98   \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}}\\

   109 

   110 \end{tabular}

   111 \end{center}

   112 

   113 And the two helper functions are:

   114 \begin{center}

   115   \begin{tabular}{lcl}

   116   \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}}\\

   117   \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}}\\

   118   \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}\\

   119 

   125   \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}}}\\

   146   \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}}}}\\

   126   \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}}}}\\

   171 \isa{blexer{\isacharunderscore}{\kern0pt}simp\ r\ s\ {\isacharequal}{\kern0pt}\ lexer\ r\ s}

   191 \isa{lexer\ r\ s\ {\isacharequal}{\kern0pt}\ blexer{\isacharunderscore}{\kern0pt}simp\ r\ s}

   172 \end{lemma}%

   192 \end{lemma}

   193 

   194 The nice thing about the aove%

  1816 %:%181=251%:%

  1838 %:%173=247%:%

  1817 %:%193=257%:%

  1839 %:%174=248%:%

  1818 %:%194=258%:%

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  1821 %:%196=261%:%

  1843 %:%178=252%:%

  1822 %:%197=262%:%

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  1823 %:%198=263%:%

  1845 %:%180=254%:%

  1824 %:%199=264%:%

  1846 %:%181=255%:%

  1825 %:%200=265%:%

  1847 %:%182=256%:%

  1826 %:%201=266%:%

  1848 %:%183=257%:%

  1827 %:%202=267%:%

  1849 %:%184=258%:%

  1828 %:%203=268%:%

  1850 %:%185=259%:%

  1829 %:%204=269%:%

  1851 %:%186=260%:%

  1830 %:%205=270%:%

  1852 %:%187=261%:%

  1831 %:%206=271%:%

  1853 %:%188=262%:%

  1832 %:%207=272%:%

  1854 %:%189=263%:%

  1833 %:%208=273%:%

  1855 %:%190=264%:%

  1834 %:%209=274%:%

  1856 %:%191=265%:%

  1835 %:%210=275%:%

  1857 %:%192=266%:%

  1836 %:%211=276%:%

  1858 %:%193=267%:%

  1837 %:%212=277%:%

  1859 %:%194=268%:%

  1838 %:%213=278%:%

  1860 %:%203=273%:%

  1839 %:%214=279%:%

  1861 %:%215=279%:%

  1840 %:%215=280%:%

  1862 %:%216=280%:%

  1841 %:%216=281%:%

  1863 %:%217=281%:%

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  1864 %:%218=282%:%

  1886 %:%260=326%:%

  1908 %:%261=326%:%

  1887 %:%261=327%:%

  1909 %:%262=327%:%

  1888 %:%262=328%:%

  1910 %:%263=328%:%

  1889 %:%263=329%:%

  1911 %:%264=329%:%

  1890 %:%264=330%:%

  1912 %:%265=330%:%

  1891 %:%265=331%:%

  1913 %:%266=331%:%

  1892 %:%266=332%:%

  1914 %:%267=332%:%

  1893 %:%267=333%:%

  1915 %:%268=333%:%

  1894 %:%268=334%:%

  1916 %:%269=334%:%

  1895 %:%269=335%:%

  1917 %:%270=335%:%

  1896 %:%270=336%:%

  1918 %:%271=336%:%

  1897 %:%271=337%:%

  1919 %:%272=337%:%

  1898 %:%272=338%:%

  1920 %:%273=338%:%

  1899 %:%273=339%:%

  1921 %:%274=339%:%

  1900 %:%274=340%:%

  1922 %:%275=340%:%

  1901 %:%275=341%:%

  1923 %:%276=341%:%

  1902 %:%276=342%:%

  1924 %:%277=342%:%

  1903 %:%277=343%:%

  1925 %:%278=343%:%

  1904 %:%278=344%:%

  1926 %:%279=344%:%

  1905 %:%279=345%:%

  1927 %:%280=345%:%

  1906 %:%280=346%:%

  1928 %:%281=346%:%

  1907 %:%281=347%:%

  1929 %:%282=347%:%

  1992 %:%374=438%:%

  2014 %:%366=432%:%

  1993 %:%386=440%:%

  2015 %:%367=433%:%

  1994 %:%387=441%:%

  2016 %:%368=434%:%

  1995 %:%387=442%:%

  2017 %:%369=435%:%

  1996 %:%388=443%:%

  2018 %:%370=436%:%

  1997 %:%389=444%:%

  2019 %:%371=437%:%

  1998 %:%390=445%:%

  2020 %:%372=438%:%

  1999 %:%391=446%:%

  2021 %:%373=439%:%

  2000 %:%392=447%:%

  2022 %:%374=440%:%

  2001 %:%393=448%:%

  2023 %:%375=441%:%

  2002 %:%394=449%:%

  2024 %:%376=442%:%

  2003 %:%395=450%:%

  2025 %:%377=443%:%

  2004 %:%396=451%:%

  2026 %:%378=444%:%

  2005 %:%397=452%:%

  2027 %:%379=445%:%

  2006 %:%398=453%:%

  2028 %:%380=446%:%

  2007 %:%399=454%:%

  2029 %:%381=447%:%

  2008 %:%400=455%:%

  2030 %:%382=448%:%

  2009 %:%401=456%:%

  2031 %:%383=449%:%

  2010 %:%402=457%:%

  2032 %:%384=450%:%

  2011 %:%403=458%:%

