:%
-%:%276=342%:%
-%:%277=343%:%
-%:%278=344%:%
-%:%279=345%:%
-%:%280=346%:%
-%:%281=347%:%
+%:%261=326%:%
+%:%262=327%:%
+%:%263=328%:%
+%:%264=329%:%
+%:%265=330%:%
+%:%266=331%:%
+%:%267=332%:%
+%:%268=333%:%
+%:%269=334%:%
+%:%270=335%:%
+%:%271=336%:%
+%:%272=337%:%
+%:%273=338%:%
+%:%274=339%:%
+%:%275=340%:%
+%:%276=341%:%
+%:%277=342%:%
+%:%278=343%:%
+%:%279=344%:%
+%:%280=345%:%
+%:%281=346%:%
+%:%282=347%:%
 %:%282=348%:%
 %:%283=349%:%
 %:%284=350%:%
@@ -1989,31 +2011,31 @@
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 %:%364=430%:%
 %:%365=431%:%
-%:%374=438%:%
-%:%386=440%:%
-%:%387=441%:%
-%:%387=442%:%
-%:%388=443%:%
-%:%389=444%:%
-%:%390=445%:%
-%:%391=446%:%
-%:%392=447%:%
-%:%393=448%:%
-%:%394=449%:%
-%:%395=450%:%
-%:%396=451%:%
-%:%397=452%:%
-%:%398=453%:%
-%:%399=454%:%
-%:%400=455%:%
-%:%401=456%:%
-%:%402=457%:%
-%:%403=458%:%
-%:%404=459%:%
-%:%405=460%:%
-%:%406=461%:%
-%:%407=462%:%
-%:%408=463%:%
+%:%366=432%:%
+%:%367=433%:%
+%:%368=434%:%
+%:%369=435%:%
+%:%370=436%:%
+%:%371=437%:%
+%:%372=438%:%
+%:%373=439%:%
+%:%374=440%:%
+%:%375=441%:%
+%:%376=442%:%
+%:%377=443%:%
+%:%378=444%:%
+%:%379=445%:%
+%:%380=446%:%
+%:%381=447%:%
+%:%382=448%:%
+%:%383=449%:%
+%:%384=450%:%
+%:%385=451%:%
+%:%386=452%:%
+%:%387=453%:%
+%:%396=460%:%
+%:%408=462%:%
+%:%409=463%:%
 %:%409=464%:%
 %:%410=465%:%
 %:%411=466%:%
@@ -2032,34 +2054,34 @@
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 %:%425=480%:%
 %:%426=481%:%
-%:%426=482%:%
-%:%427=483%:%
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-%:%432=489%:%
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-%:%435=492%:%
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-%:%437=494%:%
-%:%438=495%:%
-%:%439=496%:%
-%:%440=497%:%
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-%:%442=499%:%
-%:%443=500%:%
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-%:%446=503%:%
-%:%447=504%:%
-%:%448=505%:%
-%:%449=506%:%
-%:%450=507%:%
-%:%451=508%:%
-%:%452=509%:%
+%:%427=482%:%
+%:%428=483%:%
+%:%429=484%:%
+%:%430=485%:%
+%:%431=486%:%
+%:%432=487%:%
+%:%433=488%:%
+%:%434=489%:%
+%:%435=490%:%
+%:%436=491%:%
+%:%437=492%:%
+%:%438=493%:%
+%:%439=494%:%
+%:%440=495%:%
+%:%441=496%:%
+%:%442=497%:%
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+%:%444=499%:%
+%:%445=500%:%
+%:%446=501%:%
+%:%447=502%:%
+%:%448=503%:%
+%:%448=504%:%
+%:%449=505%:%
+%:%450=506%:%
+%:%451=507%:%
+%:%452=508%:%
+%:%453=509%:%
 %:%453=510%:%
 %:%454=511%:%
 %:%455=512%:%
@@ -2128,29 +2150,29 @@
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-%:%529=581%:%
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-%:%542=586%:%
-%:%543=587%:%
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-%:%555=599%:%
-%:%556=600%:%
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-%:%558=602%:%
-%:%559=603%:%
-%:%560=604%:%
-%:%561=605%:%
-%:%562=606%:%
+%:%521=578%:%
+%:%522=579%:%
+%:%523=580%:%
+%:%524=581%:%
+%:%525=582%:%
