/usr/bin/diffoscope --timeout 7200 --html /srv/reproducible-results/rbuild-debian/r-b-build.k9wunuFe/coq_8.18.0+dfsg-1.diffoscope.html --text /srv/reproducible-results/rbuild-debian/r-b-build.k9wunuFe/coq_8.18.0+dfsg-1.diffoscope.txt --json /srv/reproducible-results/rbuild-debian/r-b-build.k9wunuFe/coq_8.18.0+dfsg-1.diffoscope.json --profile=- /srv/reproducible-results/rbuild-debian/r-b-build.k9wunuFe/b1/coq_8.18.0+dfsg-1_armhf.changes /srv/reproducible-results/rbuild-debian/r-b-build.k9wunuFe/b2/coq_8.18.0+dfsg-1

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/srv/reproducible-results/rbuild-debian/r-b-build.k9wunuFe/b2/coq_8.18.0+dfsg-1_armhf.changes ¶

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coq_8.18.0+dfsg-1_armhf.deb ¶

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./usr/bin/coqidetop.byte ¶

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libcoq-core-ocaml-dev_8.18.0+dfsg-1_armhf.deb ¶

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./usr/lib/ocaml/coq-core/clib/cString.cmti ¶

Format-specific differences are supported for OCaml interface files but no file-specific differences were detected; falling back to a binary diff. file(1) reports: OCaml interface file (.cmi) (Version 031)

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./usr/lib/ocaml/coq-core/clib/orderedType.cmti ¶

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libcoq-stdlib_8.18.0+dfsg-1_armhf.deb ¶

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Offset 1, 9 lines modified		Offset 1, 9 lines modified

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024669d0:·4140·4040·4040·046a·4040·4092·0403·a326··A@@@@@.j@@@....&		024669d0:·4041·4040·4040·4004·6b40·4040·9204·03a3··@A@@@@@.k@@@....
024669e0:·6c61·7a79·5f74·4e08·0000·3800·a0c0·043a··lazy_tN...8....:		024669e0:·266c·617a·795f·744e·0800·0038·00a0·c004··&lazy_tN...8....
024669f0:·0205·f5e1·0040·4f40·4140·4140·a059·40a0··.....@O@A@A@.Y@.		024669f0:·3a02·05f5·e100·404f·4041·4041·40a0·5940··:.....@O@A@A@.Y@
02466a00:·4040·4040·0472·4040·4092·0407·a324·6c69··@@@@.r@@@....$li		02466a00:·a040·4040·4004·7340·4040·9204·07a3·246c··.@@@@.s@@@....$l
02466a10:·7374·4908·0000·3800·a0c0·0442·0205·f5e1··stI...8....B....		02466a10:·6973·7449·0800·0038·00a0·c004·4202·05f5··istI...8....B...
02466a20:·0040·5040·41a1·a0e0·a322·5b5d·6190·4040··.@P@A...."[]a.@@		02466a20:·e100·4050·4041·a1a0·e0a3·225b·5d61·9040··..@P@A...."[]a.@
02466a30:·04~~7e·~~4092·0403·a0e0·a322·3a3a·6290·a004··.~@......"::b...		02466a30:·4004·7f40·9204·03a0·e0a3·223a·3a62·90a0··@..@......"::b..
02466a40:·0ea0·c0b3·9004·16a0·0413·4090·4002·05f5··..........@.@...		02466a40:·040e·a0c0·b390·0416·a004·1340·9040·0205··...........@.@..
02466a50:·e100·4051·4040·04~~8b·~~4092·040a·4040·4140··..@Q@@..@...@@A@		02466a50:·f5e1·0040·5140·4004·8c40·9204·0a40·4041··...@Q@@..@...@@A
02466a60:·a059·40a0·4040·4040·~~048e~~·4040·4092·041b··.Y@.@@@@..@@@...		02466a60:·40a0·5940·a040·4040·4004·8f40·4040·9204··@.Y@.@@@@..@@@..
02466a70:·a329·6e61·7469·7665·696e·744b·0800·0038··.)nativeintK...8		02466a70:·1ba3·296e·6174·6976·6569·6e74·4b08·0000··..)nativeintK...
02466a80:·~~004~~0·4040·4140·4040·4040·~~0492~~·4040·4092··.@@@A@@@@@..@@@.		02466a80:·3800·4040·4041·4040·4040·4004·9340·4040··8.@@@A@@@@@..@@@
02466a90:·0403·a326·6f70·7469·6f6e·4a08·0000·3800··...&optionJ...8.		02466a90:·9204·03a3·266f·7074·696f·6e4a·0800·0038··....&optionJ...8
02466aa0:·a0c0·0462·0205·f5e1·0040·5340·41a1·a0e0··...b.....@S@A...		02466aa0:·00a0·c004·6202·05f5·e100·4053·4041·a1a0··....b.....@S@A..
02466ab0:·a324·4e6f·6e65·6390·4040·04~~9e·~~4092·0403··.$Nonec.@@..@...		02466ab0:·e0a3·244e·6f6e·6563·9040·4004·9f40·9204··..$Nonec.@@..@..
02466ac0:·a0e0·a324·536f·6d65·6490·a004·0e40·4004··...$Somed....@@.		02466ac0:·03a0·e0a3·2453·6f6d·6564·90a0·040e·4040··....$Somed....@@
02466ad0:·a540·9204·0440·4041·40a0·5940·a040·4040··.@...@@A@.Y@.@@@		02466ad0:·04a6·4092·0404·4040·4140·a059·40a0·4040··..@...@@A@.Y@.@@
02466ae0:·4004·~~a840~~·4040·9204·15a3·2673·7472·696e··@..@@@....&strin		02466ae0:·4040·04a9·4040·4092·0415·a326·7374·7269··@@..@@@....&stri
02466af0:·674f·0800·0038·0040·4040·4140·4040·4040··gO...8.@@@A@@@@@		02466af0:·6e67·4f08·0000·3800·4040·4041·4040·4040··ngO...8.@@@A@@@@
02466b00:·04ac·4040·4092·0403·a324·756e·6974·4608··..@@@....$unitF.		02466b00:·4004·ad40·4040·9204·03a3·2475·6e69·7446··@..@@@....$unitF
02466b10:·0000·3800·4040·a1a0·e0a3·2228·2960·9040··..8.@@...."()`.@		02466b10:·0800·0038·0040·40a1·a0e0·a322·2829·6090··...8.@@...."()`.
02466b20:·4004~~·b6~~40·9204·0340·4041·4040·4040·4004··@..@...@@A@@@@@.		02466b20:·4040·04b7·4092·0403·4040·4140·4040·4040··@@..@...@@A@@@@@
02466b30:·b740·4140·9204·0aa3·2e41·7373·6572·745f··.@A@.....Assert_		02466b30:·04b8·4041·4092·040a·a32e·4173·7365·7274··..@A@.....Assert
02466b40:·6661·696c·7572·655c·0800·0020·0090·046d··failure\...·...m		02466b40:·5f66·6169·6c75·7265·5c08·0000·2000·9004··_failure\...·...
02466b50:·4090·a0c0·92a0·c0b3·9004·1b40·9040·0205··@..........@.@..		02466b50:·6d40·90a0·c092·a0c0·b390·041b·4090·4002··m@..........@.@.
02466b60:·f5e1·0040·4aa0·c0b3·9004·6a40·9040·0205··...@J.....j@.@..		02466b60:·05f5·e100·404a·a0c0·b390·046a·4090·4002··....@J.....j@.@.
02466b70:·f5e1·0040·40a0·0405·4002·05f5·e100·4056··...@@...@.....@V		02466b70:·05f5·e100·4040·a004·0540·0205·f5e1·0040··....@@...@.....@
02466b80:·4040·4104·cba0·b0a0·3d6f·6361·6d6c·2e77··@@A.....=ocaml.w		02466b80:·5640·4041·04cc·a0b0·a03d·6f63·616d·6c2e··V@@A.....=ocaml.
02466b90:·6172·6e5f·6f6e·5f6c·6974·6572·616c·5f70··arn_on_literal_p		02466b90:·7761·726e·5f6f·6e5f·6c69·7465·7261·6c5f··warn_on_literal_
02466ba0:·6174·7465·726e·04~~cf·~~0499·04~~cf·~~4092·0417··attern......@...		02466ba0:·7061·7474·6572·6e04·d004·9904·d040·9204··pattern......@..
02466bb0:·a330·4469·7669·7369·6f6e·5f62·795f·7a65··.0Division_by_ze		02466bb0:·17a3·3044·6976·6973·696f·6e5f·6279·5f7a··..0Division_by_z
02466bc0:·726f·5908·0000·2000·0418·4090·4040·4104··roY...·...@.@@A.		02466bc0:·6572·6f59·0800·0020·0004·1840·9040·4041··eroY...·...@.@@A
02466bd0:·d4a0·b0a0·0409·04~~d7·~~04a1·04~~d7·~~4092·0407··............@...		02466bd0:·04d5·a0b0·a004·0904·d804·a104·d840·9204··.............@..
02466be0:·a32b·456e·645f·6f66·5f66·696c·6558·0800··.+End_of_fileX..		02466be0:·07a3·2b45·6e64·5f6f·665f·6669·6c65·5808··..+End_of_fileX.
02466bf0:·0020·0004·2040·9040·4041·04~~dc·~~a0b0·a004··.·..·@.@@A......		02466bf0:·0000·2000·0420·4090·4040·4104·dda0·b0a0··..·..·@.@@A.....
02466c00:·1104~~·df~~04·a904~~·df~~40·9204·07a3·2746·6169··.......@....'Fai		02466c00:·0411·04e0·04a9·04e0·4092·0407·a327·4661··........@....'Fa
02466c10:·6c75·7265·5508·0000·2000·0428·4090·a004··lureU...·..(@...		02466c10:·696c·7572·6555·0800·0020·0004·2840·90a0··ilureU...·..(@..
02466c20:·2440·4041·04~~e5·~~a0b0·a004·1a04~~·e8~~04·b204··$@@A............		02466c20:·0424·4040·4104·e6a0·b0a0·041a·04e9·04b2··.$@@A...........
02466c30:·e840·9204·08a3·3049·6e76·616c·6964·5f61··.@....0Invalid_a		02466c30:·04e9·4092·0408·a330·496e·7661·6c69·645f··..@....0Invalid_
02466c40:·7267·756d·656e·7454·0800·0020·0004·3140··rgumentT...·..1@		02466c40:·6172·6775·6d65·6e74·5408·0000·2000·0431··argumentT...·..1
02466c50:·90a0·042d·4040·4104~~·ee~~a0·b0a0·0423·04f1··...-@@A......#..		02466c50:·4090·a004·2d40·4041·04ef·a0b0·a004·2304··@...-@@A......#.
02466c60:·04bb·04~~f1·~~4092·0408·a32d·4d61·7463·685f··....@....-Match_		02466c60:·f204·bb04·f240·9204·08a3·2d4d·6174·6368··.....@....-Match
02466c70:·6661·696c·7572·6552·0800·0020·0004·3a40··failureR...·..:@		02466c70:·5f66·6169·6c75·7265·5208·0000·2000·043a··_failureR...·..:
02466c80:·90a0·c092·a004·39a0·0435·a004·3640·0205··......9..5..6@..		02466c80:·4090·a0c0·92a0·0439·a004·35a0·0436·4002··@......9..5..6@.
02466c90:·f5e1·0040·5c40·4041·04~~fc·~~a0b0·a004·3104··...@\@@A......1.		02466c90:·05f5·e100·405c·4040·4104·fda0·b0a0·0431··....@\@@A......1
02466ca0:·ff04·c904·~~ff4~~0·9204·0da3·294e·6f74·5f~~66··~~.....@....)No~~t_f~~		02466ca0:·0501·0004·c905·0100·4092·040d·a329·4e6f··........@....)No
02466cb0:·~~6f75~~·6e64·5608·~~0000~~·2000·0~~448~~·4090·4040··oundV...·..H~~@.@~~@		02466cb0:·745f·666f·756e·6456·0800·0020·0004·4840··t_foundV...·..H@
02466cc0:·410~~5·01~~04·a0b0·~~a004~~·~~3905~~·0~~107~~·04d1·0501··~~A...~~....9.......		02466cc0:·9040·4041·0501·05a0·b0a0·0439·0501·0804··.@@A.......9....
02466cd0:·0740·9204·07a3·2d4f·7574·5f6f·665f·6~~d65··~~.@....-Out_of~~_me~~		02466cd0:·d105·0108·4092·0407·a32d·4f75·745f·6f66··....@....-Out_of
02466ce0:·6d6f·7279·5308·0000·2000·0450·4090·4040··moryS...·..P~~@.@~~@		02466ce0:·5f6d·656d·6f72·7953·0800·0020·0004·5040··_memoryS...·..P@
02466cf0:·4105·010c·a0b0·a004·4105·01~~0f·~~04d9·05~~01··~~A.......A~~...~~....		02466cf0:·9040·4041·0501·0da0·b0a0·0441·0501·1004··.@@A.......A....
02466d00:·0f40·9204·07a3·2e53·7461·636b·5f6f·76~~65··~~.@.....Stack_~~ove~~		02466d00:·d905·0110·4092·0407·a32e·5374·6163·6b5f··....@.....Stack_
02466d10:·7266·6c6f·775a·0800·0020·0004·5840·90~~40··~~rflowZ...·..X~~@.@~~		02466d10:·6f76·6572·666c·6f77·5a08·0000·2000·0458··overflowZ...·..X
02466d20:·4041·0501·14a0·~~b0a0~~·~~0449~~·0501·1704·e105··@~~A...~~....I......		02466d20:·4090·4040·4105·0115·a0b0·a004·4905·0118··@.@@A.......I...
02466d30:·0117·4092·0407·a32e·5379·735f·626c·6f~~63··~~..@.....Sys_b~~loc~~		02466d30:·04e1·0501·1840·9204·07a3·2e53·7973·5f62··.....@.....Sys_b
02466d40:·6b65·6~~45f~~·696f·5~~b08~~·~~0000~~·2000·0460·4090··ked_io[...·..`@.		02466d40:·6c6f·636b·6564·5f69·6f5b·0800·0020·0004··locked_io[...·..
02466d50:·4040·4105·01~~1c·~~a0b0·a004·5105·011f·04~~e9··~~@@A.......Q~~...~~..		02466d50:·6040·9040·4041·0501·1da0·b0a0·0451·0501··`@.@@A.......Q..
02466d60:·0501~~·1f~~40·9204·07a3·2953·7973·5f65·~~727~~2··...@....)Sys_~~err~~		02466d60:·2004·e905·0120·4092·0407·a329·5379·735f···....·@....)Sys_
02466d70:·6f72·5708·0000·2000·0468·4090·a004·64~~40··~~orW...·..h@...d@		02466d70:·6572·726f·7257·0800·0020·0004·6840·90a0··errorW...·..h@..
02466d80:·4041·0501~~·25~~a0·b0a0·045a·0501·2804·f2~~05··~~@A..%....Z~~..(~~...		02466d80:·0464·4040·4105·0126·a0b0·a004·5a05·0129··.d@@A..&....Z..)
02466d90:·0128·4092·0408·a33a·556e·6465·6669·6~~e65··~~.(@....:Undef~~ine~~		02466d90:·04f2·0501·2940·9204·08a3·3a55·6e64·6566··....)@....:Undef
02466da0:·645f·7265·6375·7273·6976·655f·6d6f·64~~75··~~d_recursive_m~~odu~~		02466da0:·696e·6564·5f72·6563·7572·7369·7665·5f6d··ined_recursive_m
02466db0:·6c65·~~5d08~~·~~0000~~·2000·0~~471~~·4090·~~a0c~~0·92a0··le]...·..q@~~...~~..		02466db0:·6f64·756c·655d·0800·0020·0004·7140·90a0··odule]...·..q@..
02466dc0:·~~0470~~·a004·6ca0·046d·4002·~~05f5~~·e100·~~4063~~··.p..l..m@.....@c		02466dc0:·c092·a004·70a0·046c·a004·6d40·0205·f5e1··....p..l..m@....
02466dd0:·4040·4105·0133·a0b0·a004·6805·0136·05~~01··~~@@A..3....h~~..6~~..		02466dd0:·0040·6340·4041·0501·34a0·b0a0·0468·0501··.@c@@A..4....h..
02466de0:·0005·01~~36·~~4092·040d·a325·6279·7465·7~~343~~··...6@....%byt~~esC~~		02466de0:·3705·0100·0501·3740·9204·0da3·2562·7974··7.....7@....%byt
02466df0:·~~0800~~·~~003~~8·0040·~~404~~0·4140·4040·4040·0501··...8.@@@A@@@@@..		02466df0:·6573·4308·0000·3800·4040·4041·4040·4040··esC...8.@@@A@@@@
02466e00:·~~3a4~~0·4040·9204·0390·9226·5374·646c·69~~62··:~~@@@.....&Std~~lib~~		02466e00:·4005·013b·4040·4092·0403·9092·2653·7464··@..;@@@.....&Std
02466e10:·~~9226~~·~~4f70~~·~~746~~9·6~~f6e~~·b12e·4~~861~~·7368·636f··.~~&Optio~~n..~~Hashc~~o		02466e10:·6c69·6292·2349·6e74·9226·4f70·7469·6f6e··lib.#Int.&Option
02466e20:·6e73·6564·5479·7065·~~0101~~·1043·c0~~90·91a0··~~nsedType~~...C....~~		02466e20:·b12e·4861·7368·636f·6e73·6564·5479·7065··..HashconsedType
02466e30:·c1b1·2174·0101·~~0b41~~·~~0800~~·~~0038~~·0~~040~~·4040··..!t...A...8.~~@@@~~		02466e30:·0101·1043·c090·91a0·c1b1·2174·0101·0b41··...C......!t...A
02466e40:·~~414~~0·4040·4040·~~b0c~~0·3063·~~6c69~~·~~622f~~·68~~61··~~A@@@@@..~~0clib/ha~~		02466e40:·0800·0038·0040·4040·4140·4040·4040·b0c0··...8.@@@A@@@@@..
02466e50:·7368·636f·6~~e73~~·2e6d·~~6c5b~~·~~0105~~·~~3101~~·~~0535~~··~~shcons.ml[..1.~~.5		02466e50:·3063·6c69·622f·6861·7368·636f·6e73·2e6d··0clib/hashcons.m
02466e60:·~~c004·~~025b·0105·3101·053b·4040·4040·a105··...[..1..;~~@@@@.~~.		02466e60:·6c5b·0105·3101·0535·c004·025b·0105·3101··l[..1..5...[..1.
02466e70:·0~~150~~·4041·40a0·c1b1·2175·~~010~~1·~~0c42~~·~~0800~~··.P@A@...~~!u..~~.B..		02466e70:·053b·4040·4040·a105·0153·4041·40a0·c1b1··.;@@@@...S@A@...
02466e80:·~~0038~~·0~~040~~·4040·~~414~~0·4040·4040·b0c0·040a··.8.~~@@@A@@~~@@@....		02466e80:·2175·0101·0c42·0800·0038·0040·4040·4140··!u...B...8.@@@A@
02466e90:·5c01·053c·0105·40c0·040b·5c01·053c·0105··~~\..<.~~.@...\..<..		02466e90:·4040·4040·b0c0·040a·5c01·053c·0105·40c0··@@@@....\..<..@.
02466ea0:·4640·~~4040~~·~~40a1~~·0501·5941·4140·a0b0·~~a028~~··~~F@@@@.~~..~~YAA~~@...(		02466ea0:·040b·5c01·053c·0105·4640·4040·40a1·0501··..\..<..F@@@@...
02466eb0:·~~686~~1·~~7368~~·~~636f~~·~~6e73~~·~~010~~1·~~0dd0~~·~~c0c1~~·~~40c0~~··~~hashcons......@.~~		02466eb0:·5c41·4140·a0b0·a028·6861·7368·636f·6e73··\AA@...(hashcons
02466ec0:·~~b390~~·0~~411~~·4090·4002·~~05f5~~·~~e100~~·4001·~~05a5~~··....@.@.....@...		02466ec0:·0101·0dd0·c0c1·40c0·b390·0411·4090·4002··......@.....@.@.
02466ed0:·~~c0c1~~·~~40c~~0·~~b390~~·0~~421~~·4090·4002·~~05f5~~·~~e100~~··..@....!@.@.....		02466ed0:·05f5·e100·4001·05a5·c0c1·40c0·b390·0421··....@.....@....!
02466ee0:·4001·05a6·~~c0b3~~·9004·2540·9040·020~~5·f5~~e1··@.......%@.@....		02466ee0:·4090·4002·05f5·e100·4001·05a6·c0b3·9004··@.@.....@.......
02466ef0:·0040·010~~5·a7~~40·0205·f5e1·0040·0105·a840·~~·.@..~~.@.....@...@		02466ef0:·2540·9040·0205·f5e1·0040·0105·a740·0205··%@.@.....@...@..
02466f00:·~~0205·~~f5e1·0040·0105·a940·b0c0·0~~423~~·5d01··.....@...@...#].		02466f00:·f5e1·0040·0105·a840·0205·f5e1·0040·0105··...@...@.....@..
02466f10:·054~~7·01~~05·4bc0·0424·5d01·0547·0105·~~664~~0·~~·.G~~..K..$]..G..f@		02466f10:·a940·b0c0·0423·5d01·0547·0105·4bc0·0424··.@...#]..G..K..$
02466f20:·~~40a~~1·0501·~~7242~~·~~40a~~0·b0a0·~~2265~~·7~~101~~·010e··@...rB@..."~~eq..~~.		02466f20:·5d01·0547·0105·6640·40a1·0501·7542·40a0··]..G..f@@...uB@.
02466f30:·d0c0·~~c140~~·~~c0b3~~·9004·~~344~~0·9040·~~0205~~·~~f5e1~~··..~~.@.~~...4@.@....		02466f30:·b0a0·2265·7101·010e·d0c0·c140·c0b3·9004··.."eq......@....
Max diff block lines reached; 32776433/34456966 bytes (95.12%) of diff not shown.