  2033 %:%385=451%:%

  2012 %:%404=459%:%

  2034 %:%386=452%:%

  2013 %:%405=460%:%

  2035 %:%387=453%:%

  2014 %:%406=461%:%

  2036 %:%396=460%:%

  2015 %:%407=462%:%

  2037 %:%408=462%:%

  2016 %:%408=463%:%

  2038 %:%409=463%:%

  2035 %:%426=482%:%

  2057 %:%427=482%:%

  2036 %:%427=483%:%

  2058 %:%428=483%:%

  2037 %:%428=484%:%

  2059 %:%429=484%:%

  2038 %:%429=485%:%

  2060 %:%430=485%:%

  2039 %:%430=486%:%

  2061 %:%431=486%:%

  2040 %:%431=487%:%

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  2041 %:%431=488%:%

  2063 %:%433=488%:%

  2042 %:%432=489%:%

  2064 %:%434=489%:%

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  2065 %:%435=490%:%

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  2066 %:%436=491%:%

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  2062 %:%452=509%:%

  2084 %:%453=509%:%

  2131 %:%529=581%:%

  2153 %:%521=578%:%

  2132 %:%541=585%:%

  2154 %:%522=579%:%

  2133 %:%542=586%:%

  2155 %:%523=580%:%

  2134 %:%543=587%:%

  2156 %:%524=581%:%

  2135 %:%544=588%:%

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  2137 %:%546=590%:%

  2159 %:%527=584%:%

  2138 %:%547=591%:%

  2160 %:%528=585%:%

  2139 %:%548=592%:%

  2161 %:%529=586%:%

  2140 %:%549=593%:%

  2162 %:%530=587%:%

  2141 %:%550=594%:%

  2163 %:%531=588%:%

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  2164 %:%532=589%:%

  2143 %:%552=596%:%

  2165 %:%533=590%:%

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  2173 %:%541=598%:%

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  2174 %:%542=599%:%

  2153 %:%562=606%:%

  2175 %:%551=603%:%

  2247 %:%655=700%:%

  2269 %:%656=700%:%

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  2270 %:%657=701%:%

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  2271 %:%658=702%:%

  2250 %:%657=703%:%

  2272 %:%659=703%:%

  2251 %:%658=704%:%

  2273 %:%660=704%:%

  2252 %:%658=705%:%

  2274 %:%661=705%:%

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  2254 %:%660=707%:%

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  2255 %:%661=708%:%

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  2278 %:%665=709%:%

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  2280 %:%667=711%:%

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  2281 %:%668=712%:%

  2260 %:%666=713%:%

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  2261 %:%667=714%:%

  2283 %:%670=714%:%

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  2264 %:%670=717%:%

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  2267 %:%673=720%:%

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  2290 %:%677=721%:%

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  2270 %:%676=723%:%

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  2309 %:%714=762%:%

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  2332 %:%716=763%:%

  2311 %:%715=764%:%

  2333 %:%717=764%:%

  2312 %:%716=765%:%

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  2313 %:%717=766%:%

  2335 %:%719=766%:%

  2314 %:%718=767%:%

  2336 %:%720=767%:%

  2315 %:%719=768%:%

  2337 %:%721=768%:%

  2316 %:%720=769%:%

  2338 %:%722=769%:%

  2317 %:%721=770%:%

  2339 %:%723=770%:%

  2318 %:%722=771%:%

  2340 %:%724=771%:%

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  2320 %:%723=773%:%

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  2322 %:%725=775%:%

  2344 %:%728=775%:%

  2323 %:%726=776%:%

  2345 %:%729=776%:%

  2324 %:%727=777%:%

  2346 %:%730=777%:%

  2325 %:%728=778%:%

  2347 %:%731=778%:%

  2326 %:%729=779%:%

  2348 %:%732=779%:%

  2327 %:%730=780%:%

  2349 %:%733=780%:%

  2328 %:%731=781%:%

  2350 %:%734=781%:%

  2329 %:%732=782%:%

  2351 %:%735=782%:%

  2330 %:%733=783%:%

  2352 %:%736=783%:%

  2331 %:%734=784%:%

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  2332 %:%735=785%:%

  2354 %:%736=785%:%

  2333 %:%736=786%:%