+%:%526=583%:%
+%:%527=584%:%
+%:%528=585%:%
+%:%529=586%:%
+%:%530=587%:%
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+%:%542=599%:%
+%:%551=603%:%
 %:%563=607%:%
 %:%564=608%:%
 %:%565=609%:%
@@ -2244,33 +2266,33 @@
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-%:%668=715%:%
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-%:%674=721%:%
-%:%675=722%:%
-%:%676=723%:%
-%:%677=724%:%
-%:%678=725%:%
-%:%679=726%:%
+%:%656=700%:%
+%:%657=701%:%
+%:%658=702%:%
+%:%659=703%:%
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+%:%678=723%:%
+%:%678=724%:%
+%:%679=725%:%
+%:%680=726%:%
 %:%680=727%:%
 %:%681=728%:%
 %:%682=729%:%
@@ -2306,39 +2328,39 @@
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+%:%715=762%:%
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+%:%745=794%:%
 %:%745=795%:%
 %:%746=796%:%
 %:%747=797%:%
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-%:%799=854%:%
-%:%800=855%:%
-%:%801=856%:%
-%:%802=857%:%
-%:%803=858%:%
-%:%804=859%:%
+%:%759=809%:%
+%:%760=810%:%
+%:%761=811%:%
+%:%762=812%:%
+%:%763=813%:%
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+%:%787=838%:%
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+%:%797=850%:%
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+%:%801=854%:%
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+%:%803=857%:%
+%:%804=858%:%
+%:%805=859%:%
 %:%805=860%:%
 %:%806=861%:%
 %:%807=862%:%
@@ -2441,28 +2463,28 @@
 %:%839=894%:%
 %:%840=895%:%
 %:%841=896%:%
-%:%841=897%:%
-%:%842=898%:%
-%:%843=899%:%
-%:%844=900%:%
-%:%845=901%:%
-%:%846=902%:%
-%:%847=903%:%
-%:%848=904%:%
-%:%849=905%:%
-%:%850=906%:%
-%:%851=907%:%
-%:%852=908%:%
-%:%853=909%:%
-%:%854=910%:%
-%:%855=911%:%
-%:%856=912%:%
-%:%857=913%:%
-%:%858=914%:%
-%:%859=915%:%
-%:%860=916%:%
-%:%861=917%:%
-%:%862=918%:%
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+%:%843=898%:%
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+%:%846=901%:%
+%:%847=902%:%
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+%:%861=916%:%
+%:%862=917%:%
+%:%863=918%:%
 %:%863=919%:%
 %:%864=920%:%
 %:%865=921%:%
@@ -2475,28 +2497,28 @@
 %:%872=928%:%
 %:%873=929%:%
 %:%874=930%:%
-%:%874=931%:%
-%:%875=932%:%
-%:%876=933%:%
-%:%877=934%:%
-%:%878=935%:%
-%:%879=936%:%
-%:%880=937%:%
-%:%881=938%:%
-%:%882=939%:%
-%:%883=940%:%
-%:%884=941%:%
-%:%885=942%:%
-%:%886=943%:%
-%:%887=944%:%
-%:%888=945%:%
-%:%889=946%:%
-%:%890=947%:%
-%:%891=948%:%
-%:%892=949%:%
-%:%893=950%:%
-%:%894=951%:%
-%:%895=952%:%
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+%:%879=935%:%
+%:%880=936%:%
+%:%881=937%:%
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+%:%884=940%:%
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+%:%893=949%:%
+%:%894=950%:%
+%:%895=951%:%
+%:%896=952%:%
 %:%896=953%:%
 %:%897=954%:%
 %:%898=955%:%
@@ -2506,37 +2528,37 @@
 %:%902=959%:%
 %:%903=960%:%
 %:%904=961%:%
-%:%904=962%:%
-%:%905=963%:%
-%:%906=964%:%