Offset 1, 3 lines modified		Offset 1, 3 lines modified
1	-rw-r--r--···0········0········0········4·2023-12-21·13:34:31.000000·debian-binary	1	-rw-r--r--···0········0········0········4·2023-12-21·13:34:31.000000·debian-binary
2	-rw-r--r--···0········0········0····63732·2023-12-21·13:34:31.000000·control.tar.xz	2	-rw-r--r--···0········0········0····63724·2023-12-21·13:34:31.000000·control.tar.xz
3	-rw-r--r--···0········0········0·4473~~6584~~·2023-12-21·13:34:31.000000·data.tar.xz	3	-rw-r--r--···0········0········0·44737700·2023-12-21·13:34:31.000000·data.tar.xz


Offset 7, 15 lines modified		Offset 7, 15 lines modified
7	-rwxr-xr-x···0·root·········(0)·root·········(0)···760860·2023-12-21·13:34:31.000000·./usr/bin/coq-tex	7	-rwxr-xr-x···0·root·········(0)·root·········(0)···760860·2023-12-21·13:34:31.000000·./usr/bin/coq-tex
8	-rwxr-xr-x···0·root·········(0)·root·········(0)··1969872·2023-12-21·13:34:31.000000·./usr/bin/coq_makefile	8	-rwxr-xr-x···0·root·········(0)·root·········(0)··1969872·2023-12-21·13:34:31.000000·./usr/bin/coq_makefile
9	-rwxr-xr-x···0·root·········(0)·root·········(0)·15091412·2023-12-21·13:34:31.000000·./usr/bin/coqc	9	-rwxr-xr-x···0·root·········(0)·root·········(0)·15091412·2023-12-21·13:34:31.000000·./usr/bin/coqc
10	-rwxr-xr-x···0·root·········(0)·root·········(0)·41620865·2023-12-21·13:34:31.000000·./usr/bin/coqc.byte	10	-rwxr-xr-x···0·root·········(0)·root·········(0)·41620865·2023-12-21·13:34:31.000000·./usr/bin/coqc.byte
11	-rwxr-xr-x···0·root·········(0)·root·········(0)··5472080·2023-12-21·13:34:31.000000·./usr/bin/coqchk	11	-rwxr-xr-x···0·root·········(0)·root·········(0)··5472080·2023-12-21·13:34:31.000000·./usr/bin/coqchk
12	-rwxr-xr-x···0·root·········(0)·root·········(0)··2167288·2023-12-21·13:34:31.000000·./usr/bin/coqdep	12	-rwxr-xr-x···0·root·········(0)·root·········(0)··2167288·2023-12-21·13:34:31.000000·./usr/bin/coqdep
13	-rwxr-xr-x···0·root·········(0)·root·········(0)··1995004·2023-12-21·13:34:31.000000·./usr/bin/coqdoc	13	-rwxr-xr-x···0·root·········(0)·root·········(0)··1995004·2023-12-21·13:34:31.000000·./usr/bin/coqdoc
14	-rwxr-xr-x···0·root·········(0)·root·········(0)·42164108·2023-12-21·13:34:31.000000·./usr/bin/coqidetop.byte	14	-rwxr-xr-x···0·root·········(0)·root·········(0)·42164116·2023-12-21·13:34:31.000000·./usr/bin/coqidetop.byte
15	-rwxr-xr-x···0·root·········(0)·root·········(0)·15287940·2023-12-21·13:34:31.000000·./usr/bin/coqidetop.opt	15	-rwxr-xr-x···0·root·········(0)·root·········(0)·15287940·2023-12-21·13:34:31.000000·./usr/bin/coqidetop.opt
16	-rwxr-xr-x···0·root·········(0)·root·········(0)··5632048·2023-12-21·13:34:31.000000·./usr/bin/coqnative	16	-rwxr-xr-x···0·root·········(0)·root·········(0)··5632048·2023-12-21·13:34:31.000000·./usr/bin/coqnative
17	-rwxr-xr-x···0·root·········(0)·root·········(0)···988276·2023-12-21·13:34:31.000000·./usr/bin/coqpp	17	-rwxr-xr-x···0·root·········(0)·root·········(0)···988276·2023-12-21·13:34:31.000000·./usr/bin/coqpp
18	-rwxr-xr-x···0·root·········(0)·root·········(0)··1239392·2023-12-21·13:34:31.000000·./usr/bin/coqtimelog2html	18	-rwxr-xr-x···0·root·········(0)·root·········(0)··1239392·2023-12-21·13:34:31.000000·./usr/bin/coqtimelog2html
19	-rwxr-xr-x···0·root·········(0)·root·········(0)·15091512·2023-12-21·13:34:31.000000·./usr/bin/coqtop	19	-rwxr-xr-x···0·root·········(0)·root·········(0)·15091512·2023-12-21·13:34:31.000000·./usr/bin/coqtop
20	-rwxr-xr-x···0·root·········(0)·root·········(0)·59905510·2023-12-21·13:34:31.000000·./usr/bin/coqtop.byte	20	-rwxr-xr-x···0·root·········(0)·root·········(0)·59905510·2023-12-21·13:34:31.000000·./usr/bin/coqtop.byte
21	-rwxr-xr-x···0·root·········(0)·root·········(0)·15091512·2023-12-21·13:34:31.000000·./usr/bin/coqtop.opt	21	-rwxr-xr-x···0·root·········(0)·root·········(0)·15091512·2023-12-21·13:34:31.000000·./usr/bin/coqtop.opt