  2355 %:%737=786%:%

  2334 %:%737=787%:%

  2356 %:%738=787%:%

  2335 %:%738=788%:%

  2357 %:%739=788%:%

  2336 %:%739=789%:%

  2358 %:%740=789%:%

  2337 %:%740=790%:%

  2359 %:%741=790%:%

  2338 %:%741=791%:%

  2360 %:%742=791%:%

  2339 %:%742=792%:%

  2361 %:%743=792%:%

  2340 %:%743=793%:%

  2362 %:%744=793%:%

  2341 %:%744=794%:%

  2363 %:%745=794%:%

  2356 %:%758=809%:%

  2378 %:%759=809%:%

  2357 %:%759=810%:%

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  2358 %:%760=811%:%

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  2359 %:%761=812%:%

  2381 %:%762=812%:%

  2360 %:%762=813%:%

  2382 %:%763=813%:%

  2361 %:%763=814%:%

  2383 %:%764=814%:%

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  2384 %:%765=815%:%

  2363 %:%765=816%:%

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  2364 %:%765=817%:%

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  2365 %:%766=818%:%

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  2388 %:%769=819%:%

  2367 %:%768=820%:%

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  2368 %:%768=821%:%

  2390 %:%771=821%:%

  2369 %:%769=822%:%

  2391 %:%772=822%:%

  2370 %:%770=823%:%

  2392 %:%773=823%:%

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  2393 %:%774=824%:%

  2372 %:%772=825%:%

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  2373 %:%773=826%:%

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  2396 %:%777=827%:%

  2375 %:%775=828%:%

  2397 %:%778=828%:%

  2376 %:%776=829%:%

  2398 %:%779=829%:%

  2377 %:%777=830%:%

  2399 %:%780=830%:%

  2378 %:%778=831%:%

  2400 %:%780=831%:%

  2379 %:%779=832%:%

  2401 %:%781=832%:%

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  2381 %:%780=834%:%

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  2387 %:%785=840%:%

  2409 %:%788=840%:%

  2388 %:%786=841%:%

  2410 %:%789=841%:%

  2389 %:%787=842%:%

  2411 %:%790=842%:%

  2390 %:%788=843%:%

  2412 %:%790=843%:%

  2391 %:%789=844%:%

  2413 %:%791=844%:%

  2392 %:%790=845%:%

  2414 %:%792=845%:%

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  2415 %:%793=846%:%

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  2416 %:%794=847%:%

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  2420 %:%798=851%:%

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  2400 %:%798=853%:%

  2422 %:%800=853%:%

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  2423 %:%801=854%:%

  2402 %:%800=855%:%

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  2425 %:%802=856%:%

  2404 %:%802=857%:%

  2426 %:%803=857%:%

  2405 %:%803=858%:%

  2427 %:%804=858%:%

  2406 %:%804=859%:%

  2428 %:%805=859%:%

  2444 %:%841=897%:%

  2466 %:%842=897%:%

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  2467 %:%843=898%:%

  2446 %:%843=899%:%

  2468 %:%844=899%:%

  2447 %:%844=900%:%

  2469 %:%845=900%:%

  2448 %:%845=901%:%

  2470 %:%846=901%:%

  2449 %:%846=902%:%

  2471 %:%847=902%:%

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  2472 %:%848=903%:%

  2451 %:%848=904%:%

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  2474 %:%850=905%:%

  2453 %:%850=906%:%

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  2454 %:%851=907%:%

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  2455 %:%852=908%:%

  2477 %:%853=908%:%

  2456 %:%853=909%:%

  2478 %:%854=909%:%

  2457 %:%854=910%:%

  2479 %:%855=910%:%

  2458 %:%855=911%:%

  2480 %:%856=911%:%

  2459 %:%856=912%:%

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  2460 %:%857=913%:%

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  2479 %:%875=932%:%

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  2480 %:%876=933%:%

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  2506 %:%881=937%:%

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  2514 %:%889=945%:%

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