-%:%907=965%:%
-%:%908=966%:%
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-%:%910=968%:%
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-%:%912=970%:%
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-%:%919=978%:%
-%:%920=979%:%
-%:%921=980%:%
-%:%922=981%:%
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-%:%924=983%:%
-%:%925=984%:%
-%:%926=985%:%
-%:%927=986%:%
-%:%928=987%:%
-%:%929=988%:%
-%:%930=989%:%
-%:%931=990%:%
-%:%932=991%:%
-%:%933=992%:%
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+%:%932=990%:%
+%:%933=991%:%
+%:%934=992%:%
 %:%934=993%:%
 %:%935=994%:%
 %:%936=995%:%
@@ -2553,35 +2575,35 @@
 %:%947=1006%:%
 %:%948=1007%:%
 %:%949=1008%:%
-%:%949=1009%:%
-%:%949=1010%:%
-%:%950=1011%:%
-%:%950=1012%:%
-%:%950=1013%:%
-%:%951=1014%:%
-%:%952=1015%:%
-%:%952=1016%:%
-%:%953=1017%:%
-%:%954=1018%:%
-%:%955=1019%:%
-%:%956=1020%:%
-%:%957=1021%:%
-%:%958=1022%:%
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-%:%960=1024%:%
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-%:%967=1031%:%
-%:%968=1032%:%
-%:%969=1033%:%
-%:%970=1034%:%
-%:%971=1035%:%
-%:%972=1036%:%
-%:%973=1037%:%
+%:%950=1009%:%
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+%:%956=1015%:%
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+%:%964=1023%:%
+%:%965=1024%:%
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 %:%974=1038%:%
 %:%975=1039%:%
 %:%976=1040%:%
@@ -2595,34 +2617,34 @@
 %:%984=1048%:%
 %:%985=1049%:%
 %:%986=1050%:%
-%:%986=1051%:%
-%:%987=1052%:%
-%:%988=1053%:%
-%:%989=1054%:%
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-%:%989=1056%:%
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-%:%992=1060%:%
-%:%993=1061%:%
-%:%994=1062%:%
-%:%995=1063%:%
-%:%996=1064%:%
-%:%997=1065%:%
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-%:%999=1067%:%
-%:%1000=1068%:%
-%:%1001=1069%:%
-%:%1002=1070%:%
-%:%1003=1071%:%
-%:%1004=1072%:%
-%:%1005=1073%:%
-%:%1006=1074%:%
-%:%1007=1075%:%
-%:%1008=1076%:%
-%:%1009=1077%:%
-%:%1010=1078%:%
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+%:%999=1063%:%
+%:%1000=1064%:%
+%:%1001=1065%:%
+%:%1002=1066%:%
+%:%1003=1067%:%
+%:%1004=1068%:%
+%:%1005=1069%:%
+%:%1006=1070%:%
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+%:%1011=1078%:%
 %:%1011=1079%:%
 %:%1012=1080%:%
 %:%1013=1081%:%
@@ -2639,29 +2661,29 @@
 %:%1024=1092%:%
 %:%1025=1093%:%
 %:%1026=1094%:%
-%:%1035=1098%:%
-%:%1047=1102%:%
-%:%1048=1103%:%
-%:%1049=1104%:%
-%:%1050=1105%:%
-%:%1051=1106%:%
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-%:%1055=1110%:%
-%:%1056=1111%:%
-%:%1057=1112%:%
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-%:%1060=1115%:%
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-%:%1063=1118%:%
-%:%1064=1119%:%
-%:%1065=1120%:%
-%:%1066=1121%:%
-%:%1067=1122%:%
-%:%1068=1123%:%
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+%:%1032=1100%:%