Offset 72, 15 lines modified		Offset 72, 15 lines modified
72	-rw-r--r--···0·root·········(0)·root·········(0)·····1924·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cSet.ml	72	-rw-r--r--···0·root·········(0)·root·········(0)·····1924·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cSet.ml
73	-rw-r--r--···0·root·········(0)·root·········(0)·····1181·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cSet.mli	73	-rw-r--r--···0·root·········(0)·root·········(0)·····1181·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cSet.mli
74	-rw-r--r--···0·root·········(0)·root·········(0)·····8506·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cSig.cmi	74	-rw-r--r--···0·root·········(0)·root·········(0)·····8506·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cSig.cmi
75	-rw-r--r--···0·root·········(0)·root·········(0)····40563·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cSig.cmti	75	-rw-r--r--···0·root·········(0)·root·········(0)····40563·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cSig.cmti
76	-rw-r--r--···0·root·········(0)·root·········(0)·····3238·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cSig.mli	76	-rw-r--r--···0·root·········(0)·root·········(0)·····3238·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cSig.mli
77	-rw-r--r--···0·root·········(0)·root·········(0)····60927·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.cmi	77	-rw-r--r--···0·root·········(0)·root·········(0)····60927·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.cmi
78	-rw-r--r--···0·root·········(0)·root·········(0)···156380·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.cmt	78	-rw-r--r--···0·root·········(0)·root·········(0)···156380·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.cmt
79	-rw-r--r--···0·root·········(0)·root·········(0)···142256·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.cmti	79	-rw-r--r--···0·root·········(0)·root·········(0)···142250·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.cmti
80	-rw-r--r--···0·root·········(0)·root·········(0)······780·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.cmx	80	-rw-r--r--···0·root·········(0)·root·········(0)······780·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.cmx
81	-rw-r--r--···0·root·········(0)·root·········(0)·····4410·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.ml	81	-rw-r--r--···0·root·········(0)·root·········(0)·····4410·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.ml
82	-rw-r--r--···0·root·········(0)·root·········(0)·····2719·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.mli	82	-rw-r--r--···0·root·········(0)·root·········(0)·····2719·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cString.mli
83	-rw-r--r--···0·root·········(0)·root·········(0)·····1609·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cThread.cmi	83	-rw-r--r--···0·root·········(0)·root·········(0)·····1609·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cThread.cmi
84	-rw-r--r--···0·root·········(0)·root·········(0)····45321·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cThread.cmt	84	-rw-r--r--···0·root·········(0)·root·········(0)····45321·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cThread.cmt
85	-rw-r--r--···0·root·········(0)·root·········(0)·····8820·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cThread.cmti	85	-rw-r--r--···0·root·········(0)·root·········(0)·····8820·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cThread.cmti
86	-rw-r--r--···0·root·········(0)·root·········(0)······880·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cThread.cmx	86	-rw-r--r--···0·root·········(0)·root·········(0)······880·2023-12-21·13:34:31.000000·./usr/lib/ocaml/coq-core/clib/cThread.cmx


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Offset 53, 360 lines modified		Offset 53, 359 lines modified
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1	Package:·libcoq-stdlib	1	Package:·libcoq-stdlib
2	Source:·coq	2	Source:·coq
3	Version:·8.18.0+dfsg-1	3	Version:·8.18.0+dfsg-1
4	Architecture:·armhf	4	Architecture:·armhf
5	Maintainer:·Debian·OCaml·Maintainers·<debian-ocaml-maint@lists.debian.org>	5	Maintainer:·Debian·OCaml·Maintainers·<debian-ocaml-maint@lists.debian.org>
6	Installed-Size:·156369	6	Installed-Size:·156370
7	Recommends:·coq	7	Recommends:·coq
8	Breaks:·coq-doc·(<=·8.0pl1.0-2),·coq-libs·(<<·8.2.pl1),·coq-theories	8	Breaks:·coq-doc·(<=·8.0pl1.0-2),·coq-libs·(<<·8.2.pl1),·coq-theories
9	Replaces:·coq-libs·(<<·8.2.pl1),·coq-theories	9	Replaces:·coq-libs·(<<·8.2.pl1),·coq-theories
10	Provides:·coq-theories·(=·8.18.0+dfsg-1),·libcoq-stdlib-7lcj3	10	Provides:·coq-theories·(=·8.18.0+dfsg-1),·libcoq-stdlib-7lcj3
11	Section:·math	11	Section:·math
12	Priority:·optional	12	Priority:·optional
13	Homepage:·http://coq.inria.fr/	13	Homepage:·http://coq.inria.fr/


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2460	-rw-r--r--···0·root·········(0)·root·········(0)····56279·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Between.html	2460	-rw-r--r--···0·root·········(0)·root·········(0)····56279·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Between.html
2461	-rw-r--r--···0·root·········(0)·root·········(0)····13646·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Bool_nat.html	2461	-rw-r--r--···0·root·········(0)·root·········(0)····13646·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Bool_nat.html
2462	-rw-r--r--···0·root·········(0)·root·········(0)····22063·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Cantor.html	2462	-rw-r--r--···0·root·········(0)·root·········(0)····22063·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Cantor.html
2463	-rw-r--r--···0·root·········(0)·root·········(0)····14226·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Compare.html	2463	-rw-r--r--···0·root·········(0)·root·········(0)····14226·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Compare.html
2464	-rw-r--r--···0·root·········(0)·root·········(0)····64268·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Compare_dec.html	2464	-rw-r--r--···0·root·········(0)·root·········(0)····64268·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Compare_dec.html
2465	-rw-r--r--···0·root·········(0)·root·········(0)····42751·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Div2.html	2465	-rw-r--r--···0·root·········(0)·root·········(0)····42751·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Div2.html
2466	-rw-r--r--···0·root·········(0)·root·········(0)····21503·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.EqNat.html	2466	-rw-r--r--···0·root·········(0)·root·········(0)····21501·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.EqNat.html
2467	-rw-r--r--···0·root·········(0)·root·········(0)····14148·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Euclid.html	2467	-rw-r--r--···0·root·········(0)·root·········(0)····14148·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Euclid.html
2468	-rw-r--r--···0·root·········(0)·root·········(0)····76375·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Even.html	2468	-rw-r--r--···0·root·········(0)·root·········(0)····76371·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Even.html
2469	-rw-r--r--···0·root·········(0)·root·········(0)·····7674·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Factorial.html	2469	-rw-r--r--···0·root·········(0)·root·········(0)·····7674·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Factorial.html
2470	-rw-r--r--···0·root·········(0)·root·········(0)····25529·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Gt.html	2470	-rw-r--r--···0·root·········(0)·root·········(0)····25521·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Gt.html
2471	-rw-r--r--···0·root·········(0)·root·········(0)····18068·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Le.html	2471	-rw-r--r--···0·root·········(0)·root·········(0)····18062·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Le.html
2472	-rw-r--r--···0·root·········(0)·root·········(0)····24104·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Lt.html	2472	-rw-r--r--···0·root·········(0)·root·········(0)····24094·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Lt.html
2473	-rw-r--r--···0·root·········(0)·root·········(0)····15942·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Max.html	2473	-rw-r--r--···0·root·········(0)·root·········(0)····15941·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Max.html
2474	-rw-r--r--···0·root·········(0)·root·········(0)····15168·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Min.html	2474	-rw-r--r--···0·root·········(0)·root·········(0)····15168·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Min.html
2475	-rw-r--r--···0·root·········(0)·root·········(0)····17~~406~~·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Minus.html	2475	-rw-r--r--···0·root·········(0)·root·········(0)····17399·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Minus.html
2476	-rw-r--r--···0·root·········(0)·root·········(0)····30832·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Mult.html	2476	-rw-r--r--···0·root·········(0)·root·········(0)····30819·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Mult.html
2477	-rw-r--r--···0·root·········(0)·root·········(0)···307653·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.PeanoNat.html	2477	-rw-r--r--···0·root·········(0)·root·········(0)···307638·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.PeanoNat.html
2478	-rw-r--r--···0·root·········(0)·root·········(0)·····9262·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Peano_dec.html	2478	-rw-r--r--···0·root·········(0)·root·········(0)·····9262·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Peano_dec.html
2479	-rw-r--r--···0·root·········(0)·root·········(0)····41517·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Plus.html	2479	-rw-r--r--···0·root·········(0)·root·········(0)····41517·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Plus.html
2480	-rw-r--r--···0·root·········(0)·root·········(0)····79333·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Wf_nat.html	2480	-rw-r--r--···0·root·········(0)·root·········(0)····79333·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Arith.Wf_nat.html
2481	-rw-r--r--···0·root·········(0)·root·········(0)····40548·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Array.PArray.html	2481	-rw-r--r--···0·root·········(0)·root·········(0)····40548·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Array.PArray.html
2482	-rw-r--r--···0·root·········(0)·root·········(0)···226068·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.Bool.html	2482	-rw-r--r--···0·root·········(0)·root·········(0)···226068·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.Bool.html
2483	-rw-r--r--···0·root·········(0)·root·········(0)····16136·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.BoolEq.html	2483	-rw-r--r--···0·root·········(0)·root·········(0)····16136·2023-12-21·13:34:31.000000·./usr/share/doc/libcoq-stdlib/html/Coq.Bool.BoolEq.html
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Offset 45, 31 lines modified		Offset 45, 31 lines modified

45	<div·class="code">	45	<div·class="code">

46	<br/>	46	<br/>
47	</div>	47	</div>

48	<div·class="doc">	48	<div·class="doc">
49	<a·id="lab~~999~~"></a><h1·class="section">DO·NOT·REQUIRE·OR·IMPORT!·This·is·a·temporary·file·preparing·deprecation</h1>	49	<a·id="lab244"></a><h1·class="section">DO·NOT·REQUIRE·OR·IMPORT!·This·is·a·temporary·file·preparing·deprecation</h1>

50	</div>	50	</div>
51	<div·class="code">	51	<div·class="code">

52	<br/>	52	<br/>
53	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#"><span·class="id"·title="library">PeanoNat</span></a>.<br/>	53	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#"><span·class="id"·title="library">PeanoNat</span></a>.<br/>

54	<br/>	54	<br/>
55	</div>	55	</div>

56	<div·class="doc">	56	<div·class="doc">
57	<a·id="lab1~~000~~"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">arith</span></span>·hint·database</h1>	57	<a·id="lab245"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">arith</span></span>·hint·database</h1>

58	<div·class="paragraph">·</div>	58	<div·class="paragraph">·</div>

59	<a·id="lab1~~001~~"></a><h2·class="section"><span·class="inlinecode"><span·class="id"·title="var">lt</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">le</span></span></h2>	59	<a·id="lab246"></a><h2·class="section"><span·class="inlinecode"><span·class="id"·title="var">lt</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">le</span></span></h2>

60	</div>	60	</div>
61	<div·class="code">	61	<div·class="code">
62	#[<span·class="id"·title="var">global</span>]<br/>	62	#[<span·class="id"·title="var">global</span>]<br/>
63	<span·class="id"·title="keyword">Hint</span>·<span·class="id"·title="keyword">Resolve</span>·<span·class="id"·title="var">Nat.le_trans</span>:·<span·class="id"·title="var">arith</span>.·#[<span·class="id"·title="var">global</span>]<br/>	63	<span·class="id"·title="keyword">Hint</span>·<span·class="id"·title="keyword">Resolve</span>·<span·class="id"·title="var">Nat.le_trans</span>:·<span·class="id"·title="var">arith</span>.·#[<span·class="id"·title="var">global</span>]<br/>
64	<span·class="id"·title="keyword">Hint</span>·<span·class="id"·title="keyword">Immediate</span>·<span·class="id"·title="var">Nat.le_antisymm</span>:·<span·class="id"·title="var">arith</span>.·#[<span·class="id"·title="var">global</span>]<br/>	64	<span·class="id"·title="keyword">Hint</span>·<span·class="id"·title="keyword">Immediate</span>·<span·class="id"·title="var">Nat.le_antisymm</span>:·<span·class="id"·title="var">arith</span>.·#[<span·class="id"·title="var">global</span>]<br/>
65	<span·class="id"·title="keyword">Hint</span>·<span·class="id"·title="keyword">Resolve</span>·<span·class="id"·title="var">Nat.le_0_l</span>·<span·class="id"·title="var">Nat.nle_succ_0</span>:·<span·class="id"·title="var">arith</span>.·#[<span·class="id"·title="var">global</span>]<br/>	65	<span·class="id"·title="keyword">Hint</span>·<span·class="id"·title="keyword">Resolve</span>·<span·class="id"·title="var">Nat.le_0_l</span>·<span·class="id"·title="var">Nat.nle_succ_0</span>:·<span·class="id"·title="var">arith</span>.·#[<span·class="id"·title="var">global</span>]<br/>


Offset 52, 15 lines modified		Offset 52, 15 lines modified
52	<br/>	52	<br/>
53	</div>	53	</div>

54	<div·class="doc">	54	<div·class="doc">
55	Equality·on·natural·numbers·	55	Equality·on·natural·numbers·
56	<div·class="paragraph">·</div>	56	<div·class="paragraph">·</div>

57	<a·id="lab1048"></a><h1·class="section">Propositional·equality</h1>	57	<a·id="lab191"></a><h1·class="section">Propositional·equality</h1>

58	</div>	58	</div>
59	<div·class="code">	59	<div·class="code">

60	<br/>	60	<br/>
61	<span·class="id"·title="keyword">Fixpoint</span>·<a·id="eq_nat"·class="idref"·href="#eq_nat"><span·class="id"·title="definition">eq_nat</span></a>·<a·id="n:1"·class="idref"·href="#n:1"><span·class="id"·title="binder">n</span></a>·<a·id="m:2"·class="idref"·href="#m:2"><span·class="id"·title="binder">m</span></a>·:·<span·class="id"·title="keyword">Prop</span>·:=<br/>	61	<span·class="id"·title="keyword">Fixpoint</span>·<a·id="eq_nat"·class="idref"·href="#eq_nat"><span·class="id"·title="definition">eq_nat</span></a>·<a·id="n:1"·class="idref"·href="#n:1"><span·class="id"·title="binder">n</span></a>·<a·id="m:2"·class="idref"·href="#m:2"><span·class="id"·title="binder">m</span></a>·:·<span·class="id"·title="keyword">Prop</span>·:=<br/>
62	<span·class="id"·title="keyword">match</span>·<a·class="idref"·href="Coq.Arith.EqNat.html#n:1"><span·class="id"·title="variable">n</span></a>,·<a·class="idref"·href="Coq.Arith.EqNat.html#m:2"><span·class="id"·title="variable">m</span></a>·<span·class="id"·title="keyword">with</span><br/>	62	<span·class="id"·title="keyword">match</span>·<a·class="idref"·href="Coq.Arith.EqNat.html#n:1"><span·class="id"·title="variable">n</span></a>,·<a·class="idref"·href="Coq.Arith.EqNat.html#m:2"><span·class="id"·title="variable">m</span></a>·<span·class="id"·title="keyword">with</span><br/>


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69	<br/>	69	<br/>
70	<span·class="id"·title="keyword">Implicit</span>·<span·class="id"·title="keyword">Types</span>·<span·class="id"·title="var">m</span>·<span·class="id"·title="var">n</span>·:·<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>.<br/>	70	<span·class="id"·title="keyword">Implicit</span>·<span·class="id"·title="keyword">Types</span>·<span·class="id"·title="var">m</span>·<span·class="id"·title="var">n</span>·:·<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>.<br/>

71	<br/>	71	<br/>
72	</div>	72	</div>

73	<div·class="doc">	73	<div·class="doc">
74	<a·id="lab1050"></a><h1·class="section">Inductive·definition·of·<span·class="inlinecode"><span·class="id"·title="var">even</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">odd</span></span></h1>	74	<a·id="lab209"></a><h1·class="section">Inductive·definition·of·<span·class="inlinecode"><span·class="id"·title="var">even</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">odd</span></span></h1>

75	</div>	75	</div>
76	<div·class="code">	76	<div·class="code">

77	<br/>	77	<br/>
78	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Even·file·is·obsolete.·Use·Nat.Even·or·Nat.Even_alt·instead.")]<br/>	78	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Even·file·is·obsolete.·Use·Nat.Even·or·Nat.Even_alt·instead.")]<br/>
79	<span·class="id"·title="keyword">Notation</span>·<a·id="even"·class="idref"·href="#even"><span·class="id"·title="abbreviation">even</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.Even_alt"><span·class="id"·title="inductive">Nat.Even_alt</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/>	79	<span·class="id"·title="keyword">Notation</span>·<a·id="even"·class="idref"·href="#even"><span·class="id"·title="abbreviation">even</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.Even_alt"><span·class="id"·title="inductive">Nat.Even_alt</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/>


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48	<br/>	48	<br/>
49	</div>	49	</div>

50	<div·class="doc">	50	<div·class="doc">
51	Theorems·about·<span·class="inlinecode"><span·class="id"·title="var">gt</span></span>·in·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span>.·	51	Theorems·about·<span·class="inlinecode"><span·class="id"·title="var">gt</span></span>·in·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span>.·
52	<div·class="paragraph">·</div>	52	<div·class="paragraph">·</div>

53	<a·id="lab1054"></a><h1·class="section">This·file·is·OBSOLETE,·see·<span·class="inlinecode"><span·class="id"·title="var">Arith_base</span></span>·instead.</h1>	53	<a·id="lab201"></a><h1·class="section">This·file·is·OBSOLETE,·see·<span·class="inlinecode"><span·class="id"·title="var">Arith_base</span></span>·instead.</h1>

54	</div>	54	</div>
55	<div·class="code">	55	<div·class="code">

56	<br/>	56	<br/>
57	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#"><span·class="id"·title="library">Arith_prebase</span></a>.<br/>	57	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#"><span·class="id"·title="library">Arith_prebase</span></a>.<br/>

58	<br/>	58	<br/>
59	<span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/>	59	<span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/>

60	<br/>	60	<br/>
61	</div>	61	</div>

62	<div·class="doc">	62	<div·class="doc">
63	<a·id="lab1055"></a><h1·class="section">Order·and·successor</h1>	63	<a·id="lab202"></a><h1·class="section">Order·and·successor</h1>

64	</div>	64	</div>
65	<div·class="code">	65	<div·class="code">

66	<br/>	66	<br/>
67	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Gt·file·is·obsolete.·Use·Nat.lt_0_succ·instead.")]<br/>	67	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Gt·file·is·obsolete.·Use·Nat.lt_0_succ·instead.")]<br/>
68	<span·class="id"·title="keyword">Notation</span>·<a·id="gt_Sn_O"·class="idref"·href="#gt_Sn_O"><span·class="id"·title="abbreviation">gt_Sn_O</span></a>·:=·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#gt_Sn_O_stt"><span·class="id"·title="definition">Arith_prebase.gt_Sn_O_stt</span></a>.<br/>	68	<span·class="id"·title="keyword">Notation</span>·<a·id="gt_Sn_O"·class="idref"·href="#gt_Sn_O"><span·class="id"·title="abbreviation">gt_Sn_O</span></a>·:=·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#gt_Sn_O_stt"><span·class="id"·title="definition">Arith_prebase.gt_Sn_O_stt</span></a>.<br/>


Offset 145, 15 lines modified		Offset 145, 15 lines modified
145	<a·class="idref"·href="Coq.Arith.PeanoNat.html#Aeq:11"><span·class="id"·title="variable">Aeq</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#a:12"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#a:12"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#Proper"><span·class="id"·title="class">Proper</span></a>·(<a·class="idref"·href="Coq.Init.Logic.html#eq"><span·class="id"·title="inductive">eq</span></a><a·class="idref"·href="Coq.Classes.Morphisms.html#8dc5652698a6e16f72dd37bd17d3b973"><span·class="id"·title="notation">==></span></a><a·class="idref"·href="Coq.Arith.PeanoNat.html#Aeq:11"><span·class="id"·title="variable">Aeq</span></a><a·class="idref"·href="Coq.Classes.Morphisms.html#8dc5652698a6e16f72dd37bd17d3b973"><span·class="id"·title="notation">==></span></a><a·class="idref"·href="Coq.Arith.PeanoNat.html#Aeq:11"><span·class="id"·title="variable">Aeq</span></a>)·<a·class="idref"·href="Coq.Arith.PeanoNat.html#f:13"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a><br/>	145	<a·class="idref"·href="Coq.Arith.PeanoNat.html#Aeq:11"><span·class="id"·title="variable">Aeq</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#a:12"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#a:12"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a>·<a·class="idref"·href="Coq.Classes.Morphisms.html#Proper"><span·class="id"·title="class">Proper</span></a>·(<a·class="idref"·href="Coq.Init.Logic.html#eq"><span·class="id"·title="inductive">eq</span></a><a·class="idref"·href="Coq.Classes.Morphisms.html#8dc5652698a6e16f72dd37bd17d3b973"><span·class="id"·title="notation">==></span></a><a·class="idref"·href="Coq.Arith.PeanoNat.html#Aeq:11"><span·class="id"·title="variable">Aeq</span></a><a·class="idref"·href="Coq.Classes.Morphisms.html#8dc5652698a6e16f72dd37bd17d3b973"><span·class="id"·title="notation">==></span></a><a·class="idref"·href="Coq.Arith.PeanoNat.html#Aeq:11"><span·class="id"·title="variable">Aeq</span></a>)·<a·class="idref"·href="Coq.Arith.PeanoNat.html#f:13"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a><br/>
146	<span·class="id"·title="keyword">forall</span>·<a·id="n:14"·class="idref"·href="#n:14"><span·class="id"·title="binder">n</span></a>·:·<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>,·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Aeq:11"><span·class="id"·title="variable">Aeq</span></a>·(<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.recursion"><span·class="id"·title="definition">recursion</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#a:12"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#f:13"><span·class="id"·title="variable">f</span></a>·(<a·class="idref"·href="Coq.Init.Datatypes.html#S"><span·class="id"·title="constructor">S</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#n:14"><span·class="id"·title="variable">n</span></a>))·(<a·class="idref"·href="Coq.Arith.PeanoNat.html#f:13"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#n:14"><span·class="id"·title="variable">n</span></a>·(<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.recursion"><span·class="id"·title="definition">recursion</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#a:12"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#f:13"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#n:14"><span·class="id"·title="variable">n</span></a>)).<br/>	146	<span·class="id"·title="keyword">forall</span>·<a·id="n:14"·class="idref"·href="#n:14"><span·class="id"·title="binder">n</span></a>·:·<a·class="idref"·href="Coq.Init.Datatypes.html#nat"><span·class="id"·title="inductive">nat</span></a>,·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Aeq:11"><span·class="id"·title="variable">Aeq</span></a>·(<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.recursion"><span·class="id"·title="definition">recursion</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#a:12"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#f:13"><span·class="id"·title="variable">f</span></a>·(<a·class="idref"·href="Coq.Init.Datatypes.html#S"><span·class="id"·title="constructor">S</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#n:14"><span·class="id"·title="variable">n</span></a>))·(<a·class="idref"·href="Coq.Arith.PeanoNat.html#f:13"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#n:14"><span·class="id"·title="variable">n</span></a>·(<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.recursion"><span·class="id"·title="definition">recursion</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#a:12"><span·class="id"·title="variable">a</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#f:13"><span·class="id"·title="variable">f</span></a>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#n:14"><span·class="id"·title="variable">n</span></a>)).<br/>

147	<br/>	147	<br/>
148	</div>	148	</div>

149	<div·class="doc">	149	<div·class="doc">
150	<a·id="lab1033"></a><h2·class="section">Remaining·constants·not·defined·in·Coq.Init.Nat</h2>	150	<a·id="lab213"></a><h2·class="section">Remaining·constants·not·defined·in·Coq.Init.Nat</h2>

151	<div·class="paragraph">·</div>	151	<div·class="paragraph">·</div>

152	·NB:·Aliasing·<span·class="inlinecode"><span·class="id"·title="var">le</span></span>·is·mandatory,·since·only·a·Definition·can·implement	152	·NB:·Aliasing·<span·class="inlinecode"><span·class="id"·title="var">le</span></span>·is·mandatory,·since·only·a·Definition·can·implement
153	····an·interface·Parameter...·	153	····an·interface·Parameter...·
154	</div>	154	</div>
155	<div·class="code">	155	<div·class="code">


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00000660:·226c·6962·7469·746c·6522·3e4c·6962·7261··"libtitle">Libra		00000660:·226c·6962·7469·746c·6522·3e4c·6962·7261··"libtitle">Libra
00000670:·7279·2043·6f71·2e43·6c61·7373·6573·2e52··ry·Coq.Classes.R		00000670:·7279·2043·6f71·2e43·6c61·7373·6573·2e52··ry·Coq.Classes.R
00000680:·656c·6174·696f·6e43·6c61·7373·6573·3c2f··elationClasses</		00000680:·656c·6174·696f·6e43·6c61·7373·6573·3c2f··elationClasses</
00000690:·6831·3e0a·0a3c·6469·7620·636c·6173·733d··h1>..<div·class=		00000690:·6831·3e0a·0a3c·6469·7620·636c·6173·733d··h1>..<div·class=
000006a0:·2263·6f64·6522·3e0a·0a3c·6272·2f3e·0a3c··"code">..<br/>.<		000006a0:·2263·6f64·6522·3e0a·0a3c·6272·2f3e·0a3c··"code">..<br/>.<
000006b0:·2f64·6976·3e0a·0a3c·6469·7620·636c·6173··/div>..<div·clas		000006b0:·2f64·6976·3e0a·0a3c·6469·7620·636c·6173··/div>..<div·clas
000006c0:·733d·2264·6f63·223e·0a3c·6120·6964·3d22··s="doc">.<a·id="		000006c0:·733d·2264·6f63·223e·0a3c·6120·6964·3d22··s="doc">.<a·id="
000006d0:·6c61·6232·3631·223e·3c2f·613e·3c68·3120··lab~~261~~"></a><h1·		000006d0:·6c61·6237·3039·223e·3c2f·613e·3c68·3120··lab709"></a><h1·
000006e0:·636c·6173·733d·2273·6563·7469·6f6e·223e··class="section">		000006e0:·636c·6173·733d·2273·6563·7469·6f6e·223e··class="section">
000006f0:·5479·7065·636c·6173·732d·6261·7365·6420··Typeclass-based·		000006f0:·5479·7065·636c·6173·732d·6261·7365·6420··Typeclass-based·
00000700:·7265·6c61·7469·6f6e·732c·2074·6163·7469··relations,·tacti		00000700:·7265·6c61·7469·6f6e·732c·2074·6163·7469··relations,·tacti
00000710:·6373·2061·6e64·2073·7461·6e64·6172·6420··cs·and·standard·		00000710:·6373·2061·6e64·2073·7461·6e64·6172·6420··cs·and·standard·
00000720:·696e·7374·616e·6365·733c·2f68·313e·0a0a··instances</h1>..		00000720:·696e·7374·616e·6365·733c·2f68·313e·0a0a··instances</h1>..
00000730:·0a3c·6469·7620·636c·6173·733d·2270·6172··.<div·class="par		00000730:·0a3c·6469·7620·636c·6173·733d·2270·6172··.<div·class="par
00000740:·6167·7261·7068·223e·203c·2f64·6976·3e0a··agraph">·</div>.		00000740:·6167·7261·7068·223e·203c·2f64·6976·3e0a··agraph">·</div>.