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+%:%1034=1102%:%
+%:%1035=1103%:%
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+%:%1043=1111%:%
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+%:%1045=1113%:%
+%:%1046=1114%:%
+%:%1047=1115%:%
+%:%1048=1116%:%
+%:%1057=1120%:%
 %:%1069=1124%:%
 %:%1070=1125%:%
 %:%1071=1126%:%
@@ -2756,40 +2778,40 @@
 %:%1160=1215%:%
 %:%1161=1216%:%
 %:%1162=1217%:%
-%:%1162=1218%:%
-%:%1163=1219%:%
-%:%1164=1220%:%
-%:%1165=1221%:%
-%:%1166=1222%:%
-%:%1167=1223%:%
-%:%1168=1224%:%
-%:%1169=1225%:%
-%:%1170=1226%:%
-%:%1171=1227%:%
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-%:%1173=1229%:%
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-%:%1175=1232%:%
-%:%1176=1233%:%
-%:%1177=1234%:%
-%:%1178=1235%:%
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-%:%1180=1237%:%
-%:%1181=1238%:%
-%:%1182=1239%:%
-%:%1183=1240%:%
-%:%1184=1241%:%
-%:%1185=1242%:%
-%:%1186=1243%:%
-%:%1187=1244%:%
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-%:%1190=1247%:%
-%:%1191=1248%:%
-%:%1192=1249%:%
-%:%1193=1250%:%
-%:%1194=1251%:%
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+%:%1195=1251%:%
 %:%1195=1252%:%
 %:%1196=1253%:%
 %:%1197=1254%:%
@@ -2823,40 +2845,40 @@
 %:%1225=1282%:%
 %:%1226=1283%:%
 %:%1227=1284%:%
-%:%1227=1285%:%
-%:%1227=1286%:%
-%:%1228=1287%:%
-%:%1229=1288%:%
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-%:%1229=1290%:%
-%:%1229=1291%:%
-%:%1230=1292%:%
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-%:%1233=1295%:%
-%:%1234=1296%:%
-%:%1234=1297%:%
-%:%1235=1298%:%
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-%:%1237=1300%:%
-%:%1238=1301%:%
-%:%1239=1302%:%
-%:%1240=1303%:%
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-%:%1250=1313%:%
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-%:%1254=1317%:%
-%:%1255=1318%:%
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 %:%1256=1319%:%
 %:%1257=1320%:%
 %:%1258=1321%:%
@@ -2884,44 +2906,44 @@
 %:%1280=1343%:%
 %:%1281=1344%:%
 %:%1282=1345%:%
-%:%1282=1346%:%
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-%:%1295=1364%:%
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-%:%1300=1369%:%
-%:%1301=1370%:%
-%:%1302=1371%:%
-%:%1303=1372%:%
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-%:%1307=1376%:%
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-%:%1310=1379%:%
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-%:%1312=1381%:%
-%:%1313=1382%:%
-%:%1314=1383%:%
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 %:%1315=1384%:%
 %:%1316=1385%:%
 %:%1317=1386%:%
@@ -2932,83 +2954,83 @@
 %:%1322=1391%:%
 %:%1323=1392%:%
 %:%1324=1393%:%
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+%:%1350=1420%:%
+%:%1351=1421%:%
+%:%1352=1422%:%
+%:%1353=1423%:%
+%:%1353=1424%:%
+%:%1354=1425%:%
+%:%1355=1426%:%
+%:%1356=1427%:%
+%:%1356=1428%:%
+%:%1357=1429%:%
+%:%1358=1430%:%
+%:%1359=1431%:%
+%:%1359=1432%:%
+%:%1360=1433%:%
+%:%1360=1434%:%