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48	<br/>	48	<br/>
49	</div>	49	</div>

50	<div·class="doc">	50	<div·class="doc">
51	Order·on·natural·numbers.·	51	Order·on·natural·numbers.·
52	<div·class="paragraph">·</div>	52	<div·class="paragraph">·</div>

53	<a·id="lab1~~062~~"></a><h1·class="section">This·file·is·OBSOLETE,·see·<span·class="inlinecode"><span·class="id"·title="var">Arith_base</span></span>·instead.</h1>	53	<a·id="lab228"></a><h1·class="section">This·file·is·OBSOLETE,·see·<span·class="inlinecode"><span·class="id"·title="var">Arith_base</span></span>·instead.</h1>

54	</div>	54	</div>
55	<div·class="code">	55	<div·class="code">

56	<br/>	56	<br/>
57	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#"><span·class="id"·title="library">Arith_prebase</span></a>.<br/>	57	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#"><span·class="id"·title="library">Arith_prebase</span></a>.<br/>

58	<br/>	58	<br/>
59	</div>	59	</div>

60	<div·class="doc">	60	<div·class="doc">
61	<a·id="lab1~~063~~"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">le</span></span>·is·an·order·on·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span></h1>	61	<a·id="lab229"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">le</span></span>·is·an·order·on·<span·class="inlinecode"><span·class="id"·title="var">nat</span></span></h1>

62	</div>	62	</div>
63	<div·class="code">	63	<div·class="code">

64	<br/>	64	<br/>
65	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Le·file·is·obsolete.·Use·Nat.le_refl·instead.")]<br/>	65	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Le·file·is·obsolete.·Use·Nat.le_refl·instead.")]<br/>
66	<span·class="id"·title="keyword">Notation</span>·<a·id="le_refl"·class="idref"·href="#le_refl"><span·class="id"·title="abbreviation">le_refl</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.le_refl"><span·class="id"·title="lemma">Nat.le_refl</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/>	66	<span·class="id"·title="keyword">Notation</span>·<a·id="le_refl"·class="idref"·href="#le_refl"><span·class="id"·title="abbreviation">le_refl</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.le_refl"><span·class="id"·title="lemma">Nat.le_refl</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).<br/>


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48	<br/>	48	<br/>
49	</div>	49	</div>

50	<div·class="doc">	50	<div·class="doc">
51	Strict·order·on·natural·numbers.·	51	Strict·order·on·natural·numbers.·
52	<div·class="paragraph">·</div>	52	<div·class="paragraph">·</div>

53	<a·id="lab1~~010~~"></a><h1·class="section">This·file·is·OBSOLETE,·see·<span·class="inlinecode"><span·class="id"·title="var">Arith_base</span></span>·instead.</h1>	53	<a·id="lab234"></a><h1·class="section">This·file·is·OBSOLETE,·see·<span·class="inlinecode"><span·class="id"·title="var">Arith_base</span></span>·instead.</h1>

54	</div>	54	</div>
55	<div·class="code">	55	<div·class="code">

56	<br/>	56	<br/>
57	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#"><span·class="id"·title="library">Arith_prebase</span></a>.<br/>	57	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#"><span·class="id"·title="library">Arith_prebase</span></a>.<br/>

58	<br/>	58	<br/>
59	</div>	59	</div>

60	<div·class="doc">	60	<div·class="doc">
61	<a·id="lab1~~011~~"></a><h1·class="section">Irreflexivity</h1>	61	<a·id="lab235"></a><h1·class="section">Irreflexivity</h1>

62	</div>	62	</div>
63	<div·class="code">	63	<div·class="code">

64	<br/>	64	<br/>
65	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Lt·file·is·obsolete.·Use·Nat.lt_irrefl·instead.")]<br/>	65	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Lt·file·is·obsolete.·Use·Nat.lt_irrefl·instead.")]<br/>
66	<span·class="id"·title="keyword">Notation</span>·<a·id="lt_irrefl"·class="idref"·href="#lt_irrefl"><span·class="id"·title="abbreviation">lt_irrefl</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.lt_irrefl"><span·class="id"·title="lemma">Nat.lt_irrefl</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·	66	<span·class="id"·title="keyword">Notation</span>·<a·id="lt_irrefl"·class="idref"·href="#lt_irrefl"><span·class="id"·title="abbreviation">lt_irrefl</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.lt_irrefl"><span·class="id"·title="lemma">Nat.lt_irrefl</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·
67	<br/>	67	<br/>
68	</div>	68	</div>

69	<div·class="doc">	69	<div·class="doc">
70	<a·id="lab1~~012~~"></a><h1·class="section">Relationship·between·<span·class="inlinecode"><span·class="id"·title="var">le</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">lt</span></span></h1>	70	<a·id="lab236"></a><h1·class="section">Relationship·between·<span·class="inlinecode"><span·class="id"·title="var">le</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">lt</span></span></h1>

71	</div>	71	</div>
72	<div·class="code">	72	<div·class="code">

73	<br/>	73	<br/>
74	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Lt·file·is·obsolete.·Use·the·bidirectional·version·Nat.le_succ_l·instead.")]<br/>	74	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Lt·file·is·obsolete.·Use·the·bidirectional·version·Nat.le_succ_l·instead.")]<br/>
75	<span·class="id"·title="keyword">Notation</span>·<a·id="lt_le_S"·class="idref"·href="#lt_le_S"><span·class="id"·title="abbreviation">lt_le_S</span></a>·:=·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#lt_le_S_stt"><span·class="id"·title="definition">Arith_prebase.lt_le_S_stt</span></a>.<br/>	75	<span·class="id"·title="keyword">Notation</span>·<a·id="lt_le_S"·class="idref"·href="#lt_le_S"><span·class="id"·title="abbreviation">lt_le_S</span></a>·:=·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#lt_le_S_stt"><span·class="id"·title="definition">Arith_prebase.lt_le_S_stt</span></a>.<br/>


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45	<div·class="code">	45	<div·class="code">

46	<br/>	46	<br/>
47	</div>	47	</div>

48	<div·class="doc">	48	<div·class="doc">
49	<a·id="lab1009"></a><h1·class="section">THIS·FILE·IS·DEPRECATED.·Use·<span·class="inlinecode"><span·class="id"·title="var">PeanoNat.Nat</span></span>·or·<span·class="inlinecode"><span·class="id"·title="var">Arith.Arith_base</span></span>·instead.</h1>	49	<a·id="lab200"></a><h1·class="section">THIS·FILE·IS·DEPRECATED.·Use·<span·class="inlinecode"><span·class="id"·title="var">PeanoNat.Nat</span></span>·or·<span·class="inlinecode"><span·class="id"·title="var">Arith.Arith_base</span></span>·instead.</h1>

50	</div>	50	</div>
51	<div·class="code">	51	<div·class="code">

52	<br/>	52	<br/>
53	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#"><span·class="id"·title="library">PeanoNat</span></a>.<br/>	53	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Arith.PeanoNat.html#"><span·class="id"·title="library">PeanoNat</span></a>.<br/>


Offset 48, 43 lines modified		Offset 48, 43 lines modified
48	<br/>	48	<br/>
49	</div>	49	</div>

50	<div·class="doc">	50	<div·class="doc">
51	Properties·of·subtraction·between·natural·numbers.·	51	Properties·of·subtraction·between·natural·numbers.·
52	<div·class="paragraph">·</div>	52	<div·class="paragraph">·</div>

53	<a·id="lab1002"></a><h1·class="section">This·file·is·OBSOLETE,·see·<span·class="inlinecode"><span·class="id"·title="var">Arith_base</span></span>·instead.</h1>	53	<a·id="lab193"></a><h1·class="section">This·file·is·OBSOLETE,·see·<span·class="inlinecode"><span·class="id"·title="var">Arith_base</span></span>·instead.</h1>

54	</div>	54	</div>
55	<div·class="code">	55	<div·class="code">

56	<br/>	56	<br/>
57	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#"><span·class="id"·title="library">Arith_prebase</span></a>.<br/>	57	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#"><span·class="id"·title="library">Arith_prebase</span></a>.<br/>

58	<br/>	58	<br/>
59	<span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/>	59	<span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/>

60	<br/>	60	<br/>
61	</div>	61	</div>

62	<div·class="doc">	62	<div·class="doc">
63	<a·id="lab1003"></a><h1·class="section">0·is·right·neutral</h1>	63	<a·id="lab194"></a><h1·class="section">0·is·right·neutral</h1>

64	</div>	64	</div>
65	<div·class="code">	65	<div·class="code">

66	<br/>	66	<br/>
67	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Minus·file·is·obsolete.·Use·Nat.sub_0_r·(and·symmetry·of·equality)·instead.")]<br/>	67	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Minus·file·is·obsolete.·Use·Nat.sub_0_r·(and·symmetry·of·equality)·instead.")]<br/>
68	<span·class="id"·title="keyword">Notation</span>·<a·id="minus_n_O"·class="idref"·href="#minus_n_O"><span·class="id"·title="abbreviation">minus_n_O</span></a>·:=·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#minus_n_O_stt"><span·class="id"·title="definition">Arith_prebase.minus_n_O_stt</span></a>.<br/>	68	<span·class="id"·title="keyword">Notation</span>·<a·id="minus_n_O"·class="idref"·href="#minus_n_O"><span·class="id"·title="abbreviation">minus_n_O</span></a>·:=·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#minus_n_O_stt"><span·class="id"·title="definition">Arith_prebase.minus_n_O_stt</span></a>.<br/>

69	<br/>	69	<br/>
70	</div>	70	</div>

71	<div·class="doc">	71	<div·class="doc">
72	<a·id="lab1004"></a><h1·class="section">Permutation·with·successor</h1>	72	<a·id="lab195"></a><h1·class="section">Permutation·with·successor</h1>

73	</div>	73	</div>
74	<div·class="code">	74	<div·class="code">

75	<br/>	75	<br/>
76	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Minus·file·is·obsolete.·Use·Nat.sub_succ_l·(and·symmetry·of·equality)·instead.")]<br/>	76	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Minus·file·is·obsolete.·Use·Nat.sub_succ_l·(and·symmetry·of·equality)·instead.")]<br/>
77	<span·class="id"·title="keyword">Notation</span>·<a·id="minus_Sn_m"·class="idref"·href="#minus_Sn_m"><span·class="id"·title="abbreviation">minus_Sn_m</span></a>·:=·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#minus_Sn_m_stt"><span·class="id"·title="definition">Arith_prebase.minus_Sn_m_stt</span></a>.<br/>	77	<span·class="id"·title="keyword">Notation</span>·<a·id="minus_Sn_m"·class="idref"·href="#minus_Sn_m"><span·class="id"·title="abbreviation">minus_Sn_m</span></a>·:=·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#minus_Sn_m_stt"><span·class="id"·title="definition">Arith_prebase.minus_Sn_m_stt</span></a>.<br/>


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45	<div·class="code">	45	<div·class="code">

46	<br/>	46	<br/>
47	</div>	47	</div>

48	<div·class="doc">	48	<div·class="doc">
49	<a·id="lab1~~020~~"></a><h1·class="section">Properties·of·multiplication.</h1>	49	<a·id="lab247"></a><h1·class="section">Properties·of·multiplication.</h1>

50	<div·class="paragraph">·</div>	50	<div·class="paragraph">·</div>

51	<a·id="lab1~~021~~"></a><h1·class="section">This·file·is·OBSOLETE,·see·<span·class="inlinecode"><span·class="id"·title="var">Arith_base</span></span>·instead.</h1>	51	<a·id="lab248"></a><h1·class="section">This·file·is·OBSOLETE,·see·<span·class="inlinecode"><span·class="id"·title="var">Arith_base</span></span>·instead.</h1>

52	</div>	52	</div>
53	<div·class="code">	53	<div·class="code">

54	<br/>	54	<br/>
55	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#"><span·class="id"·title="library">Arith_prebase</span></a>.<br/>	55	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Export</span>·<a·class="idref"·href="Coq.Arith.Arith_prebase.html#"><span·class="id"·title="library">Arith_prebase</span></a>.<br/>

56	<br/>	56	<br/>
57	<span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/>	57	<span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/>

58	<br/>	58	<br/>
59	</div>	59	</div>

60	<div·class="doc">	60	<div·class="doc">
61	<a·id="lab1~~022~~"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">nat</span></span>·is·a·semi-ring</h1>	61	<a·id="lab249"></a><h1·class="section"><span·class="inlinecode"><span·class="id"·title="var">nat</span></span>·is·a·semi-ring</h1>

62	<div·class="paragraph">·</div>	62	<div·class="paragraph">·</div>

63	<a·id="lab1~~023~~"></a><h2·class="section">Zero·property</h2>	63	<a·id="lab250"></a><h2·class="section">Zero·property</h2>

64	</div>	64	</div>
65	<div·class="code">	65	<div·class="code">

66	<br/>	66	<br/>
67	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_0_l·instead.")]<br/>	67	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_0_l·instead.")]<br/>
68	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_0_l"·class="idref"·href="#mult_0_l"><span·class="id"·title="abbreviation">mult_0_l</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.mul_0_l"><span·class="id"·title="lemma">Nat.mul_0_l</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_0_r·instead.")]<br/>	68	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_0_l"·class="idref"·href="#mult_0_l"><span·class="id"·title="abbreviation">mult_0_l</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.mul_0_l"><span·class="id"·title="lemma">Nat.mul_0_l</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_0_r·instead.")]<br/>
69	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_0_r"·class="idref"·href="#mult_0_r"><span·class="id"·title="abbreviation">mult_0_r</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.mul_0_r"><span·class="id"·title="lemma">Nat.mul_0_r</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·	69	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_0_r"·class="idref"·href="#mult_0_r"><span·class="id"·title="abbreviation">mult_0_r</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.mul_0_r"><span·class="id"·title="lemma">Nat.mul_0_r</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·
70	<br/>	70	<br/>
71	</div>	71	</div>

72	<div·class="doc">	72	<div·class="doc">
73	<a·id="lab1~~024~~"></a><h2·class="section">1·is·neutral</h2>	73	<a·id="lab251"></a><h2·class="section">1·is·neutral</h2>

74	</div>	74	</div>
75	<div·class="code">	75	<div·class="code">

76	<br/>	76	<br/>
77	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_1_l·instead.")]<br/>	77	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_1_l·instead.")]<br/>
78	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_1_l"·class="idref"·href="#mult_1_l"><span·class="id"·title="abbreviation">mult_1_l</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.mul_1_l"><span·class="id"·title="lemma">Nat.mul_1_l</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_1_r·instead.")]<br/>	78	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_1_l"·class="idref"·href="#mult_1_l"><span·class="id"·title="abbreviation">mult_1_l</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.mul_1_l"><span·class="id"·title="lemma">Nat.mul_1_l</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_1_r·instead.")]<br/>
79	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_1_r"·class="idref"·href="#mult_1_r"><span·class="id"·title="abbreviation">mult_1_r</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.mul_1_r"><span·class="id"·title="lemma">Nat.mul_1_r</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·	79	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_1_r"·class="idref"·href="#mult_1_r"><span·class="id"·title="abbreviation">mult_1_r</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.mul_1_r"><span·class="id"·title="lemma">Nat.mul_1_r</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·
80	<br/>	80	<br/>
81	</div>	81	</div>

82	<div·class="doc">	82	<div·class="doc">
83	<a·id="lab1025"></a><h2·class="section">Commutativity</h2>	83	<a·id="lab252"></a><h2·class="section">Commutativity</h2>

84	</div>	84	</div>
85	<div·class="code">	85	<div·class="code">

86	<br/>	86	<br/>
87	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_comm·instead.")]<br/>	87	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_comm·instead.")]<br/>
88	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_comm"·class="idref"·href="#mult_comm"><span·class="id"·title="abbreviation">mult_comm</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.mul_comm"><span·class="id"·title="lemma">Nat.mul_comm</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·	88	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_comm"·class="idref"·href="#mult_comm"><span·class="id"·title="abbreviation">mult_comm</span></a>·:=·<a·class="idref"·href="Coq.Arith.PeanoNat.html#Nat.mul_comm"><span·class="id"·title="lemma">Nat.mul_comm</span></a>·(<span·class="id"·title="var">only</span>·<span·class="id"·title="var">parsing</span>).·
89	<br/>	89	<br/>
90	</div>	90	</div>