+%:%1361=1435%:%
+%:%1361=1436%:%
+%:%1362=1437%:%
+%:%1363=1438%:%
+%:%1364=1439%:%
+%:%1364=1440%:%
+%:%1365=1441%:%
+%:%1365=1442%:%
+%:%1366=1443%:%
+%:%1366=1444%:%
+%:%1366=1445%:%
+%:%1366=1446%:%
+%:%1367=1447%:%
+%:%1367=1448%:%
+%:%1368=1449%:%
+%:%1369=1450%:%
+%:%1369=1452%:%
+%:%1369=1453%:%
+%:%1369=1454%:%
+%:%1369=1455%:%
+%:%1369=1456%:%
+%:%1370=1457%:%
+%:%1370=1458%:%
+%:%1371=1459%:%
+%:%1371=1460%:%
+%:%1372=1461%:%
+%:%1372=1462%:%
+%:%1373=1463%:%
+%:%1374=1464%:%
+%:%1375=1465%:%
+%:%1376=1466%:%
+%:%1376=1467%:%
+%:%1377=1468%:%
+%:%1377=1469%:%
+%:%1378=1470%:%
+%:%1379=1471%:%
 %:%1379=1472%:%
 %:%1380=1473%:%
 %:%1381=1474%:%
@@ -3039,37 +3061,37 @@
 %:%1406=1499%:%
 %:%1407=1500%:%
 %:%1408=1501%:%
-%:%1417=1505%:%
-%:%1429=1512%:%
-%:%1430=1513%:%
-%:%1431=1514%:%
-%:%1432=1515%:%
-%:%1433=1516%:%
-%:%1434=1517%:%
-%:%1435=1518%:%
-%:%1444=1523%:%
-%:%1456=1527%:%
-%:%1457=1528%:%
-%:%1458=1529%:%
-%:%1459=1530%:%
-%:%1460=1531%:%
-%:%1461=1532%:%
-%:%1462=1533%:%
-%:%1463=1534%:%
-%:%1464=1535%:%
-%:%1465=1536%:%
-%:%1466=1537%:%
-%:%1467=1538%:%
-%:%1468=1539%:%
-%:%1469=1540%:%
-%:%1470=1541%:%
-%:%1471=1542%:%
-%:%1472=1543%:%
-%:%1473=1544%:%
-%:%1474=1545%:%
-%:%1475=1546%:%
-%:%1476=1547%:%
-%:%1477=1548%:%
+%:%1409=1502%:%
+%:%1410=1503%:%
+%:%1411=1504%:%
+%:%1412=1505%:%
+%:%1413=1506%:%
+%:%1414=1507%:%
+%:%1415=1508%:%
+%:%1416=1509%:%
+%:%1417=1510%:%
+%:%1418=1511%:%
+%:%1419=1512%:%
+%:%1420=1513%:%
+%:%1421=1514%:%
+%:%1422=1515%:%
+%:%1423=1516%:%
+%:%1424=1517%:%
+%:%1425=1518%:%
+%:%1426=1519%:%
+%:%1427=1520%:%
+%:%1428=1521%:%
+%:%1429=1522%:%
+%:%1430=1523%:%
+%:%1439=1527%:%
+%:%1451=1534%:%
+%:%1452=1535%:%
+%:%1453=1536%:%
+%:%1454=1537%:%
+%:%1455=1538%:%
+%:%1456=1539%:%
+%:%1457=1540%:%
+%:%1466=1545%:%
 %:%1478=1549%:%
 %:%1479=1550%:%
 %:%1480=1551%:%
@@ -3138,106 +3160,106 @@
 %:%1543=1614%:%
 %:%1544=1615%:%
 %:%1545=1616%:%
-%:%1545=1732%:%
-%:%1546=1733%:%
-%:%1547=1734%:%
-%:%1548=1735%:%
-%:%1549=1736%:%
-%:%1549=1897%:%
-%:%1550=1898%:%
-%:%1551=1899%:%
-%:%1552=1900%:%
-%:%1553=1901%:%
-%:%1554=1902%:%
-%:%1555=1903%:%
-%:%1556=1904%:%
-%:%1557=1905%:%
-%:%1558=1906%:%
-%:%1559=1907%:%
-%:%1560=1908%:%
-%:%1561=1909%:%
-%:%1562=1910%:%
-%:%1563=1911%:%
-%:%1564=1912%:%
-%:%1565=1913%:%
-%:%1566=1914%:%
-%:%1567=1915%:%
-%:%1568=1916%:%
-%:%1568=1917%:%
-%:%1569=1918%:%
-%:%1569=1919%:%
-%:%1569=1920%:%
-%:%1570=1921%:%
-%:%1570=1922%:%
-%:%1571=1923%:%
-%:%1572=1924%:%
-%:%1573=1925%:%
-%:%1574=1926%:%
-%:%1575=1927%:%
-%:%1576=1928%:%
-%:%1577=1929%:%
-%:%1578=1930%:%
-%:%1579=1931%:%
-%:%1580=1932%:%
-%:%1581=1933%:%
-%:%1582=1934%:%
-%:%1583=1935%:%
-%:%1584=1936%:%
-%:%1585=1937%:%
-%:%1586=1938%:%
-%:%1587=1939%:%
-%:%1587=1940%:%
-%:%1588=1941%:%
-%:%1589=1942%:%
-%:%1590=1943%:%
-%:%1590=1944%:%
-%:%1590=1945%:%
-%:%1591=1946%:%
-%:%1592=1947%:%
-%:%1593=1948%:%
-%:%1593=1949%:%
-%:%1594=1950%:%
-%:%1594=1951%:%
-%:%1595=1952%:%