91	<div·class="doc">	91	<div·class="doc">
92	<a·id="lab1~~026~~"></a><h2·class="section">Distributivity</h2>	92	<a·id="lab253"></a><h2·class="section">Distributivity</h2>

93	</div>	93	</div>
94	<div·class="code">	94	<div·class="code">

95	<br/>	95	<br/>
96	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_add_distr_r·instead.")]<br/>	96	#[<span·class="id"·title="var">deprecated</span>(<span·class="id"·title="var">since</span>="8.16",<span·class="id"·title="var">note</span>="The·Arith.Mult·file·is·obsolete.·Use·Nat.mul_add_distr_r·instead.")]<br/>
97	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_plus_distr_r"·class="idref"·href="#mult_plus_distr_r"><span·class="id"·title="abbreviation">mult_plus_distr_r</span></a>·:=<br/>	97	<span·class="id"·title="keyword">Notation</span>·<a·id="mult_plus_distr_r"·class="idref"·href="#mult_plus_distr_r"><span·class="id"·title="abbreviation">mult_plus_distr_r</span></a>·:=<br/>


Offset 86, 27 lines modified		Offset 86, 27 lines modified
86	\|·<a·class="idref"·href="Coq.Init.Datatypes.html#false"><span·class="id"·title="constructor">false</span></a>·=>·<a·class="idref"·href="Coq.Init.Logic.html#False"><span·class="id"·title="inductive">False</span></a><br/>	86	\|·<a·class="idref"·href="Coq.Init.Datatypes.html#false"><span·class="id"·title="constructor">false</span></a>·=>·<a·class="idref"·href="Coq.Init.Logic.html#False"><span·class="id"·title="inductive">False</span></a><br/>
87	<span·class="id"·title="keyword">end</span>.<br/>	87	<span·class="id"·title="keyword">end</span>.<br/>

88	<br/>	88	<br/>
89	</div>	89	</div>

90	<div·class="doc">	90	<div·class="doc">
91	<a·id="lab~~178~~"></a><h1·class="section">Decidability</h1>	91	<a·id="lab692"></a><h1·class="section">Decidability</h1>

92	</div>	92	</div>
93	<div·class="code">	93	<div·class="code">

94	<br/>	94	<br/>
95	<span·class="id"·title="keyword">Lemma</span>·<a·id="bool_dec"·class="idref"·href="#bool_dec"><span·class="id"·title="lemma">bool_dec</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="b1:3"·class="idref"·href="#b1:3"><span·class="id"·title="binder">b1</span></a>·<a·id="b2:4"·class="idref"·href="#b2:4"><span·class="id"·title="binder">b2</span></a>·:·<a·class="idref"·href="Coq.Init.Datatypes.html#bool"><span·class="id"·title="inductive">bool</span></a>,·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.Bool.Bool.html#b1:3"><span·class="id"·title="variable">b1</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Bool.Bool.html#b2:4"><span·class="id"·title="variable">b2</span></a><a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">}</span></a>·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.Bool.Bool.html#b1:3"><span·class="id"·title="variable">b1</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<>'_x"><span·class="id"·title="notation"><></span></a>·<a·class="idref"·href="Coq.Bool.Bool.html#b2:4"><span·class="id"·title="variable">b2</span></a><a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">}</span></a>.<br/>	95	<span·class="id"·title="keyword">Lemma</span>·<a·id="bool_dec"·class="idref"·href="#bool_dec"><span·class="id"·title="lemma">bool_dec</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="b1:3"·class="idref"·href="#b1:3"><span·class="id"·title="binder">b1</span></a>·<a·id="b2:4"·class="idref"·href="#b2:4"><span·class="id"·title="binder">b2</span></a>·:·<a·class="idref"·href="Coq.Init.Datatypes.html#bool"><span·class="id"·title="inductive">bool</span></a>,·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.Bool.Bool.html#b1:3"><span·class="id"·title="variable">b1</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·<a·class="idref"·href="Coq.Bool.Bool.html#b2:4"><span·class="id"·title="variable">b2</span></a><a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">}</span></a>·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">{</span></a><a·class="idref"·href="Coq.Bool.Bool.html#b1:3"><span·class="id"·title="variable">b1</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<>'_x"><span·class="id"·title="notation"><></span></a>·<a·class="idref"·href="Coq.Bool.Bool.html#b2:4"><span·class="id"·title="variable">b2</span></a><a·class="idref"·href="Coq.Init.Specif.html#87727981cdc1579fef00b9d9c1d3b9da"><span·class="id"·title="notation">}</span></a>.<br/>

96	<br/>	96	<br/>
97	</div>	97	</div>

98	<div·class="doc">	98	<div·class="doc">
99	<a·id="lab~~179~~"></a><h1·class="section">Discrimination</h1>	99	<a·id="lab693"></a><h1·class="section">Discrimination</h1>

100	</div>	100	</div>
101	<div·class="code">	101	<div·class="code">

102	<br/>	102	<br/>
103	<span·class="id"·title="keyword">Lemma</span>·<a·id="diff_true_false"·class="idref"·href="#diff_true_false"><span·class="id"·title="lemma">diff_true_false</span></a>·:·<a·class="idref"·href="Coq.Init.Datatypes.html#true"><span·class="id"·title="constructor">true</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<>'_x"><span·class="id"·title="notation"><></span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#false"><span·class="id"·title="constructor">false</span></a>.<br/>	103	<span·class="id"·title="keyword">Lemma</span>·<a·id="diff_true_false"·class="idref"·href="#diff_true_false"><span·class="id"·title="lemma">diff_true_false</span></a>·:·<a·class="idref"·href="Coq.Init.Datatypes.html#true"><span·class="id"·title="constructor">true</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'<>'_x"><span·class="id"·title="notation"><></span></a>·<a·class="idref"·href="Coq.Init.Datatypes.html#false"><span·class="id"·title="constructor">false</span></a>.<br/>
104	#[<span·class="id"·title="var">global</span>]<br/>	104	#[<span·class="id"·title="var">global</span>]<br/>


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62	<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Bool.Bool.html#BoolNotations"><span·class="id"·title="module">BoolNotations</span></a>.<br/>	62	<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Bool.Bool.html#BoolNotations"><span·class="id"·title="module">BoolNotations</span></a>.<br/>
63	<span·class="id"·title="keyword">Local·Ltac</span>·<span·class="id"·title="var">Tauto.intuition_solver</span>·::=·<span·class="id"·title="tactic">auto</span>·<span·class="id"·title="keyword">with</span>·<span·class="id"·title="var">typeclass_instances</span>·<span·class="id"·title="var">relations</span>.<br/>	63	<span·class="id"·title="keyword">Local·Ltac</span>·<span·class="id"·title="var">Tauto.intuition_solver</span>·::=·<span·class="id"·title="tactic">auto</span>·<span·class="id"·title="keyword">with</span>·<span·class="id"·title="var">typeclass_instances</span>·<span·class="id"·title="var">relations</span>.<br/>

64	<br/>	64	<br/>
65	</div>	65	</div>

66	<div·class="doc">	66	<div·class="doc">
67	<a·id="lab~~175~~"></a><h1·class="section">Order·<span·class="inlinecode"><span·class="id"·title="var">le</span></span></h1>	67	<a·id="lab689"></a><h1·class="section">Order·<span·class="inlinecode"><span·class="id"·title="var">le</span></span></h1>

68	</div>	68	</div>
69	<div·class="code">	69	<div·class="code">

70	<br/>	70	<br/>
71	<span·class="id"·title="keyword">Lemma</span>·<a·id="le_refl"·class="idref"·href="#le_refl"><span·class="id"·title="lemma">le_refl</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="b:1"·class="idref"·href="#b:1"><span·class="id"·title="binder">b</span></a>,·<a·class="idref"·href="Coq.Bool.BoolOrder.html#b:1"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.Bool.Bool.html#b6c5208a24d231af77d2816ac22122c4"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.Bool.BoolOrder.html#b:1"><span·class="id"·title="variable">b</span></a>.<br/>	71	<span·class="id"·title="keyword">Lemma</span>·<a·id="le_refl"·class="idref"·href="#le_refl"><span·class="id"·title="lemma">le_refl</span></a>·:·<span·class="id"·title="keyword">forall</span>·<a·id="b:1"·class="idref"·href="#b:1"><span·class="id"·title="binder">b</span></a>,·<a·class="idref"·href="Coq.Bool.BoolOrder.html#b:1"><span·class="id"·title="variable">b</span></a>·<a·class="idref"·href="Coq.Bool.Bool.html#b6c5208a24d231af77d2816ac22122c4"><span·class="id"·title="notation"><=</span></a>·<a·class="idref"·href="Coq.Bool.BoolOrder.html#b:1"><span·class="id"·title="variable">b</span></a>.<br/>
72	·	72	·


Offset 47, 15 lines modified		Offset 47, 15 lines modified

47	<br/>	47	<br/>

48	<br/>	48	<br/>
49	</div>	49	</div>

50	<div·class="doc">	50	<div·class="doc">
51	<a·id="lab585"></a><h1·class="section">FMapAVL</h1>	51	<a·id="lab500"></a><h1·class="section">FMapAVL</h1>

52	<div·class="paragraph">·</div>	52	<div·class="paragraph">·</div>

53	·This·module·implements·maps·using·AVL·trees.	53	·This·module·implements·maps·using·AVL·trees.
54	····It·follows·the·implementation·from·Ocaml's·standard·library.	54	····It·follows·the·implementation·from·Ocaml's·standard·library.

55	<div·class="paragraph">·</div>	55	<div·class="paragraph">·</div>


Offset 71, 15 lines modified		Offset 71, 15 lines modified
71	<span·class="id"·title="keyword">Module</span>·<a·id="WDecide_fun"·class="idref"·href="#WDecide_fun"><span·class="id"·title="module">WDecide_fun</span></a>·(<span·class="id"·title="var">E</span>·:·<a·class="idref"·href="Coq.Structures.DecidableType.html#DecidableType"><span·class="id"·title="module">DecidableType</span></a>)(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">M</span>·:·<a·class="idref"·href="Coq.FSets.FSetInterface.html#WSfun"><span·class="id"·title="module">WSfun</span></a>·<a·class="idref"·href="Coq.FSets.FSetDecide.html#E"><span·class="id"·title="module">E</span></a>).<br/>	71	<span·class="id"·title="keyword">Module</span>·<a·id="WDecide_fun"·class="idref"·href="#WDecide_fun"><span·class="id"·title="module">WDecide_fun</span></a>·(<span·class="id"·title="var">E</span>·:·<a·class="idref"·href="Coq.Structures.DecidableType.html#DecidableType"><span·class="id"·title="module">DecidableType</span></a>)(<span·class="id"·title="keyword">Import</span>·<span·class="id"·title="var">M</span>·:·<a·class="idref"·href="Coq.FSets.FSetInterface.html#WSfun"><span·class="id"·title="module">WSfun</span></a>·<a·class="idref"·href="Coq.FSets.FSetDecide.html#E"><span·class="id"·title="module">E</span></a>).<br/>
72	<span·class="id"·title="keyword">Module</span>·<a·id="WDecide_fun.F"·class="idref"·href="#WDecide_fun.F"><span·class="id"·title="module">F</span></a>·:=·<a·class="idref"·href="Coq.FSets.FSetFacts.html#WFacts_fun"><span·class="id"·title="module">FSetFacts.WFacts_fun</span></a>·<a·class="idref"·href="Coq.FSets.FSetDecide.html#E"><span·class="id"·title="module">E</span></a>·<a·class="idref"·href="Coq.FSets.FSetDecide.html#M"><span·class="id"·title="module">M</span></a>.<br/>	72	<span·class="id"·title="keyword">Module</span>·<a·id="WDecide_fun.F"·class="idref"·href="#WDecide_fun.F"><span·class="id"·title="module">F</span></a>·:=·<a·class="idref"·href="Coq.FSets.FSetFacts.html#WFacts_fun"><span·class="id"·title="module">FSetFacts.WFacts_fun</span></a>·<a·class="idref"·href="Coq.FSets.FSetDecide.html#E"><span·class="id"·title="module">E</span></a>·<a·class="idref"·href="Coq.FSets.FSetDecide.html#M"><span·class="id"·title="module">M</span></a>.<br/>

73	<br/>	73	<br/>
74	</div>	74	</div>

75	<div·class="doc">	75	<div·class="doc">
76	<a·id="lab543"></a><h1·class="section">Overview</h1>	76	<a·id="lab556"></a><h1·class="section">Overview</h1>

77	····This·functor·defines·the·tactic·<span·class="inlinecode"><span·class="id"·title="var">fsetdec</span></span>,·which·will	77	····This·functor·defines·the·tactic·<span·class="inlinecode"><span·class="id"·title="var">fsetdec</span></span>,·which·will
78	····solve·any·valid·goal·of·the·form	78	····solve·any·valid·goal·of·the·form
79	<pre>	79	<pre>
80	····forall·s1·...·sn,	80	····forall·s1·...·sn,
81	····forall·x1·...·xm,	81	····forall·x1·...·xm,
82	····P1·->·...·->·Pk·->·P	82	····P1·->·...·->·Pk·->·P


Offset 45, 28 lines modified		Offset 45, 28 lines modified

45	<div·class="code">	45	<div·class="code">

46	<br/>	46	<br/>
47	</div>	47	</div>

48	<div·class="doc">	48	<div·class="doc">
49	<a·id="lab570"></a><h1·class="section">Finite·sets·library·:·conversion·to·old·<span·class="inlinecode"><span·class="id"·title="var">Finite_sets</span></span></h1>	49	<a·id="lab545"></a><h1·class="section">Finite·sets·library·:·conversion·to·old·<span·class="inlinecode"><span·class="id"·title="var">Finite_sets</span></span></h1>

50	</div>	50	</div>
51	<div·class="code">	51	<div·class="code">

52	<br/>	52	<br/>
53	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Sets.Ensembles.html#"><span·class="id"·title="library">Ensembles</span></a>·<a·class="idref"·href="Coq.Sets.Finite_sets.html#"><span·class="id"·title="library">Finite_sets</span></a>.<br/>	53	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Sets.Ensembles.html#"><span·class="id"·title="library">Ensembles</span></a>·<a·class="idref"·href="Coq.Sets.Finite_sets.html#"><span·class="id"·title="library">Finite_sets</span></a>.<br/>
54	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.FSets.FSetInterface.html#"><span·class="id"·title="library">FSetInterface</span></a>·<a·class="idref"·href="Coq.FSets.FSetProperties.html#"><span·class="id"·title="library">FSetProperties</span></a>·<a·class="idref"·href="Coq.Structures.OrderedTypeEx.html#"><span·class="id"·title="library">OrderedTypeEx</span></a>·<a·class="idref"·href="Coq.Structures.DecidableTypeEx.html#"><span·class="id"·title="library">DecidableTypeEx</span></a>.<br/>	54	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.FSets.FSetInterface.html#"><span·class="id"·title="library">FSetInterface</span></a>·<a·class="idref"·href="Coq.FSets.FSetProperties.html#"><span·class="id"·title="library">FSetProperties</span></a>·<a·class="idref"·href="Coq.Structures.OrderedTypeEx.html#"><span·class="id"·title="library">OrderedTypeEx</span></a>·<a·class="idref"·href="Coq.Structures.DecidableTypeEx.html#"><span·class="id"·title="library">DecidableTypeEx</span></a>.<br/>

55	<br/>	55	<br/>
56	</div>	56	</div>

57	<div·class="doc">	57	<div·class="doc">
58	<a·id="lab571"></a><h1·class="section">Going·from·<span·class="inlinecode"><span·class="id"·title="var">FSets</span></span>·with·usual·Leibniz·equality</h1>	58	<a·id="lab546"></a><h1·class="section">Going·from·<span·class="inlinecode"><span·class="id"·title="var">FSets</span></span>·with·usual·Leibniz·equality</h1>

59	····to·the·good·old·<span·class="inlinecode"><span·class="id"·title="var">Ensembles</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Finite_sets</span></span>·theory.·	59	····to·the·good·old·<span·class="inlinecode"><span·class="id"·title="var">Ensembles</span></span>·and·<span·class="inlinecode"><span·class="id"·title="var">Finite_sets</span></span>·theory.·
60	</div>	60	</div>
61	<div·class="code">	61	<div·class="code">

62	<br/>	62	<br/>
63	<span·class="id"·title="keyword">Module</span>·<a·id="WS_to_Finite_set"·class="idref"·href="#WS_to_Finite_set"><span·class="id"·title="module">WS_to_Finite_set</span></a>·(<span·class="id"·title="var">U</span>:<a·class="idref"·href="Coq.Structures.DecidableTypeEx.html#UsualDecidableType"><span·class="id"·title="module">UsualDecidableType</span></a>)(<span·class="id"·title="var">M</span>:·<a·class="idref"·href="Coq.FSets.FSetInterface.html#WSfun"><span·class="id"·title="module">WSfun</span></a>·<a·class="idref"·href="Coq.FSets.FSetToFiniteSet.html#U"><span·class="id"·title="module">U</span></a>).<br/>	63	<span·class="id"·title="keyword">Module</span>·<a·id="WS_to_Finite_set"·class="idref"·href="#WS_to_Finite_set"><span·class="id"·title="module">WS_to_Finite_set</span></a>·(<span·class="id"·title="var">U</span>:<a·class="idref"·href="Coq.Structures.DecidableTypeEx.html#UsualDecidableType"><span·class="id"·title="module">UsualDecidableType</span></a>)(<span·class="id"·title="var">M</span>:·<a·class="idref"·href="Coq.FSets.FSetInterface.html#WSfun"><span·class="id"·title="module">WSfun</span></a>·<a·class="idref"·href="Coq.FSets.FSetToFiniteSet.html#U"><span·class="id"·title="module">U</span></a>).<br/>


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48	<br/>	48	<br/>
49	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int63.Uint63.html#"><span·class="id"·title="library">Uint63</span></a>·<a·class="idref"·href="Coq.Floats.SpecFloat.html#"><span·class="id"·title="library">SpecFloat</span></a>·<a·class="idref"·href="Coq.Floats.PrimFloat.html#"><span·class="id"·title="library">PrimFloat</span></a>·<a·class="idref"·href="Coq.Floats.FloatOps.html#"><span·class="id"·title="library">FloatOps</span></a>.<br/>	49	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int63.Uint63.html#"><span·class="id"·title="library">Uint63</span></a>·<a·class="idref"·href="Coq.Floats.SpecFloat.html#"><span·class="id"·title="library">SpecFloat</span></a>·<a·class="idref"·href="Coq.Floats.PrimFloat.html#"><span·class="id"·title="library">PrimFloat</span></a>·<a·class="idref"·href="Coq.Floats.FloatOps.html#"><span·class="id"·title="library">FloatOps</span></a>.<br/>

50	<br/>	50	<br/>
51	</div>	51	</div>

52	<div·class="doc">	52	<div·class="doc">
53	<a·id="lab~~777~~"></a><h1·class="section">Properties·of·the·primitive·operators·for·the·Binary64·format</h1>	53	<a·id="lab940"></a><h1·class="section">Properties·of·the·primitive·operators·for·the·Binary64·format</h1>

54	</div>	54	</div>
55	<div·class="code">	55	<div·class="code">

56	<br/>	56	<br/>
57	<span·class="id"·title="keyword">Notation</span>·<a·id="valid_binary"·class="idref"·href="#valid_binary"><span·class="id"·title="abbreviation">valid_binary</span></a>·:=·(<a·class="idref"·href="Coq.Floats.SpecFloat.html#valid_binary"><span·class="id"·title="definition">valid_binary</span></a>·<a·class="idref"·href="Coq.Floats.FloatOps.html#prec"><span·class="id"·title="definition">prec</span></a>·<a·class="idref"·href="Coq.Floats.FloatOps.html#emax"><span·class="id"·title="definition">emax</span></a>).<br/>	57	<span·class="id"·title="keyword">Notation</span>·<a·id="valid_binary"·class="idref"·href="#valid_binary"><span·class="id"·title="abbreviation">valid_binary</span></a>·:=·(<a·class="idref"·href="Coq.Floats.SpecFloat.html#valid_binary"><span·class="id"·title="definition">valid_binary</span></a>·<a·class="idref"·href="Coq.Floats.FloatOps.html#prec"><span·class="id"·title="definition">prec</span></a>·<a·class="idref"·href="Coq.Floats.FloatOps.html#emax"><span·class="id"·title="definition">emax</span></a>).<br/>


Offset 49, 15 lines modified		Offset 49, 15 lines modified
49	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int63.Uint63.html#"><span·class="id"·title="library">Uint63</span></a>·<a·class="idref"·href="Coq.Floats.SpecFloat.html#"><span·class="id"·title="library">SpecFloat</span></a>·<a·class="idref"·href="Coq.Floats.PrimFloat.html#"><span·class="id"·title="library">PrimFloat</span></a>·<a·class="idref"·href="Coq.Floats.FloatOps.html#"><span·class="id"·title="library">FloatOps</span></a>·<a·class="idref"·href="Coq.Floats.FloatAxioms.html#"><span·class="id"·title="library">FloatAxioms</span></a>.<br/>	49	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.ZArith.ZArith.html#"><span·class="id"·title="library">ZArith</span></a>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int63.Uint63.html#"><span·class="id"·title="library">Uint63</span></a>·<a·class="idref"·href="Coq.Floats.SpecFloat.html#"><span·class="id"·title="library">SpecFloat</span></a>·<a·class="idref"·href="Coq.Floats.PrimFloat.html#"><span·class="id"·title="library">PrimFloat</span></a>·<a·class="idref"·href="Coq.Floats.FloatOps.html#"><span·class="id"·title="library">FloatOps</span></a>·<a·class="idref"·href="Coq.Floats.FloatAxioms.html#"><span·class="id"·title="library">FloatAxioms</span></a>.<br/>
50	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Psatz.html#"><span·class="id"·title="library">Psatz</span></a>.<br/>	50	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.micromega.Psatz.html#"><span·class="id"·title="library">Psatz</span></a>.<br/>

51	<br/>	51	<br/>
52	</div>	52	</div>

53	<div·class="doc">	53	<div·class="doc">
54	<a·id="lab~~776~~"></a><h1·class="section">Support·results·involving·frexp·and·ldexp</h1>	54	<a·id="lab953"></a><h1·class="section">Support·results·involving·frexp·and·ldexp</h1>

55	</div>	55	</div>
56	<div·class="code">	56	<div·class="code">

57	<br/>	57	<br/>
58	<span·class="id"·title="keyword">Lemma</span>·<a·id="shift_value"·class="idref"·href="#shift_value"><span·class="id"·title="lemma">shift_value</span></a>·:·<a·class="idref"·href="Coq.Floats.FloatOps.html#shift"><span·class="id"·title="definition">shift</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·(2<a·class="idref"·href="Coq.ZArith.BinInt.html#d3ea1afb7d81263dc23c4eb0da2a3c4e"><span·class="id"·title="notation">*</span></a><a·class="idref"·href="Coq.Floats.FloatOps.html#emax"><span·class="id"·title="definition">emax</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#46584eddd5fdb16176a10a2843177d3a"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Floats.FloatOps.html#prec"><span·class="id"·title="definition">prec</span></a>)%<span·class="id"·title="var">Z</span>.<br/>	58	<span·class="id"·title="keyword">Lemma</span>·<a·id="shift_value"·class="idref"·href="#shift_value"><span·class="id"·title="lemma">shift_value</span></a>·:·<a·class="idref"·href="Coq.Floats.FloatOps.html#shift"><span·class="id"·title="definition">shift</span></a>·<a·class="idref"·href="Coq.Init.Logic.html#6cd0f7b28b6092304087c7049437bb1a"><span·class="id"·title="notation">=</span></a>·(2<a·class="idref"·href="Coq.ZArith.BinInt.html#d3ea1afb7d81263dc23c4eb0da2a3c4e"><span·class="id"·title="notation">*</span></a><a·class="idref"·href="Coq.Floats.FloatOps.html#emax"><span·class="id"·title="definition">emax</span></a>·<a·class="idref"·href="Coq.ZArith.BinInt.html#46584eddd5fdb16176a10a2843177d3a"><span·class="id"·title="notation">+</span></a>·<a·class="idref"·href="Coq.Floats.FloatOps.html#prec"><span·class="id"·title="definition">prec</span></a>)%<span·class="id"·title="var">Z</span>.<br/>


Offset 48, 24 lines modified		Offset 48, 24 lines modified
48	<br/>	48	<br/>
49	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int63.PrimInt63.html#"><span·class="id"·title="library">PrimInt63</span></a>·<a·class="idref"·href="Coq.Floats.FloatClass.html#"><span·class="id"·title="library">FloatClass</span></a>.<br/>	49	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Numbers.Cyclic.Int63.PrimInt63.html#"><span·class="id"·title="library">PrimInt63</span></a>·<a·class="idref"·href="Coq.Floats.FloatClass.html#"><span·class="id"·title="library">FloatClass</span></a>.<br/>

50	<br/>	50	<br/>
51	</div>	51	</div>

52	<div·class="doc">	52	<div·class="doc">
53	<a·id="lab~~783~~"></a><h1·class="section">Definition·of·the·interface·for·primitive·floating-point·arithmetic</h1>	53	<a·id="lab941"></a><h1·class="section">Definition·of·the·interface·for·primitive·floating-point·arithmetic</h1>


54	<div·class="paragraph">·</div>	54	<div·class="paragraph">·</div>

55	This·interface·provides·processor·operators·for·the·Binary64·format·of·the	55	This·interface·provides·processor·operators·for·the·Binary64·format·of·the
56	IEEE·754-2008·standard.·	56	IEEE·754-2008·standard.·
57	<div·class="paragraph">·</div>	57	<div·class="paragraph">·</div>

58	<a·id="lab~~784~~"></a><h2·class="section">Type·definition·for·the·co-domain·of·<span·class="inlinecode"><span·class="id"·title="var">compare</span></span></h2>	58	<a·id="lab942"></a><h2·class="section">Type·definition·for·the·co-domain·of·<span·class="inlinecode"><span·class="id"·title="var">compare</span></span></h2>

59	</div>	59	</div>
60	<div·class="code">	60	<div·class="code">
61	<span·class="id"·title="keyword">Variant</span>·<a·id="float_comparison"·class="idref"·href="#float_comparison"><span·class="id"·title="inductive">float_comparison</span></a>·:·<span·class="id"·title="keyword">Set</span>·:=·<a·id="FEq"·class="idref"·href="#FEq"><span·class="id"·title="constructor">FEq</span></a>·\|·<a·id="FLt"·class="idref"·href="#FLt"><span·class="id"·title="constructor">FLt</span></a>·\|·<a·id="FGt"·class="idref"·href="#FGt"><span·class="id"·title="constructor">FGt</span></a>·\|·<a·id="FNotComparable"·class="idref"·href="#FNotComparable"><span·class="id"·title="constructor">FNotComparable</span></a>.<br/>	61	<span·class="id"·title="keyword">Variant</span>·<a·id="float_comparison"·class="idref"·href="#float_comparison"><span·class="id"·title="inductive">float_comparison</span></a>·:·<span·class="id"·title="keyword">Set</span>·:=·<a·id="FEq"·class="idref"·href="#FEq"><span·class="id"·title="constructor">FEq</span></a>·\|·<a·id="FLt"·class="idref"·href="#FLt"><span·class="id"·title="constructor">FLt</span></a>·\|·<a·id="FGt"·class="idref"·href="#FGt"><span·class="id"·title="constructor">FGt</span></a>·\|·<a·id="FNotComparable"·class="idref"·href="#FNotComparable"><span·class="id"·title="constructor">FNotComparable</span></a>.<br/>

62	<br/>	62	<br/>
63	<span·class="id"·title="keyword">Register</span>·<span·class="id"·title="var">float_comparison</span>·<span·class="id"·title="keyword">as</span>·<span·class="id"·title="var">kernel.ind_f_cmp</span>.<br/>	63	<span·class="id"·title="keyword">Register</span>·<span·class="id"·title="var">float_comparison</span>·<span·class="id"·title="keyword">as</span>·<span·class="id"·title="var">kernel.ind_f_cmp</span>.<br/>


Offset 53, 15 lines modified		Offset 53, 15 lines modified
53	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Ltac.html#"><span·class="id"·title="library">Ltac</span></a>.<br/>	53	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Ltac.html#"><span·class="id"·title="library">Ltac</span></a>.<br/>
54	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Logic.html#"><span·class="id"·title="library">Logic</span></a>.<br/>	54	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Logic.html#"><span·class="id"·title="library">Logic</span></a>.<br/>