-%:%1596=1953%:%
-%:%1597=1954%:%
-%:%1598=1955%:%
-%:%1599=1956%:%
-%:%1600=1957%:%
-%:%1601=1958%:%
-%:%1602=1959%:%
-%:%1603=1960%:%
-%:%1604=1961%:%
-%:%1605=1962%:%
-%:%1606=1963%:%
-%:%1607=1964%:%
-%:%1608=1965%:%
-%:%1609=1966%:%
-%:%1610=1967%:%
-%:%1611=1968%:%
-%:%1620=1973%:%
-%:%1632=1977%:%
-%:%1633=1978%:%
-%:%1634=1979%:%
-%:%1635=1980%:%
-%:%1636=1981%:%
-%:%1637=1982%:%
-%:%1638=1983%:%
-%:%1639=1984%:%
-%:%1640=1985%:%
-%:%1641=1986%:%
-%:%1642=1987%:%
-%:%1643=1988%:%
-%:%1644=1989%:%
-%:%1645=1990%:%
-%:%1646=1991%:%
-%:%1647=1992%:%
-%:%1648=1993%:%
-%:%1649=1994%:%
-%:%1650=1995%:%
-%:%1651=1996%:%
-%:%1652=1997%:%
-%:%1653=1998%:%
+%:%1546=1617%:%
+%:%1547=1618%:%
+%:%1548=1619%:%
+%:%1549=1620%:%
+%:%1550=1621%:%
+%:%1551=1622%:%
+%:%1552=1623%:%
+%:%1553=1624%:%
+%:%1554=1625%:%
+%:%1555=1626%:%
+%:%1556=1627%:%
+%:%1557=1628%:%
+%:%1558=1629%:%
+%:%1559=1630%:%
+%:%1560=1631%:%
+%:%1561=1632%:%
+%:%1562=1633%:%
+%:%1563=1634%:%
+%:%1564=1635%:%
+%:%1565=1636%:%
+%:%1566=1637%:%
+%:%1567=1638%:%
+%:%1567=1754%:%
+%:%1568=1755%:%
+%:%1569=1756%:%
+%:%1570=1757%:%
+%:%1571=1758%:%
+%:%1571=1919%:%
+%:%1572=1920%:%
+%:%1573=1921%:%
+%:%1574=1922%:%
+%:%1575=1923%:%
+%:%1576=1924%:%
+%:%1577=1925%:%
+%:%1578=1926%:%
+%:%1579=1927%:%
+%:%1580=1928%:%
+%:%1581=1929%:%
+%:%1582=1930%:%
+%:%1583=1931%:%
+%:%1584=1932%:%
+%:%1585=1933%:%
+%:%1586=1934%:%
+%:%1587=1935%:%
+%:%1588=1936%:%
+%:%1589=1937%:%
+%:%1590=1938%:%
+%:%1590=1939%:%
+%:%1591=1940%:%
+%:%1591=1941%:%
+%:%1591=1942%:%
+%:%1592=1943%:%
+%:%1592=1944%:%
+%:%1593=1945%:%
+%:%1594=1946%:%
+%:%1595=1947%:%
+%:%1596=1948%:%
+%:%1597=1949%:%
+%:%1598=1950%:%
+%:%1599=1951%:%
+%:%1600=1952%:%
+%:%1601=1953%:%
+%:%1602=1954%:%
+%:%1603=1955%:%
+%:%1604=1956%:%
+%:%1605=1957%:%
+%:%1606=1958%:%
+%:%1607=1959%:%
+%:%1608=1960%:%
+%:%1609=1961%:%
+%:%1609=1962%:%
+%:%1610=1963%:%
+%:%1611=1964%:%
+%:%1612=1965%:%
+%:%1612=1966%:%
+%:%1612=1967%:%
+%:%1613=1968%:%
+%:%1614=1969%:%
+%:%1615=1970%:%
+%:%1615=1971%:%
+%:%1616=1972%:%
+%:%1616=1973%:%
+%:%1617=1974%:%
+%:%1618=1975%:%
+%:%1619=1976%:%
+%:%1620=1977%:%
+%:%1621=1978%:%
+%:%1622=1979%:%
+%:%1623=1980%:%
+%:%1624=1981%:%
+%:%1625=1982%:%
+%:%1626=1983%:%
+%:%1627=1984%:%
+%:%1628=1985%:%
+%:%1629=1986%:%
+%:%1630=1987%:%
+%:%1631=1988%:%
+%:%1632=1989%:%
+%:%1633=1990%:%
+%:%1642=1995%:%
 %:%1654=1999%:%
 %:%1655=2000%:%
 %:%1656=2001%:%
@@ -3269,4 +3291,26 @@
 %:%1682=2027%:%
 %:%1683=2028%:%
 %:%1684=2029%:%
-%:%1697=2035%:%
\ No newline at end of file
+%:%1685=2030%:%
+%:%1686=2031%:%
+%:%1687=2032%:%
+%:%1688=2033%:%
+%:%1689=2034%:%
+%:%1690=2035%:%
+%:%1691=2036%:%
+%:%1692=2037%:%
+%:%1693=2038%:%
+%:%1694=2039%:%
+%:%1695=2040%:%
+%:%1696=2041%:%
+%:%1697=2042%:%
+%:%1698=2043%:%
+%:%1699=2044%:%
+%:%1700=2045%:%
+%:%1701=2046%:%
+%:%1702=2047%:%
+%:%1703=2048%:%
+%:%1704=2049%:%
+%:%1705=2050%:%
+%:%1706=2051%:%
+%:%1719=2057%:%
\ No newline at end of file