55	<br/>	55	<br/>
56	</div>	56	</div>

57	<div·class="doc">	57	<div·class="doc">
58	<a·id="lab767"></a><h1·class="section">Datatypes·with·zero·and·one·element</h1>	58	<a·id="lab729"></a><h1·class="section">Datatypes·with·zero·and·one·element</h1>

59	<div·class="paragraph">·</div>	59	<div·class="paragraph">·</div>

60	·<span·class="inlinecode"><span·class="id"·title="var">Empty_set</span></span>·is·a·datatype·with·no·inhabitant·	60	·<span·class="inlinecode"><span·class="id"·title="var">Empty_set</span></span>·is·a·datatype·with·no·inhabitant·
61	</div>	61	</div>
62	<div·class="code">	62	<div·class="code">


Offset 159, 15 lines modified		Offset 159, 15 lines modified
000009e0:·7222·3e42·3c2f·7370·616e·3e29·203a·203c··r">B</span>)·:·<		000009e0:·7222·3e42·3c2f·7370·616e·3e29·203a·203c··r">B</span>)·:·<
000009f0:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"·		000009f0:·7370·616e·2063·6c61·7373·3d22·6964·2220··span·class="id"·
00000a00:·7469·746c·653d·2276·6172·223e·7479·7065··title="var">type		00000a00:·7469·746c·653d·2276·6172·223e·7479·7065··title="var">type
00000a10:·5f73·636f·7065·3c2f·7370·616e·3e2e·3c62··_scope</span>.<b		00000a10:·5f73·636f·7065·3c2f·7370·616e·3e2e·3c62··_scope</span>.<b
00000a20:·722f·3e0a·0a3c·6272·2f3e·0a3c·2f64·6976··r/>..<br/>.</div		00000a20:·722f·3e0a·0a3c·6272·2f3e·0a3c·2f64·6976··r/>..<br/>.</div
00000a30:·3e0a·0a3c·6469·7620·636c·6173·733d·2264··>..<div·class="d		00000a30:·3e0a·0a3c·6469·7620·636c·6173·733d·2264··>..<div·class="d
00000a40:·6f63·223e·0a3c·6120·6964·3d22·6c61·6237··oc">.<a·id="lab7		00000a40:·6f63·223e·0a3c·6120·6964·3d22·6c61·6237··oc">.<a·id="lab7
00000a50:·3438·223e·3c2f·613e·3c68·3120·636c·6173··48"></a><h1·clas		00000a50:·3536·223e·3c2f·613e·3c68·3120·636c·6173··56"></a><h1·clas
00000a60:·733d·2273·6563·7469·6f6e·223e·5072·6f70··s="section">Prop		00000a60:·733d·2273·6563·7469·6f6e·223e·5072·6f70··s="section">Prop
00000a70:·6f73·6974·696f·6e61·6c20·636f·6e6e·6563··ositional·connec		00000a70:·6f73·6974·696f·6e61·6c20·636f·6e6e·6563··ositional·connec
00000a80:·7469·7665·733c·2f68·313e·0a0a·3c64·6976··tives</h1>..<div		00000a80:·7469·7665·733c·2f68·313e·0a0a·3c64·6976··tives</h1>..<div
00000a90:·2063·6c61·7373·3d22·7061·7261·6772·6170···class="paragrap		00000a90:·2063·6c61·7373·3d22·7061·7261·6772·6170···class="paragrap
00000aa0:·6822·3e20·3c2f·6469·763e·0a0a·203c·7370··h">·</div>..·<sp		00000aa0:·6822·3e20·3c2f·6469·763e·0a0a·203c·7370··h">·</div>..·<sp
00000ab0:·616e·2063·6c61·7373·3d22·696e·6c69·6e65··an·class="inline		00000ab0:·616e·2063·6c61·7373·3d22·696e·6c69·6e65··an·class="inline
00000ac0:·636f·6465·223e·3c73·7061·6e20·636c·6173··code"><span·clas		00000ac0:·636f·6465·223e·3c73·7061·6e20·636c·6173··code"><span·clas


Offset 50, 15 lines modified		Offset 50, 15 lines modified
50	<span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.Init.Decimal.html#"><span·class="id"·title="library">Decimal</span></a>·<a·class="idref"·href="Coq.Init.Hexadecimal.html#"><span·class="id"·title="library">Hexadecimal</span></a>·<a·class="idref"·href="Coq.Init.Number.html#"><span·class="id"·title="library">Number</span></a>.<br/>	50	<span·class="id"·title="keyword">Require</span>·<a·class="idref"·href="Coq.Init.Decimal.html#"><span·class="id"·title="library">Decimal</span></a>·<a·class="idref"·href="Coq.Init.Hexadecimal.html#"><span·class="id"·title="library">Hexadecimal</span></a>·<a·class="idref"·href="Coq.Init.Number.html#"><span·class="id"·title="library">Number</span></a>.<br/>
51	<span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/>	51	<span·class="id"·title="keyword">Local·Open</span>·<span·class="id"·title="keyword">Scope</span>·<span·class="id"·title="var">nat_scope</span>.<br/>

52	<br/>	52	<br/>
53	</div>	53	</div>

54	<div·class="doc">	54	<div·class="doc">
55	<a·id="lab753"></a><h1·class="section">Peano·natural·numbers,·definitions·of·operations</h1>	55	<a·id="lab736"></a><h1·class="section">Peano·natural·numbers,·definitions·of·operations</h1>

56	<div·class="paragraph">·</div>	56	<div·class="paragraph">·</div>

57	·This·file·is·meant·to·be·used·as·a·whole·module,	57	·This·file·is·meant·to·be·used·as·a·whole·module,
58	····without·importing·it,·leading·to·qualified·definitions	58	····without·importing·it,·leading·to·qualified·definitions
59	····(e.g.·Nat.pred)·	59	····(e.g.·Nat.pred)·
60	</div>	60	</div>


Offset 51, 15 lines modified		Offset 51, 15 lines modified
51	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Logic.html#"><span·class="id"·title="library">Logic</span></a>.<br/>	51	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Logic.html#"><span·class="id"·title="library">Logic</span></a>.<br/>
52	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Specif.html#"><span·class="id"·title="library">Specif</span></a>.<br/>	52	<span·class="id"·title="keyword">Require</span>·<span·class="id"·title="keyword">Import</span>·<a·class="idref"·href="Coq.Init.Specif.html#"><span·class="id"·title="library">Specif</span></a>.<br/>

53	<br/>	53	<br/>
54	</div>	54	</div>

55	<div·class="doc">	55	<div·class="doc">
56	<a·id="lab744"></a><h1·class="section">Useful·tactics</h1>	56	<a·id="lab753"></a><h1·class="section">Useful·tactics</h1>

57	<div·class="paragraph">·</div>	57	<div·class="paragraph">·</div>

58	·Ex·falso·quodlibet·:·a·tactic·for·proving·False·instead·of·the·current·goal.	58	·Ex·falso·quodlibet·:·a·tactic·for·proving·False·instead·of·the·current·goal.
59	····This·is·just·a·nicer·name·for·tactics·such·as·<span·class="inlinecode"><span·class="id"·title="tactic">cut</span></span>·<span·class="inlinecode"><span·class="id"·title="var">False</span></span>.·	59	····This·is·just·a·nicer·name·for·tactics·such·as·<span·class="inlinecode"><span·class="id"·title="tactic">cut</span></span>·<span·class="inlinecode"><span·class="id"·title="var">False</span></span>.·
60	</div>	60	</div>
61	<div·class="code">	61	<div·class="code">


Offset 46, 15 lines modified		Offset 46, 15 lines modified
46	<div·class="code">	46	<div·class="code">

47	<br/>	47	<br/>
48	</div>	48	</div>

49	<div·class="doc">	49	<div·class="doc">
50	Some·facts·and·definitions·concerning·choice·and·description·in	50	Some·facts·and·definitions·concerning·choice·and·description·in
51	·······intuitionistic·logic.·<a·id="lab1~~279~~"></a><h1·class="section">References:</h1>	51	·······intuitionistic·logic.·<a·id="lab381"></a><h1·class="section">References:</h1>

52	<div·class="paragraph">·</div>	52	<div·class="paragraph">·</div>

53	<span·class="inlinecode">[<span·class="id"·title="var">Bell</span>]</span>·John·L.·Bell,·Choice·principles·in·intuitionistic·set·theory,	53	<span·class="inlinecode">[<span·class="id"·title="var">Bell</span>]</span>·John·L.·Bell,·Choice·principles·in·intuitionistic·set·theory,
54	unpublished.	54	unpublished.

55	<div·class="paragraph">·</div>	55	<div·class="paragraph">·</div>


Offset 129, 15 lines modified		Offset 129, 15 lines modified
129	<br/>	129	<br/>
130	<span·class="id"·title="keyword">Opaque</span>·<a·class="idref"·href="Coq.Logic.ClassicalEpsilon.html#epsilon"><span·class="id"·title="definition">epsilon</span></a>.<br/>	130	<span·class="id"·title="keyword">Opaque</span>·<a·class="idref"·href="Coq.Logic.ClassicalEpsilon.html#epsilon"><span·class="id"·title="definition">epsilon</span></a>.<br/>

131	<br/>	131	<br/>
132	</div>	132	</div>

133	<div·class="doc">	133	<div·class="doc">
134	<a·id="lab1278"></a><h3·class="section">Weaker·lemmas·(compatibility·lemmas)</h3>	134	<a·id="lab425"></a><h3·class="section">Weaker·lemmas·(compatibility·lemmas)</h3>

135	</div>	135	</div>
136	<div·class="code">	136	<div·class="code">

137	<br/>	137	<br/>
138	<span·class="id"·title="keyword">Theorem</span>·<a·id="choice"·class="idref"·href="#choice"><span·class="id"·title="lemma">choice</span></a>·:<br/>	138	<span·class="id"·title="keyword">Theorem</span>·<a·id="choice"·class="idref"·href="#choice"><span·class="id"·title="lemma">choice</span></a>·:<br/>
139	<span·class="id"·title="keyword">forall</span>·(<a·id="A:37"·class="idref"·href="#A:37"><span·class="id"·title="binder">A</span></a>·<a·id="B:38"·class="idref"·href="#B:38"><span·class="id"·title="binder">B</span></a>·:·<span·class="id"·title="keyword">Type</span>)·(<a·id="R:39"·class="idref"·href="#R:39"><span·class="id"·title="binder">R</span></a>·:·<a·class="idref"·href="Coq.Logic.ClassicalEpsilon.html#A:37"><span·class="id"·title="variable">A</span></a><a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a><a·class="idref"·href="Coq.Logic.ClassicalEpsilon.html#B:38"><span·class="id"·title="variable">B</span></a><a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a><span·class="id"·title="keyword">Prop</span>),<br/>	139	<span·class="id"·title="keyword">forall</span>·(<a·id="A:37"·class="idref"·href="#A:37"><span·class="id"·title="binder">A</span></a>·<a·id="B:38"·class="idref"·href="#B:38"><span·class="id"·title="binder">B</span></a>·:·<span·class="id"·title="keyword">Type</span>)·(<a·id="R:39"·class="idref"·href="#R:39"><span·class="id"·title="binder">R</span></a>·:·<a·class="idref"·href="Coq.Logic.ClassicalEpsilon.html#A:37"><span·class="id"·title="variable">A</span></a><a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a><a·class="idref"·href="Coq.Logic.ClassicalEpsilon.html#B:38"><span·class="id"·title="variable">B</span></a><a·class="idref"·href="Coq.Init.Logic.html#::type_scope:x_'->'_x"><span·class="id"·title="notation">-></span></a><span·class="id"·title="keyword">Prop</span>),<br/>


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110	<div·class="paragraph">·</div>	110	<div·class="paragraph">·</div>

111	4.2·Classical·logic·=·choice·of·representatives·in·a·partition·of·bool	111	4.2·Classical·logic·=·choice·of·representatives·in·a·partition·of·bool

112	<div·class="paragraph">·</div>	112	<div·class="paragraph">·</div>

113	<a·id="lab1~~258~~"></a><h1·class="section">Prop·degeneracy·=·excluded-middle·+·prop·extensionality</h1>	113	<a·id="lab411"></a><h1·class="section">Prop·degeneracy·=·excluded-middle·+·prop·extensionality</h1>

114	<div·class="paragraph">·</div>	114	<div·class="paragraph">·</div>

115	·i.e.········<span·class="inlinecode">(<span·class="id"·title="keyword">forall</span></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>,</span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>=<span·class="id"·title="var">True</span></span>·<span·class="inlinecode">\/</span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>=<span·class="id"·title="var">False</span>)</span>	115	·i.e.········<span·class="inlinecode">(<span·class="id"·title="keyword">forall</span></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>,</span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>=<span·class="id"·title="var">True</span></span>·<span·class="inlinecode">\/</span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>=<span·class="id"·title="var">False</span>)</span>
116	·························<span·class="inlinecode"><-></span>	116	·························<span·class="inlinecode"><-></span>
117	·······<span·class="inlinecode">(<span·class="id"·title="keyword">forall</span></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>,</span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>\/~<span·class="id"·title="var">A</span>)</span>·<span·class="inlinecode">/\</span>·<span·class="inlinecode">(<span·class="id"·title="keyword">forall</span></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span></span>·<span·class="inlinecode"><span·class="id"·title="var">B</span>,</span>·<span·class="inlinecode">(<span·class="id"·title="var">A</span><-><span·class="id"·title="var">B</span>)</span>·<span·class="inlinecode">-></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>=<span·class="id"·title="var">B</span>)</span>	117	·······<span·class="inlinecode">(<span·class="id"·title="keyword">forall</span></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>,</span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>\/~<span·class="id"·title="var">A</span>)</span>·<span·class="inlinecode">/\</span>·<span·class="inlinecode">(<span·class="id"·title="keyword">forall</span></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span></span>·<span·class="inlinecode"><span·class="id"·title="var">B</span>,</span>·<span·class="inlinecode">(<span·class="id"·title="var">A</span><-><span·class="id"·title="var">B</span>)</span>·<span·class="inlinecode">-></span>·<span·class="inlinecode"><span·class="id"·title="var">A</span>=<span·class="id"·title="var">B</span>)</span>